From 2c56c3933652ea8421ea96832f11cfce9daa0c69 Mon Sep 17 00:00:00 2001
From: mvr <mitchell.v.riley@gmail.com>
Date: Wed, 29 Jul 2026 11:56:56 +0100
Subject: [PATCH 1/4] Test proof-irrelevance and parameterised records
 systematically

It feels excessive, but many of the combinations will end up being
lowered differently.

* `dependent-function-*` tests `(a : A) -> B a`
* `dependent-function-argument-*` tests `(a : A) -> (b : B a) -> C a b`
* `family-argument-*` tests `(a : A) -> B a -> Set/Prop`
* `lookup-{argument,field}-projection-*` tests families indexed by the output of a function
* `lookup-composition-*` tests the same for two a composite of functions
* `lookup-proof-result-argument` is a special case (could be expanded to 8 cases)
* `param-record-*` tests records parameterised by various things
* `param-record-type-family-* tests records parameterised by a type family specifically
* `proof-record-* tests records that contain a proof field
* `prop-record-* tests records that themselves live in `Prop`
* `equality-record-* tests equality of records
* `param-alias-*` tests parameterised records and aliases
* `empty-prop-record-function` tests functions into a trivial proposition
* `record-nested` is a minimal nested record case
---
 packages/coln-compiler/test/Main.hs           |   2 +-
 ...dent-function-argument-prop-prop-prop.coln |   9 +
 ...nt-function-argument-prop-prop-prop.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...ndent-function-argument-prop-prop-set.coln |   9 +
 ...ent-function-argument-prop-prop-set.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...ndent-function-argument-prop-set-prop.coln |   9 +
 ...ent-function-argument-prop-set-prop.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...endent-function-argument-prop-set-set.coln |   9 +
 ...dent-function-argument-prop-set-set.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...ndent-function-argument-set-prop-prop.coln |   9 +
 ...ent-function-argument-set-prop-prop.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...endent-function-argument-set-prop-set.coln |   9 +
 ...dent-function-argument-set-prop-set.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 ...endent-function-argument-set-set-prop.coln |   9 +
 ...dent-function-argument-set-set-prop.output |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 .../basic-ir/dependent-function-argument.coln |   9 +
 .../dependent-function-argument.output        |  45 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  69 +++++++
 .../dependent-function-prop-prop.coln         |   8 +
 .../dependent-function-prop-prop.output       |  31 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  50 +++++
 .../basic-ir/dependent-function-prop-set.coln |   8 +
 .../dependent-function-prop-set.output        |  31 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  50 +++++
 .../basic-ir/dependent-function-set-prop.coln |   8 +
 .../dependent-function-set-prop.output        |  31 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  50 +++++
 .../golden/basic-ir/dependent-function.coln   |   8 +
 .../golden/basic-ir/dependent-function.output |  31 +++
 .../dependent-function.ts.output/T.ts         |  13 ++
 .../dependent-function.ts.output/TRealm.json  |   1 +
 .../dependent-function.ts.output/TRealm.ts    |  50 +++++
 .../basic-ir/empty-prop-record-function.coln  |  10 +
 .../empty-prop-record-function.output         |  29 +++
 .../empty-prop-record-function.ts.output/T.ts |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  39 ++++
 .../basic-ir/equality-record-nested.coln      |  24 +++
 .../basic-ir/equality-record-nested.output    |  96 +++++++++
 .../test/golden/basic-ir/equality-record.coln |  14 ++
 .../golden/basic-ir/equality-record.output    |  59 ++++++
 .../family-argument-prop-prop-prop.coln       |   8 +
 .../family-argument-prop-prop-prop.output     |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-prop-prop-set.coln        |   8 +
 .../family-argument-prop-prop-set.output      |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-prop-set-prop.coln        |   8 +
 .../family-argument-prop-set-prop.output      |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-prop-set-set.coln         |   8 +
 .../family-argument-prop-set-set.output       |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-set-prop-prop.coln        |   8 +
 .../family-argument-set-prop-prop.output      |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-set-prop-set.coln         |   8 +
 .../family-argument-set-prop-set.output       |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../family-argument-set-set-prop.coln         |   8 +
 .../family-argument-set-set-prop.output       |  30 +++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  54 +++++
 .../test/golden/basic-ir/family-argument.coln |   8 +
 .../golden/basic-ir/family-argument.output    |  30 +++
 .../basic-ir/family-argument.ts.output/T.ts   |  13 ++
 .../family-argument.ts.output/TRealm.json     |   1 +
 .../family-argument.ts.output/TRealm.ts       |  54 +++++
 .../basic-ir/function-mixed-prop-set.coln     |   9 -
 .../basic-ir/function-mixed-prop-set.output   |  40 ----
 .../function-mixed-prop-set.ts.output/T.ts    |  15 --
 .../TRealm.json                               |   1 -
 .../basic-ir/function-multi-argument.coln     |   9 -
 .../basic-ir/function-multi-argument.output   |  37 ----
 .../function-multi-argument.ts.output/T.ts    |  15 --
 .../TRealm.json                               |   1 -
 ...p-argument-projection-prop-prop-prop.coln} |   0
 ...argument-projection-prop-prop-prop.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...up-argument-projection-prop-prop-set.coln} |   0
 ...-argument-projection-prop-prop-set.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...up-argument-projection-prop-set-prop.coln} |   0
 ...-argument-projection-prop-set-prop.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...kup-argument-projection-prop-set-set.coln} |   0
 ...p-argument-projection-prop-set-set.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...up-argument-projection-set-prop-prop.coln} |   0
 ...-argument-projection-set-prop-prop.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...kup-argument-projection-set-prop-set.coln} |   0
 ...p-argument-projection-set-prop-set.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...kup-argument-projection-set-set-prop.coln} |   0
 ...p-argument-projection-set-set-prop.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...n.coln => lookup-argument-projection.coln} |   0
 ...tput => lookup-argument-projection.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...okup-composition-prop-prop-prop-prop.coln} |   0
 ...up-composition-prop-prop-prop-prop.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...ookup-field-projection-prop-prop-prop.coln |  11 ++
 ...kup-field-projection-prop-prop-prop.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 ...lookup-field-projection-prop-prop-set.coln |  11 ++
 ...okup-field-projection-prop-prop-set.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 ...lookup-field-projection-prop-set-prop.coln |  11 ++
 ...okup-field-projection-prop-set-prop.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 .../lookup-field-projection-prop-set-set.coln |  11 ++
 ...ookup-field-projection-prop-set-set.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 ...lookup-field-projection-set-prop-prop.coln |  11 ++
 ...okup-field-projection-set-prop-prop.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 .../lookup-field-projection-set-prop-set.coln |  11 ++
 ...ookup-field-projection-set-prop-set.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 .../lookup-field-projection-set-set-prop.coln |  11 ++
 ...ookup-field-projection-set-set-prop.output |  48 +++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 .../basic-ir/lookup-field-projection.coln     |  11 ++
 .../basic-ir/lookup-field-projection.output   |  48 +++++
 .../lookup-field-projection.ts.output/T.ts    |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  66 +++++++
 .../lookup-proof-result-argument.coln         |  10 +
 .../lookup-proof-result-argument.output       |  49 +++++
 .../T.ts                                      |  17 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  76 ++++++++
 .../test/golden/basic-ir/param-alias-set.coln |  13 ++
 .../golden/basic-ir/param-alias-set.output    |  34 ++++
 .../param-alias-set.ts.output/SetAlias.ts     |   5 +
 .../basic-ir/param-alias-set.ts.output/T.ts   |  12 ++
 .../param-alias-set.ts.output/TRealm.json     |   1 +
 .../param-alias-set.ts.output/TRealm.ts       |  40 ++++
 .../test/golden/basic-ir/param-alias.coln     |  19 ++
 .../test/golden/basic-ir/param-alias.output   |  49 +++++
 .../basic-ir/param-alias.ts.output/Alias.ts   |   6 +
 .../basic-ir/param-alias.ts.output/Model.ts   |   9 +
 .../basic-ir/param-alias.ts.output/T.ts       |  13 ++
 .../param-alias.ts.output/TRealm.json         |   1 +
 .../basic-ir/param-alias.ts.output/TRealm.ts  |  48 +++++
 .../param-record-dependent-function.coln      |  18 ++
 .../param-record-dependent-function.output    |  63 ++++++
 .../T.ts                                      |  19 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  80 ++++++++
 .../param-record-dependent-model.coln         |  20 ++
 .../param-record-dependent-model.output       |  48 +++++
 .../PointOf.ts                                |   9 +
 .../T.ts                                      |  12 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  53 +++++
 .../basic-ir/param-record-function.coln       |  13 ++
 .../basic-ir/param-record-function.output     |  41 ++++
 .../param-record-function.ts.output/T.ts      |  13 ++
 .../TRealm.json                               |   1 +
 .../param-record-function.ts.output/TRealm.ts |  55 ++++++
 .../golden/basic-ir/param-record-model.coln   |   6 +-
 .../golden/basic-ir/param-record-model.output |  15 +-
 .../param-record-model.ts.output/TRealm.json  |   2 +-
 .../golden/basic-ir/param-record-nested.coln  |   2 -
 .../basic-ir/param-record-nested.output       |  26 +--
 .../param-record-nested.ts.output/T.ts        |   2 -
 .../param-record-nested.ts.output/TRealm.json |   2 +-
 .../param-record-nested.ts.output/TRealm.ts   |  11 --
 .../param-record-repeated-binders.coln        |  12 ++
 .../param-record-repeated-binders.output      |  35 ++++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  41 ++++
 .../param-record-type-family-lambda.coln      |  10 +
 .../param-record-type-family-lambda.output    |  28 +++
 .../T.ts                                      |   9 +
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  41 ++++
 ...ram-record-type-family-multi-argument.coln |  13 ++
 ...m-record-type-family-multi-argument.output |  51 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  39 ++--
 .../param-record-type-family-partial.coln     |  13 ++
 .../param-record-type-family-partial.output   |  48 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  68 +++++++
 .../param-record-type-family-prop.coln        |  12 ++
 .../param-record-type-family-prop.output      |  39 ++++
 .../T.ts                                      |  13 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  31 +--
 .../param-record-type-family-unused.coln      |  11 ++
 .../param-record-type-family-unused.output    |  29 +++
 .../T.ts                                      |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  48 +++++
 ...ln => proof-record-function-argument.coln} |   1 -
 ... => proof-record-function-argument.output} |  19 --
 .../T.ts                                      |   2 -
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  11 --
 ...ed.coln => proof-record-mixed-fields.coln} |   0
 ...utput => proof-record-mixed-fields.output} |   0
 .../T.ts                                      |   0
 .../TRealm.json                               |   0
 .../TRealm.ts                                 |   0
 ...roof-record-nested-dependent-equality.coln |  16 ++
 ...of-record-nested-dependent-equality.output |  41 ++++
 .../T.ts                                      |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  43 ++++
 .../proof-record-nested-dependent-prop.coln   |  16 ++
 .../proof-record-nested-dependent-prop.output |  39 ++++
 .../T.ts                                      |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  44 +++++
 .../TRealm.json                               |   1 -
 .../basic-ir/proof-record-prop-field.coln     |  11 ++
 .../basic-ir/proof-record-prop-field.output   |  32 +++
 .../proof-record-prop-field.ts.output/T.ts    |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  35 ++++
 .../proof-record-structural-equality.coln     |  18 ++
 .../proof-record-structural-equality.output   |  48 +++++
 .../T.ts                                      |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  39 ++++
 .../test/golden/basic-ir/prop-alias.coln      |   8 +
 .../test/golden/basic-ir/prop-alias.output    |  23 +++
 .../prop-alias.ts.output/PropAlias.ts         |   5 +
 .../golden/basic-ir/prop-alias.ts.output/T.ts |  10 +
 .../basic-ir/prop-alias.ts.output/TRealm.json |   1 +
 .../basic-ir/prop-alias.ts.output/TRealm.ts   |  27 +++
 .../prop-record-dependent-equality.coln       |  13 ++
 .../prop-record-dependent-equality.output     |  35 ++++
 .../T.ts                                      |  11 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  35 ++++
 .../prop-record-nested-dependent.coln         |  18 ++
 .../prop-record-nested-dependent.output       |  54 +++++
 .../T.ts                                      |  15 ++
 .../TRealm.json                               |   1 +
 .../TRealm.ts                                 |  61 ++++++
 .../test/golden/basic-ir/record-nested.coln   |  15 ++
 .../test/golden/basic-ir/record-nested.output |  35 ++++
 .../basic-ir/record-nested.ts.output/T.ts     |   9 +
 .../record-nested.ts.output/TRealm.json       |   1 +
 .../record-nested.ts.output/TRealm.ts         |  33 ++++
 ...t-function-argument-prop-prop-prop.test.ts |  21 ++
 ...nt-function-argument-prop-prop-set.test.ts |  21 ++
 ...nt-function-argument-prop-set-prop.test.ts |  45 +++++
 ...ent-function-argument-prop-set-set.test.ts |  21 ++
 ...nt-function-argument-set-prop-prop.test.ts |  21 ++
 ...ent-function-argument-set-prop-set.test.ts |  28 +++
 ...ent-function-argument-set-set-prop.test.ts |  21 ++
 .../dependent-function-argument.test.ts       |  21 ++
 .../dependent-function-prop-prop.test.ts      |  20 ++
 .../dependent-function-prop-set.test.ts       |  20 ++
 .../dependent-function-set-prop.test.ts       |  20 ++
 .../tests/basic-ir/dependent-function.test.ts |  20 ++
 .../empty-prop-record-function.test.ts        |  20 ++
 .../tests/basic-ir/empty-prop-record.test.ts  |   9 +-
 .../tests/basic-ir/empty-record.test.ts       |  68 +------
 .../tests/basic-ir/equality-prop.pending.ts   |  86 --------
 .../tests/basic-ir/equality-prop.test.ts      |  18 ++
 .../basic-ir/equality-record-nested.test.ts   |  37 ++++
 .../tests/basic-ir/equality-record.test.ts    |  34 ++++
 .../tests/basic-ir/equality.pending.ts        |  58 ------
 .../tests/basic-ir/equality.test.ts           |  29 +++
 .../family-argument-prop-prop-prop.test.ts    |  19 ++
 .../family-argument-prop-prop-set.test.ts     |  19 ++
 .../family-argument-prop-set-prop.test.ts     |  19 ++
 .../family-argument-prop-set-set.test.ts      |  19 ++
 .../family-argument-set-prop-prop.test.ts     |  19 ++
 .../family-argument-set-prop-set.test.ts      |  19 ++
 .../family-argument-set-set-prop.test.ts      |  19 ++
 .../tests/basic-ir/family-argument.test.ts    |  19 ++
 .../basic-ir/foreign-key-prop-prop.test.ts    |  29 ---
 .../basic-ir/foreign-key-prop-set.test.ts     |  27 ---
 .../basic-ir/foreign-key-set-prop.test.ts     |  63 +-----
 .../tests/basic-ir/foreign-key.test.ts        |   1 -
 .../basic-ir/function-mixed-prop-set.test.ts  |  49 -----
 .../basic-ir/function-multi-argument.test.ts  | 103 ----------
 .../tests/basic-ir/function-prop-prop.test.ts |  55 +-----
 .../tests/basic-ir/function-prop-set.test.ts  |  29 ---
 .../tests/basic-ir/function-set-prop.test.ts  |  49 +----
 .../tests/basic-ir/inventory.test.ts          |   7 +-
 ...argument-projection-prop-prop-prop.test.ts |  22 +++
 ...-argument-projection-prop-prop-set.test.ts |  22 +++
 ...-argument-projection-prop-set-prop.test.ts |  22 +++
 ...p-argument-projection-prop-set-set.test.ts |  22 +++
 ...-argument-projection-set-prop-prop.test.ts |  22 +++
 ...p-argument-projection-set-prop-set.test.ts |  22 +++
 ...-argument-projection-set-set-prop.test.ts} |  42 ++--
 ....ts => lookup-argument-projection.test.ts} |  14 +-
 .../tests/basic-ir/lookup-builtin.test.ts     |   3 -
 ...up-composition-prop-prop-prop-prop.test.ts |  35 ++++
 .../basic-ir/lookup-composition-prop.test.ts  | 140 -------------
 .../tests/basic-ir/lookup-composition.test.ts |   6 -
 ...up-field-projection-prop-prop-prop.test.ts |  23 +++
 ...kup-field-projection-prop-prop-set.test.ts |  23 +++
 ...kup-field-projection-prop-set-prop.test.ts |  23 +++
 ...okup-field-projection-prop-set-set.test.ts |  23 +++
 ...kup-field-projection-set-prop-prop.test.ts |  23 +++
 ...okup-field-projection-set-prop-set.test.ts |  23 +++
 ...okup-field-projection-set-set-prop.test.ts |  36 ++++
 .../basic-ir/lookup-field-projection.test.ts  |  23 +++
 .../basic-ir/lookup-literal-prop.test.ts      |  71 +------
 .../tests/basic-ir/lookup-literal.test.ts     |   2 -
 .../lookup-projection-prop-prop-prop.test.ts  | 100 ----------
 .../lookup-projection-prop-prop-set.test.ts   |  87 ---------
 .../lookup-projection-prop-set-prop.test.ts   |  79 --------
 .../lookup-projection-prop-set-set.test.ts    |  59 ------
 .../lookup-projection-set-prop-prop.test.ts   |  87 ---------
 .../lookup-projection-set-prop-set.test.ts    |  64 ------
 .../lookup-proof-result-argument.test.ts      |  22 +++
 .../lookup-record-composition.test.ts         |  14 +-
 .../basic-ir/lookup-record-expansion.test.ts  |  12 +-
 .../basic-ir/lookup-record-field.test.ts      |  15 +-
 .../tests/basic-ir/lookup-record.test.ts      |  10 +-
 .../tests/basic-ir/param-alias-set.test.ts    |  18 ++
 .../tests/basic-ir/param-alias.test.ts        |  22 +++
 .../basic-ir/param-record-concrete.test.ts    |   9 +-
 .../param-record-dependent-function.test.ts   |  22 +++
 .../param-record-dependent-model.test.ts      |  22 +++
 .../basic-ir/param-record-function.test.ts    |  21 ++
 .../tests/basic-ir/param-record-model.test.ts |  12 +-
 .../basic-ir/param-record-nested.test.ts      |  29 +--
 .../param-record-repeated-binders.pending.ts  |   5 +
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 .../tests/basic-ir/param-record.test.ts       |  10 +-
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 .../tests/basic-ir/projection.test.ts         |  52 +++--
 .../proof-record-function-argument.test.ts    |  65 +++++++
 ...t.ts => proof-record-mixed-fields.test.ts} |  22 +--
 ...f-record-nested-dependent-equality.test.ts |  29 +++
 ...proof-record-nested-dependent-prop.test.ts |  28 +++
 .../basic-ir/proof-record-parameter.test.ts   |  79 --------
 .../basic-ir/proof-record-prop-field.test.ts  |  18 ++
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 .../tests/basic-ir/prop-alias.test.ts         |  19 ++
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 .../tests/basic-ir/prop-record.test.ts        |  36 +---
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 .../tests/basic-ir/record-field-order.test.ts |  12 +-
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 ...erals.pending.ts => rule-literals.test.ts} |  15 +-
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diff --git a/packages/coln-compiler/test/Main.hs b/packages/coln-compiler/test/Main.hs
index 713dc5f3..66994243 100644
--- a/packages/coln-compiler/test/Main.hs
+++ b/packages/coln-compiler/test/Main.hs
@@ -35,7 +35,7 @@ knownFailingElaboratorTests :: [String]
 knownFailingElaboratorTests = []
 
 knownFailingTypeScriptTests :: [String]
-knownFailingTypeScriptTests = ["equality", "equality-prop", "rule-literals"]
+knownFailingTypeScriptTests = []
 
 main :: IO ()
 main = defaultMain =<< goldenTests
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.coln
new file mode 100644
index 00000000..4fa9c1b1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Prop
+  B : A -> Prop
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.output
new file mode 100644
index 00000000..37174dc2
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Prop
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.coln
new file mode 100644
index 00000000..512fd386
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Prop
+  B : A -> Prop
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.output
new file mode 100644
index 00000000..92e88604
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Prop
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.coln
new file mode 100644
index 00000000..fd903fb1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Prop
+  B : A -> Set
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.output
new file mode 100644
index 00000000..492e7d26
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Set
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.coln
new file mode 100644
index 00000000..e4be848b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Prop
+  B : A -> Set
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.output
new file mode 100644
index 00000000..b7d540ec
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Set
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.coln
new file mode 100644
index 00000000..b0cf207d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Set
+  B : A -> Prop
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.output
new file mode 100644
index 00000000..b2815b4b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Prop
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.coln
new file mode 100644
index 00000000..94f0f3d8
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Set
+  B : A -> Prop
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.output
new file mode 100644
index 00000000..856eac0e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Prop
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.coln
new file mode 100644
index 00000000..7490d23f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Set
+  B : A -> Set
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.output
new file mode 100644
index 00000000..60c767d2
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Set
+  C : (a : A) -> B a -> Prop
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.coln
new file mode 100644
index 00000000..276f3f76
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.coln
@@ -0,0 +1,9 @@
+theory T := sig
+  A : Set
+  B : A -> Set
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.output
new file mode 100644
index 00000000..2c363c41
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.output
@@ -0,0 +1,45 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Set
+  C : (a : A) -> B a -> Set
+  f : (a : A) -> (b : B a) -> C a b
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  C = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+  f = (fun [a : TRealm.A [], b : TRealm.B [a := a]] -> TRealm.C [
+    a := a,
+    b := b
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.C := [.a : ℜ.A, .b : ℜ.B]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B, .c : ℜ.C] primarykey [.a, .b]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.C.foreignKey a b := ℜ.C [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    enforced ℜ.f.foreignKey a b c := ℜ.f [
+      .a ↦ a,
+      .b ↦ b,
+      .c ↦ c
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ∧ c ∈ ℜ.C [.a ↦ a, .b ↦ b]
+    monitored ℜ.f.total a b := a ∈ ℜ.A [] ∧ b ∈ ℜ.B [.a ↦ a] ⊢ ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/T.ts
new file mode 100644
index 00000000..c765b892
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  C: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.json
new file mode 100644
index 00000000..8b098795
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["C"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["C"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["C"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["C"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["C"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.ts
new file mode 100644
index 00000000..8a4b907c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.ts
@@ -0,0 +1,69 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.C", [a, b]));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      C: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.C",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      f: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.TableCellRef.Transaction(
+            store,
+            "TRealm.f",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.coln
new file mode 100644
index 00000000..729dcd82
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Prop
+  f : (a : A) -> B a
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.output
new file mode 100644
index 00000000..94afe275
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.output
@@ -0,0 +1,31 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Prop
+  f : (a : A) -> B a
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  f = (fun [a : TRealm.A []] -> TRealm.B [a := a])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.f.foreignKey a b := ℜ.f [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    monitored ℜ.f.total a := a ∈ ℜ.A [] ⊢ ℜ.f [.a ↦ a]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..34d4081c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..c4ed98b1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..b720e351
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,50 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.coln
new file mode 100644
index 00000000..6f2a626e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Set
+  f : (a : A) -> B a
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.output
new file mode 100644
index 00000000..ea5c35ca
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.output
@@ -0,0 +1,31 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Set
+  f : (a : A) -> B a
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  f = (fun [a : TRealm.A []] -> TRealm.B [a := a])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.f.foreignKey a b := ℜ.f [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    monitored ℜ.f.total a := a ∈ ℜ.A [] ⊢ ℜ.f [.a ↦ a]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..34d4081c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..c4ed98b1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..b720e351
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,50 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.coln
new file mode 100644
index 00000000..d8a36c75
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Prop
+  f : (a : A) -> B a
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.output
new file mode 100644
index 00000000..0964e3e0
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.output
@@ -0,0 +1,31 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Prop
+  f : (a : A) -> B a
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  f = (fun [a : TRealm.A []] -> TRealm.B [a := a])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.f.foreignKey a b := ℜ.f [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    monitored ℜ.f.total a := a ∈ ℜ.A [] ⊢ ℜ.f [.a ↦ a]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..34d4081c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..c4ed98b1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..b720e351
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,50 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function.coln b/packages/coln-compiler/test/golden/basic-ir/dependent-function.coln
new file mode 100644
index 00000000..eec801fd
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Set
+  f : (a : A) -> B a
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function.output b/packages/coln-compiler/test/golden/basic-ir/dependent-function.output
new file mode 100644
index 00000000..407d9b4d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function.output
@@ -0,0 +1,31 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Set
+  f : (a : A) -> B a
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  f = (fun [a : TRealm.A []] -> TRealm.B [a := a])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.f := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.f.foreignKey a b := ℜ.f [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+    monitored ℜ.f.total a := a ∈ ℜ.A [] ⊢ ℜ.f [.a ↦ a]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/T.ts
new file mode 100644
index 00000000..34d4081c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.json
new file mode 100644
index 00000000..c4ed98b1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.ts
new file mode 100644
index 00000000..b720e351
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.ts
@@ -0,0 +1,50 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.coln b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.coln
new file mode 100644
index 00000000..b18b8a1a
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.coln
@@ -0,0 +1,10 @@
+def Truth : Prop := sig
+end
+
+theory T := sig
+  X : Set
+  trivial : (x : X) -> Truth
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.output b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.output
new file mode 100644
index 00000000..5860adee
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.output
@@ -0,0 +1,29 @@
+-- elaborated
+global entry named Truth
+type: Prop
+value: sig
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  trivial : (x : X) -> Truth
+end
+realm named TRealm
+generators: node
+  X = rel []
+  trivial = (fun [x : TRealm.X []] -> Truth)
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.trivial := [.x : ℜ.X] primarykey [.x]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.trivial.foreignKey x := ℜ.trivial [.x ↦ x] ⊢ x ∈ ℜ.X []
+    monitored ℜ.trivial.total x := x ∈ ℜ.X [] ⊢ ℜ.trivial [.x ↦ x]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/T.ts
new file mode 100644
index 00000000..8a679781
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  trivial: (x: runtime.Value) => Truth.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  trivial: (x: runtime.Value) => Truth.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.json
new file mode 100644
index 00000000..30769265
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["trivial"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["trivial"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["trivial"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["trivial"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["trivial"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.ts
new file mode 100644
index 00000000..46e80df1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.ts
@@ -0,0 +1,39 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      trivial: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.trivial", [x]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      trivial: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.trivial",
+          [x],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.coln b/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.coln
new file mode 100644
index 00000000..bd7c83be
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.coln
@@ -0,0 +1,24 @@
+def Unit : Set := sig
+end
+
+def Inner (X : Set) (P : Prop) : Set := sig
+  value : X
+  evidence : P
+end
+
+def Outer (X : Set) (P : Prop) : Set := sig
+  unit : Unit
+  inner : Inner X P
+  trailing : X
+end
+
+theory T := sig
+  X : Set
+  P : Prop
+  first : Outer X P
+  second : Outer X P
+  same : first = second
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.output b/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.output
new file mode 100644
index 00000000..ccad3a3d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/equality-record-nested.output
@@ -0,0 +1,96 @@
+-- elaborated
+global entry named Unit
+type: Set
+value: sig
+end
+global entry named Inner
+type: (X : Set) -> (P : Prop) -> Set
+value: X => P => sig
+  value : X
+  evidence : P
+end
+global entry named Outer
+type: (X : Set) -> (P : Prop) -> Set
+value: X => P => sig
+  unit : Unit
+  inner : Inner X P
+  trailing : X
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  P : Prop
+  first : Outer X P
+  second : Outer X P
+  same : first = second
+end
+realm named TRealm
+generators: node
+  X = rel []
+  P = rel []
+  first = (fun [] -> Outer (TRealm.X []) (TRealm.P []))
+  second = (fun [] -> Outer (TRealm.X []) (TRealm.P []))
+  same = (fun [] -> TRealm.first [] = TRealm.second [])
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.P := []
+    table ℜ.first := [
+      .a.inner.value : ℜ.X,
+      .a.inner.evidence : ℜ.P,
+      .a.trailing : ℜ.X
+    ] primarykey []
+    table ℜ.second := [
+      .a.inner.value : ℜ.X,
+      .a.inner.evidence : ℜ.P,
+      .a.trailing : ℜ.X
+    ] primarykey []
+    table ℜ.same := [] primarykey []
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.P.foreignKey := ℜ.P [] ⊢ ⊤
+    enforced ℜ.first.foreignKey a.inner.value a.inner.evidence a.trailing := ℜ.first [
+      .a.inner.value ↦ a.inner.value,
+      .a.inner.evidence ↦ a.inner.evidence,
+      .a.trailing ↦ a.trailing
+    ] ⊢ a.inner.value ∈ ℜ.X [] ∧ a.inner.evidence ∈ ℜ.P [] ∧ a.trailing ∈ ℜ.X []
+    monitored ℜ.first.total := ⊤ ⊢ ℜ.first []
+    enforced ℜ.second.foreignKey a.inner.value a.inner.evidence a.trailing := ℜ.second [
+      .a.inner.value ↦ a.inner.value,
+      .a.inner.evidence ↦ a.inner.evidence,
+      .a.trailing ↦ a.trailing
+    ] ⊢ a.inner.value ∈ ℜ.X [] ∧ a.inner.evidence ∈ ℜ.P [] ∧ a.trailing ∈ ℜ.X []
+    monitored ℜ.second.total := ⊤ ⊢ ℜ.second []
+    enforced ℜ.same.foreignKey a.lhs.inner.value.inner.value a.lhs.inner.value.inner.evidence a.lhs.inner.value.trailing a.lhs.inner.evidence.inner.value a.lhs.inner.evidence.inner.evidence a.lhs.inner.evidence.trailing a.lhs.trailing.inner.value a.lhs.trailing.inner.evidence a.lhs.trailing.trailing a.rhs.inner.value.inner.value a.rhs.inner.value.inner.evidence a.rhs.inner.value.trailing a.rhs.inner.evidence.inner.value a.rhs.inner.evidence.inner.evidence a.rhs.inner.evidence.trailing a.rhs.trailing.inner.value a.rhs.trailing.inner.evidence a.rhs.trailing.trailing := ℜ.same [] ∧ ℜ.first [
+      .a.inner.value ↦ a.lhs.inner.value.inner.value,
+      .a.inner.evidence ↦ a.lhs.inner.value.inner.evidence,
+      .a.trailing ↦ a.lhs.inner.value.trailing
+    ] ∧ ℜ.first [
+      .a.inner.value ↦ a.lhs.inner.evidence.inner.value,
+      .a.inner.evidence ↦ a.lhs.inner.evidence.inner.evidence,
+      .a.trailing ↦ a.lhs.inner.evidence.trailing
+    ] ∧ ℜ.first [
+      .a.inner.value ↦ a.lhs.trailing.inner.value,
+      .a.inner.evidence ↦ a.lhs.trailing.inner.evidence,
+      .a.trailing ↦ a.lhs.trailing.trailing
+    ] ∧ ℜ.second [
+      .a.inner.value ↦ a.rhs.inner.value.inner.value,
+      .a.inner.evidence ↦ a.rhs.inner.value.inner.evidence,
+      .a.trailing ↦ a.rhs.inner.value.trailing
+    ] ∧ ℜ.second [
+      .a.inner.value ↦ a.rhs.inner.evidence.inner.value,
+      .a.inner.evidence ↦ a.rhs.inner.evidence.inner.evidence,
+      .a.trailing ↦ a.rhs.inner.evidence.trailing
+    ] ∧ ℜ.second [
+      .a.inner.value ↦ a.rhs.trailing.inner.value,
+      .a.inner.evidence ↦ a.rhs.trailing.inner.evidence,
+      .a.trailing ↦ a.rhs.trailing.trailing
+    ] ⊢ a.lhs.inner.value.inner.value = a.rhs.inner.value.inner.value ∧ a.lhs.inner.evidence.inner.evidence = a.rhs.inner.evidence.inner.evidence ∧ a.lhs.trailing.trailing = a.rhs.trailing.trailing
+    monitored ℜ.same.total := ⊤ ⊢ ℜ.same []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/equality-record.coln b/packages/coln-compiler/test/golden/basic-ir/equality-record.coln
new file mode 100644
index 00000000..7712a7a5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/equality-record.coln
@@ -0,0 +1,14 @@
+def Pair (X : Set) : Set := sig
+  left : X
+  right : X
+end
+
+theory T := sig
+  X : Set
+  first : Pair X
+  second : Pair X
+  same : first = second
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/equality-record.output b/packages/coln-compiler/test/golden/basic-ir/equality-record.output
new file mode 100644
index 00000000..454a743e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/equality-record.output
@@ -0,0 +1,59 @@
+-- elaborated
+global entry named Pair
+type: (X : Set) -> Set
+value: X => sig
+  left : X
+  right : X
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  first : Pair X
+  second : Pair X
+  same : first = second
+end
+realm named TRealm
+generators: node
+  X = rel []
+  first = (fun [] -> Pair (TRealm.X []))
+  second = (fun [] -> Pair (TRealm.X []))
+  same = (fun [] -> TRealm.first [] = TRealm.second [])
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.first := [.a.left : ℜ.X, .a.right : ℜ.X] primarykey []
+    table ℜ.second := [.a.left : ℜ.X, .a.right : ℜ.X] primarykey []
+    table ℜ.same := [] primarykey []
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.first.foreignKey a.left a.right := ℜ.first [
+      .a.left ↦ a.left,
+      .a.right ↦ a.right
+    ] ⊢ a.left ∈ ℜ.X [] ∧ a.right ∈ ℜ.X []
+    monitored ℜ.first.total := ⊤ ⊢ ℜ.first []
+    enforced ℜ.second.foreignKey a.left a.right := ℜ.second [
+      .a.left ↦ a.left,
+      .a.right ↦ a.right
+    ] ⊢ a.left ∈ ℜ.X [] ∧ a.right ∈ ℜ.X []
+    monitored ℜ.second.total := ⊤ ⊢ ℜ.second []
+    enforced ℜ.same.foreignKey a.lhs.left.left a.lhs.left.right a.lhs.right.left a.lhs.right.right a.rhs.left.left a.rhs.left.right a.rhs.right.left a.rhs.right.right := ℜ.same [] ∧ ℜ.first [
+      .a.left ↦ a.lhs.left.left,
+      .a.right ↦ a.lhs.left.right
+    ] ∧ ℜ.first [
+      .a.left ↦ a.lhs.right.left,
+      .a.right ↦ a.lhs.right.right
+    ] ∧ ℜ.second [
+      .a.left ↦ a.rhs.left.left,
+      .a.right ↦ a.rhs.left.right
+    ] ∧ ℜ.second [
+      .a.left ↦ a.rhs.right.left,
+      .a.right ↦ a.rhs.right.right
+    ] ⊢ a.lhs.left.left = a.rhs.left.left ∧ a.lhs.right.right = a.rhs.right.right
+    monitored ℜ.same.total := ⊤ ⊢ ℜ.same []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.coln
new file mode 100644
index 00000000..424b4bb6
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Prop
+  R : (a : A) -> B a -> Prop
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.output
new file mode 100644
index 00000000..b39c1b54
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Prop
+  R : (a : A) -> B a -> Prop
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.coln
new file mode 100644
index 00000000..a814948d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Prop
+  R : (a : A) -> B a -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.output
new file mode 100644
index 00000000..afc50505
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Prop
+  R : (a : A) -> B a -> Set
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.coln
new file mode 100644
index 00000000..24b827fc
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Set
+  R : (a : A) -> B a -> Prop
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.output
new file mode 100644
index 00000000..4546abf0
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Set
+  R : (a : A) -> B a -> Prop
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.coln
new file mode 100644
index 00000000..301576ec
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Prop
+  B : A -> Set
+  R : (a : A) -> B a -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.output
new file mode 100644
index 00000000..c7f46af6
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : A -> Set
+  R : (a : A) -> B a -> Set
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.coln
new file mode 100644
index 00000000..bb5e4d71
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Prop
+  R : (a : A) -> B a -> Prop
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.output
new file mode 100644
index 00000000..370ca9e5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Prop
+  R : (a : A) -> B a -> Prop
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.coln
new file mode 100644
index 00000000..213f13a1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Prop
+  R : (a : A) -> B a -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.output
new file mode 100644
index 00000000..98013b31
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Prop
+  R : (a : A) -> B a -> Set
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.coln
new file mode 100644
index 00000000..86b33d04
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Set
+  R : (a : A) -> B a -> Prop
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.output
new file mode 100644
index 00000000..43195486
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Set
+  R : (a : A) -> B a -> Prop
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument.coln b/packages/coln-compiler/test/golden/basic-ir/family-argument.coln
new file mode 100644
index 00000000..75f85bcb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument.coln
@@ -0,0 +1,8 @@
+theory T := sig
+  A : Set
+  B : A -> Set
+  R : (a : A) -> B a -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument.output b/packages/coln-compiler/test/golden/basic-ir/family-argument.output
new file mode 100644
index 00000000..41e7d2d7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument.output
@@ -0,0 +1,30 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : A -> Set
+  R : (a : A) -> B a -> Set
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel [a : TRealm.A []]
+  R = rel [a : TRealm.A [], b : TRealm.B [a := a]]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.R := [.a : ℜ.A, .b : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.R.foreignKey a b := ℜ.R [.a ↦ a, .b ↦ b] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B [
+      .a ↦ a
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/T.ts
new file mode 100644
index 00000000..2cbb5a3f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.json
new file mode 100644
index 00000000..74020abb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.ts
new file mode 100644
index 00000000..4141562c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.ts
@@ -0,0 +1,54 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.B",
+          [a],
+          transaction
+        ));
+      },
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.coln
deleted file mode 100644
index b73eb6df..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.coln
+++ /dev/null
@@ -1,9 +0,0 @@
-theory T := sig
-  X : Set
-  P : Prop
-  Y : Set
-  choose : X -> P -> Y
-end
-
-realm TRealm @ T
-end
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.output
deleted file mode 100644
index 15cf11c3..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.output
+++ /dev/null
@@ -1,40 +0,0 @@
--- elaborated
-global entry named T
-type: Theory
-value: sig
-  X : Set
-  P : Prop
-  Y : Set
-  choose : X -> P -> Y
-end
-realm named TRealm
-generators: node
-  X = rel []
-  P = rel []
-  Y = rel []
-  choose = (fun [a : TRealm.X [], b : TRealm.P []] -> TRealm.Y [])
-end
-lowered: flatrealm
-  entities
-    table ℜ.X := []
-    table ℜ.P := []
-    table ℜ.Y := []
-    table ℜ.choose := [.a : ℜ.X, .b : ℜ.P, .c : ℜ.Y] primarykey [.a, .b]
-  end
-  rules
-    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
-    enforced ℜ.P.foreignKey := ℜ.P [] ⊢ ⊤
-    enforced ℜ.Y.foreignKey := ℜ.Y [] ⊢ ⊤
-    enforced ℜ.choose.foreignKey a b c := ℜ.choose [
-      .a ↦ a,
-      .b ↦ b,
-      .c ↦ c
-    ] ⊢ a ∈ ℜ.X [] ∧ b ∈ ℜ.P [] ∧ c ∈ ℜ.Y []
-    monitored ℜ.choose.total a b := a ∈ ℜ.X [] ∧ b ∈ ℜ.P [] ⊢ ℜ.choose [
-      .a ↦ a,
-      .b ↦ b
-    ]
-  end
-end
-
--- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/T.ts
deleted file mode 100644
index dfcd1682..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/T.ts
+++ /dev/null
@@ -1,15 +0,0 @@
-import * as runtime from "@coln-project/runtime";
-
-export interface View {
-  X: runtime.ColnSet.View;
-  P: runtime.ColnSet.View;
-  Y: runtime.ColnSet.View;
-  choose: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
-}
-
-export interface Transaction extends View {
-  X: runtime.ColnSet.Transaction;
-  P: runtime.ColnSet.Transaction;
-  Y: runtime.ColnSet.Transaction;
-  choose: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
-}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.json
deleted file mode 100644
index 134d1e5d..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.json
+++ /dev/null
@@ -1 +0,0 @@
-{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Y"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["choose"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["Y"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Y"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["choose"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]},{"tag":"rowId","path":[["TRealm"],["Y"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["choose"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":{"tag":"var","index":2},"values":[]}}]}},{"path":[["TRealm"],["choose"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["choose"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.coln b/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.coln
deleted file mode 100644
index b34114bb..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.coln
+++ /dev/null
@@ -1,9 +0,0 @@
-theory T := sig
-  X : Set
-  P : Prop
-  Q : Prop
-  f : P -> X -> Q
-end
-
-realm TRealm @ T
-end
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.output b/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.output
deleted file mode 100644
index f870d9ec..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.output
+++ /dev/null
@@ -1,37 +0,0 @@
--- elaborated
-global entry named T
-type: Theory
-value: sig
-  X : Set
-  P : Prop
-  Q : Prop
-  f : P -> X -> Q
-end
-realm named TRealm
-generators: node
-  X = rel []
-  P = rel []
-  Q = rel []
-  f = (fun [a : TRealm.P [], b : TRealm.X []] -> TRealm.Q [])
-end
-lowered: flatrealm
-  entities
-    table ℜ.X := []
-    table ℜ.P := []
-    table ℜ.Q := []
-    table ℜ.f := [.a : ℜ.P, .b : ℜ.X, .c : ℜ.Q] primarykey [.a, .b]
-  end
-  rules
-    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
-    enforced ℜ.P.foreignKey := ℜ.P [] ⊢ ⊤
-    enforced ℜ.Q.foreignKey := ℜ.Q [] ⊢ ⊤
-    enforced ℜ.f.foreignKey a b c := ℜ.f [
-      .a ↦ a,
-      .b ↦ b,
-      .c ↦ c
-    ] ⊢ a ∈ ℜ.P [] ∧ b ∈ ℜ.X [] ∧ c ∈ ℜ.Q []
-    monitored ℜ.f.total a b := a ∈ ℜ.P [] ∧ b ∈ ℜ.X [] ⊢ ℜ.f [.a ↦ a, .b ↦ b]
-  end
-end
-
--- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/T.ts
deleted file mode 100644
index f1b7bcbb..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/T.ts
+++ /dev/null
@@ -1,15 +0,0 @@
-import * as runtime from "@coln-project/runtime";
-
-export interface View {
-  X: runtime.ColnSet.View;
-  P: runtime.ColnSet.View;
-  Q: runtime.ColnSet.View;
-  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.View;
-}
-
-export interface Transaction extends View {
-  X: runtime.ColnSet.Transaction;
-  P: runtime.ColnSet.Transaction;
-  Q: runtime.ColnSet.Transaction;
-  f: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnRef.Transaction;
-}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.json
deleted file mode 100644
index 527a075b..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.json
+++ /dev/null
@@ -1 +0,0 @@
-{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Q"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["c"]],"type":{"tag":"rowId","path":[["TRealm"],["Q"]]}}],"primaryKey":[[["a"]],[["b"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Q"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Q"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]],[["c"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["P"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["Q"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Q"]],"rowId":{"tag":"var","index":2},"values":[]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["P"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.coln
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.output
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.coln
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.output
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.coln
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.output
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.coln
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.coln
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.output
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/T.ts
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/T.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/TRealm.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.coln
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.output
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.output
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/T.ts
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.ts.output/T.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.json
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.coln
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.output
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.output
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/T.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.json
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rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/TRealm.json
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.coln
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.output
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.ts.output/T.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.json
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection.coln
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection.output
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/T.ts
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/TRealm.json
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diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.coln
rename to packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.output
rename to packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.output
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/T.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.coln
new file mode 100644
index 00000000..48439cb4
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Prop
+  B : Prop
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.output
new file mode 100644
index 00000000..ab45dc88
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : Prop
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.coln
new file mode 100644
index 00000000..9fa82593
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Prop
+  B : Prop
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.output
new file mode 100644
index 00000000..c36c203b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : Prop
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.coln
new file mode 100644
index 00000000..08f635b9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Prop
+  B : Set
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.output
new file mode 100644
index 00000000..e9e46aec
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : Set
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.coln
new file mode 100644
index 00000000..c957f084
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Prop
+  B : Set
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.output
new file mode 100644
index 00000000..580b1b7d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Prop
+  B : Set
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.coln
new file mode 100644
index 00000000..d3584d0a
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Set
+  B : Prop
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.output
new file mode 100644
index 00000000..1833c02e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : Prop
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.coln
new file mode 100644
index 00000000..0992b49f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Set
+  B : Prop
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.output
new file mode 100644
index 00000000..e8448c26
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : Prop
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.coln
new file mode 100644
index 00000000..bf9cee65
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Set
+  B : Set
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.output
new file mode 100644
index 00000000..ccac1aec
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : Set
+  E : B -> Prop
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.coln
new file mode 100644
index 00000000..8f81f791
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.coln
@@ -0,0 +1,11 @@
+theory T := sig
+  A : Set
+  B : Set
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.output b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.output
new file mode 100644
index 00000000..91f23cc1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : Set
+  E : B -> Set
+  x : A
+  next : A -> B
+  edge : E (next x)
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  E = rel [a : TRealm.B []]
+  x = (fun [] -> TRealm.A [])
+  next = (fun [a : TRealm.A []] -> TRealm.B [])
+  edge = (fun [] -> TRealm.E [a := TRealm.next [a := TRealm.x []]])
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.E := [.a : ℜ.B]
+    table ℜ.x := [.a : ℜ.A] primarykey []
+    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.edge := [.a : ℜ.E] primarykey []
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
+    enforced ℜ.x.foreignKey a := ℜ.x [.a ↦ a] ⊢ a ∈ ℜ.A []
+    monitored ℜ.x.total := ⊤ ⊢ ℜ.x []
+    enforced ℜ.next.foreignKey a b := ℜ.next [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
+    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.edge.foreignKey a a.a a.a.a := ℜ.edge [.a ↦ a] ∧ ℜ.x [
+      .a ↦ a.a.a
+    ] ∧ ℜ.next [.a ↦ a.a.a, .b ↦ a.a] ⊢ a ∈ ℜ.E [.a ↦ a.a]
+    monitored ℜ.edge.total := ⊤ ⊢ ℜ.edge []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/T.ts
new file mode 100644
index 00000000..bbe3a9b7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  x: runtime.ColnRef.View;
+  next: (x: runtime.Value) => runtime.ColnRef.View;
+  edge: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  x: runtime.ColnRef.Transaction;
+  next: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  edge: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.json
new file mode 100644
index 00000000..51164585
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["x"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["edge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["x"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["edge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["a"],["a"]],[["a"],["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]},{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["x"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":2}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}},{"path":[["TRealm"],["edge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["edge"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.ts
new file mode 100644
index 00000000..36b5c3a9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.ts
@@ -0,0 +1,66 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      x: (new runtime.TableCellRef.View(store, "TRealm.x", [])),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      },
+      edge: (new runtime.TableCellRef.View(store, "TRealm.edge", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      x: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.x",
+        [],
+        transaction
+      )),
+      next: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.next",
+          [a],
+          transaction
+        ));
+      },
+      edge: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.edge",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln
new file mode 100644
index 00000000..f875c020
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln
@@ -0,0 +1,10 @@
+theory T := sig
+  X : Set
+  P : X -> Prop
+  witness : (x : X) -> P x
+  R : (x : X) -> P x -> Prop
+  use : (x : X) -> R x (witness x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output
new file mode 100644
index 00000000..da1ec05a
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output
@@ -0,0 +1,49 @@
+-- elaborated
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  P : X -> Prop
+  witness : (x : X) -> P x
+  R : (x : X) -> P x -> Prop
+  use : (x : X) -> R x (witness x)
+end
+realm named TRealm
+generators: node
+  X = rel []
+  P = rel [a : TRealm.X []]
+  witness = (fun [x : TRealm.X []] -> TRealm.P [a := x])
+  R = rel [x : TRealm.X [], a : TRealm.P [a := x]]
+  use = (fun [x : TRealm.X []] -> TRealm.R [
+    x := x,
+    a := TRealm.witness [x := x]
+  ])
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.P := [.a : ℜ.X]
+    table ℜ.witness := [.x : ℜ.X, .a : ℜ.P] primarykey [.x]
+    table ℜ.R := [.x : ℜ.X, .a : ℜ.P]
+    table ℜ.use := [.x : ℜ.X, .a : ℜ.R] primarykey [.x]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.P.foreignKey a := ℜ.P [.a ↦ a] ⊢ a ∈ ℜ.X []
+    enforced ℜ.witness.foreignKey x a := ℜ.witness [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.P [.a ↦ x]
+    monitored ℜ.witness.total x := x ∈ ℜ.X [] ⊢ ℜ.witness [.x ↦ x]
+    enforced ℜ.R.foreignKey x a := ℜ.R [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.P [
+      .a ↦ x
+    ]
+    enforced ℜ.use.foreignKey x a a.a := ℜ.use [.x ↦ x, .a ↦ a] ∧ ℜ.witness [
+      .x ↦ x,
+      .a ↦ a.a
+    ] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.R [.x ↦ x, .a ↦ a.a]
+    monitored ℜ.use.total x := x ∈ ℜ.X [] ⊢ ℜ.use [.x ↦ x]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts
new file mode 100644
index 00000000..b860e498
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts
@@ -0,0 +1,17 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  P: (x: runtime.Value) => runtime.ColnSet.View;
+  witness: (x: runtime.Value) => runtime.ColnRef.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  use: (x: runtime.Value) => runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  P: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  witness: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  use: (x: runtime.Value) => runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json
new file mode 100644
index 00000000..edccfea3
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["witness"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":null}},{"path":[["TRealm"],["use"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["R"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["witness"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["witness"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["use"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["R"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["use"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["use"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["use"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts
new file mode 100644
index 00000000..8f8754c3
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts
@@ -0,0 +1,76 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.P", [a]));
+      },
+      witness: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.witness", [x]));
+      },
+      R: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [x, a]));
+        };
+      },
+      use: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.use", [x]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.P",
+          [a],
+          transaction
+        ));
+      },
+      witness: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.witness",
+          [x],
+          transaction
+        ));
+      },
+      R: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      use: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.use",
+          [x],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.coln b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.coln
new file mode 100644
index 00000000..d978ab54
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.coln
@@ -0,0 +1,13 @@
+theory SetAlias := Set
+
+def Box (X : SetAlias) : Set := sig
+  value : X
+end
+
+theory T := sig
+  X : SetAlias
+  boxed : Box X -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.output b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.output
new file mode 100644
index 00000000..eaf51f20
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.output
@@ -0,0 +1,34 @@
+-- elaborated
+global entry named SetAlias
+type: Theory
+value: Set
+global entry named Box
+type: (X : Set) -> Set
+value: X => sig
+  value : X
+end
+global entry named T
+type: Theory
+value: sig
+  X : SetAlias
+  boxed : Box X -> Set
+end
+realm named TRealm
+generators: node
+  X = rel []
+  boxed = rel [a : Box (TRealm.X [])]
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.boxed := [.a.value : ℜ.X]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.boxed.foreignKey a.value := ℜ.boxed [
+      .a.value ↦ a.value
+    ] ⊢ a.value ∈ ℜ.X []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/SetAlias.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/SetAlias.ts
new file mode 100644
index 00000000..1fbce54e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/SetAlias.ts
@@ -0,0 +1,5 @@
+import * as runtime from "@coln-project/runtime";
+
+export type View = runtime.ColnSet.View;
+
+export type Transaction = runtime.ColnSet.Transaction;
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/T.ts
new file mode 100644
index 00000000..8aa5eb2c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/T.ts
@@ -0,0 +1,12 @@
+import * as runtime from "@coln-project/runtime";
+import * as SetAlias from "./SetAlias.ts";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.json
new file mode 100644
index 00000000..afd84e7d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["value"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["value"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.ts
new file mode 100644
index 00000000..e1a7677f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.ts
@@ -0,0 +1,40 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as SetAlias from "./SetAlias.ts";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.coln b/packages/coln-compiler/test/golden/basic-ir/param-alias.coln
new file mode 100644
index 00000000..c7c13f96
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.coln
@@ -0,0 +1,19 @@
+theory Model := sig
+  X : Set
+end
+
+theory Alias := Model
+
+def Box (X : Set) (M : Alias) (Y : Set) : Set := sig
+  key : X
+  modelValue : M.X
+  value : Y
+end
+
+theory T := sig
+  model : Alias
+  boxed : Box Int model String -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.output b/packages/coln-compiler/test/golden/basic-ir/param-alias.output
new file mode 100644
index 00000000..4859bd22
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.output
@@ -0,0 +1,49 @@
+-- elaborated
+global entry named Model
+type: Theory
+value: sig
+  X : Set
+end
+global entry named Alias
+type: Theory
+value: Model
+global entry named Box
+type: (X : Set) -> (M : Model) -> (Y : Set) -> Set
+value: X => M => Y => sig
+  key : X
+  modelValue : M.X
+  value : Y
+end
+global entry named T
+type: Theory
+value: sig
+  model : Alias
+  boxed : Box Int model String -> Set
+end
+realm named TRealm
+generators: node
+  model = node
+    X = rel []
+  end
+  boxed = rel [a : Box Int [X := TRealm.model.X []] String]
+end
+lowered: flatrealm
+  entities
+    table ℜ.model.X := []
+    table ℜ.boxed := [
+      .a.key : Int,
+      .a.modelValue : ℜ.model.X,
+      .a.value : String
+    ]
+  end
+  rules
+    enforced ℜ.model.X.foreignKey := ℜ.model.X [] ⊢ ⊤
+    enforced ℜ.boxed.foreignKey a.key a.modelValue a.value := ℜ.boxed [
+      .a.key ↦ a.key,
+      .a.modelValue ↦ a.modelValue,
+      .a.value ↦ a.value
+    ] ⊢ a.modelValue ∈ ℜ.model.X []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Alias.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Alias.ts
new file mode 100644
index 00000000..6ae9a74d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Alias.ts
@@ -0,0 +1,6 @@
+import * as runtime from "@coln-project/runtime";
+import * as Model from "./Model.ts";
+
+export type View = Model.View;
+
+export type Transaction = Model.Transaction;
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Model.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Model.ts
new file mode 100644
index 00000000..f8c182ce
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/Model.ts
@@ -0,0 +1,9 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/T.ts
new file mode 100644
index 00000000..69c4549d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+import * as Model from "./Model.ts";
+import * as Alias from "./Alias.ts";
+
+export interface View {
+  model: Model.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  model: Model.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.json
new file mode 100644
index 00000000..9dd8ca0f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["model"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["key"]],"type":{"tag":"builtin","type":"builtinInt"}},{"path":[["a"],["modelValue"]],"type":{"tag":"rowId","path":[["TRealm"],["model"],["X"]]}},{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["model"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["key"]],[["a"],["modelValue"]],[["a"],["value"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"},{"tag":"rowId","path":[["TRealm"],["model"],["X"]]},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.ts
new file mode 100644
index 00000000..7d9eae22
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.ts
@@ -0,0 +1,48 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as Model from "./Model.ts";
+import * as Alias from "./Alias.ts";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      model: { X: (new runtime.RowIdSet.View(store, "TRealm.model.X", [])) },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      model: {
+        X: (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.model.X",
+          [],
+          transaction
+        ))
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.coln
new file mode 100644
index 00000000..3f01d3a5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.coln
@@ -0,0 +1,18 @@
+def PointAt (X : Set) (x : X) : Set := sig
+end
+
+def Box (X : Set) (x : X) (E : X -> Set) (f : (x : X) -> E x) (p : PointAt (E x) (f x)) : Set := sig
+  image : E x
+end
+
+theory T := sig
+  Key : Set
+  key : Key
+  E : Key -> Set
+  f : (x : Key) -> E x
+  point : PointAt (E key) (f key)
+  boxed : Box Key key E f point -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.output b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.output
new file mode 100644
index 00000000..062d6148
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.output
@@ -0,0 +1,63 @@
+-- elaborated
+global entry named PointAt
+type: (X : Set) -> (x : X) -> Set
+value: X => x => sig
+end
+global entry named Box
+type: (X : Set) -> (x : X) -> (E : X -> Set) -> (f : (x : X) -> E x) -> (p : PointAt (E x) (f x)) -> Set
+value: X => x => E => f => p => sig
+  image : E x
+end
+global entry named T
+type: Theory
+value: sig
+  Key : Set
+  key : Key
+  E : Key -> Set
+  f : (x : Key) -> E x
+  point : PointAt (E key) (f key)
+  boxed : Box Key key E f point -> Set
+end
+realm named TRealm
+generators: node
+  Key = rel []
+  key = (fun [] -> TRealm.Key [])
+  E = rel [a : TRealm.Key []]
+  f = (fun [x : TRealm.Key []] -> TRealm.E [a := x])
+  point = (fun [] -> PointAt (TRealm.E [a := TRealm.key []]) (TRealm.f [
+    x := TRealm.key []
+  ]))
+  boxed = rel [
+    a : Box (TRealm.Key []) (TRealm.key []) (a => TRealm.E [
+      a := a
+    ]) (x => TRealm.f [x := x]) (TRealm.point [])
+  ]
+end
+lowered: flatrealm
+  entities
+    table ℜ.Key := []
+    table ℜ.key := [.a : ℜ.Key] primarykey []
+    table ℜ.E := [.a : ℜ.Key]
+    table ℜ.f := [.x : ℜ.Key, .a : ℜ.E] primarykey [.x]
+    table ℜ.point := [] primarykey []
+    table ℜ.boxed := [.a.image : ℜ.E]
+  end
+  rules
+    enforced ℜ.Key.foreignKey := ℜ.Key [] ⊢ ⊤
+    enforced ℜ.key.foreignKey a := ℜ.key [.a ↦ a] ⊢ a ∈ ℜ.Key []
+    monitored ℜ.key.total := ⊤ ⊢ ℜ.key []
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.Key []
+    enforced ℜ.f.foreignKey x a := ℜ.f [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.Key [] ∧ a ∈ ℜ.E [.a ↦ x]
+    monitored ℜ.f.total x := x ∈ ℜ.Key [] ⊢ ℜ.f [.x ↦ x]
+    enforced ℜ.point.foreignKey := ℜ.point [] ⊢ ⊤
+    monitored ℜ.point.total := ⊤ ⊢ ℜ.point []
+    enforced ℜ.boxed.foreignKey a.image a.image.a := ℜ.boxed [
+      .a.image ↦ a.image
+    ] ∧ ℜ.key [.a ↦ a.image.a] ⊢ a.image ∈ ℜ.E [.a ↦ a.image.a]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/T.ts
new file mode 100644
index 00000000..5ce3d59f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/T.ts
@@ -0,0 +1,19 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  Key: runtime.ColnSet.View;
+  key: runtime.ColnRef.View;
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+  point: PointAt.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  Key: runtime.ColnSet.Transaction;
+  key: runtime.ColnRef.Transaction;
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  point: PointAt.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.json
new file mode 100644
index 00000000..1506154a
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["Key"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["key"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}}],"primaryKey":[]}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}}],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["point"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":[]}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["image"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["Key"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["key"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["key"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["key"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["key"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]},{"tag":"rowId","path":[["TRealm"],["E"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["point"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["point"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["point"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["point"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["image"]],[["a"],["image"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["key"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":0},"values":[{"column":0,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.ts
new file mode 100644
index 00000000..2fa0ac50
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.ts
@@ -0,0 +1,80 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      Key: (new runtime.RowIdSet.View(store, "TRealm.Key", [])),
+      key: (new runtime.TableCellRef.View(store, "TRealm.key", [])),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      f: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [x]));
+      },
+      point: (new runtime.TableCellRef.View(store, "TRealm.point", [])),
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      Key: (new runtime.RowIdSet.Transaction(
+        store,
+        "TRealm.Key",
+        [],
+        transaction
+      )),
+      key: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.key",
+        [],
+        transaction
+      )),
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      f: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [x],
+          transaction
+        ));
+      },
+      point: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.point",
+        [],
+        transaction
+      )),
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.coln
new file mode 100644
index 00000000..1a335a43
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.coln
@@ -0,0 +1,20 @@
+theory PointOf (X : Set) := sig
+  point : X
+end
+
+def Key : Set := sig
+  rank : Int
+end
+
+def Box (X : Set) (p : PointOf X) (Y : Set) : Set := sig
+  key : X
+  value : Y
+end
+
+theory T := sig
+  pointed : PointOf Key
+  boxed : Box Key pointed String -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.output b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.output
new file mode 100644
index 00000000..d8e8cc18
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named PointOf
+type: (X : Set) -> Theory
+value: X => sig
+  point : X
+end
+global entry named Key
+type: Set
+value: sig
+  rank : Int
+end
+global entry named Box
+type: (X : Set) -> (p : PointOf X) -> (Y : Set) -> Set
+value: X => p => Y => sig
+  key : X
+  value : Y
+end
+global entry named T
+type: Theory
+value: sig
+  pointed : PointOf Key
+  boxed : Box Key pointed String -> Set
+end
+realm named TRealm
+generators: node
+  pointed = node
+    point = (fun [] -> Key)
+  end
+  boxed = rel [a : Box Key [point := TRealm.pointed.point []] String]
+end
+lowered: flatrealm
+  entities
+    table ℜ.pointed.point := [.a.rank : Int] primarykey []
+    table ℜ.boxed := [.a.key.rank : Int, .a.value : String]
+  end
+  rules
+    enforced ℜ.pointed.point.foreignKey a.rank := ℜ.pointed.point [
+      .a.rank ↦ a.rank
+    ] ⊢ ⊤
+    monitored ℜ.pointed.point.total := ⊤ ⊢ ℜ.pointed.point []
+    enforced ℜ.boxed.foreignKey a.key.rank a.value := ℜ.boxed [
+      .a.key.rank ↦ a.key.rank,
+      .a.value ↦ a.value
+    ] ⊢ ⊤
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/PointOf.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/PointOf.ts
new file mode 100644
index 00000000..09e73697
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/PointOf.ts
@@ -0,0 +1,9 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  point: runtime.ColnRef.View;
+}
+
+export interface Transaction extends View {
+  point: runtime.ColnRef.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/T.ts
new file mode 100644
index 00000000..ca51d3cf
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/T.ts
@@ -0,0 +1,12 @@
+import * as runtime from "@coln-project/runtime";
+import * as PointOf from "./PointOf.ts";
+
+export interface View {
+  pointed: PointOf.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  pointed: PointOf.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.json
new file mode 100644
index 00000000..e10a083f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["pointed"],["point"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["rank"]],"type":{"tag":"builtin","type":"builtinInt"}}],"primaryKey":[]}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["key"],["rank"]],"type":{"tag":"builtin","type":"builtinInt"}},{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["pointed"],["point"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["rank"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["pointed"],["point"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[]}},{"path":[["TRealm"],["pointed"],["point"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["pointed"],["point"]],"rowId":null,"values":[]}}]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["key"],["rank"]],[["a"],["value"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.ts
new file mode 100644
index 00000000..c2681fbf
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.ts
@@ -0,0 +1,53 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as PointOf from "./PointOf.ts";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      pointed: {
+        point: (new runtime.TableCellRef.View(
+          store,
+          "TRealm.pointed.point",
+          []
+        ))
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      pointed: {
+        point: (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.pointed.point",
+          [],
+          transaction
+        ))
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-function.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-function.coln
new file mode 100644
index 00000000..1ee091c7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-function.coln
@@ -0,0 +1,13 @@
+def Box (X : Set) (f : X -> X) (Y : Set) : Set := sig
+  key : X
+  value : Y
+end
+
+theory T := sig
+  Key : Set
+  f : Key -> Key
+  boxed : Box Key f String -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-function.output b/packages/coln-compiler/test/golden/basic-ir/param-record-function.output
new file mode 100644
index 00000000..89d9b80d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-function.output
@@ -0,0 +1,41 @@
+-- elaborated
+global entry named Box
+type: (X : Set) -> (f : X -> X) -> (Y : Set) -> Set
+value: X => f => Y => sig
+  key : X
+  value : Y
+end
+global entry named T
+type: Theory
+value: sig
+  Key : Set
+  f : Key -> Key
+  boxed : Box Key f String -> Set
+end
+realm named TRealm
+generators: node
+  Key = rel []
+  f = (fun [a : TRealm.Key []] -> TRealm.Key [])
+  boxed = rel [a : Box (TRealm.Key []) (a => TRealm.f [a := a]) String]
+end
+lowered: flatrealm
+  entities
+    table ℜ.Key := []
+    table ℜ.f := [.a : ℜ.Key, .b : ℜ.Key] primarykey [.a]
+    table ℜ.boxed := [.a.key : ℜ.Key, .a.value : String]
+  end
+  rules
+    enforced ℜ.Key.foreignKey := ℜ.Key [] ⊢ ⊤
+    enforced ℜ.f.foreignKey a b := ℜ.f [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.Key [] ∧ b ∈ ℜ.Key []
+    monitored ℜ.f.total a := a ∈ ℜ.Key [] ⊢ ℜ.f [.a ↦ a]
+    enforced ℜ.boxed.foreignKey a.key a.value := ℜ.boxed [
+      .a.key ↦ a.key,
+      .a.value ↦ a.value
+    ] ⊢ a.key ∈ ℜ.Key []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/T.ts
new file mode 100644
index 00000000..86dd4380
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  Key: runtime.ColnSet.View;
+  f: (x: runtime.Value) => runtime.ColnRef.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  Key: runtime.ColnSet.Transaction;
+  f: (x: runtime.Value) => runtime.ColnRef.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.json
new file mode 100644
index 00000000..8de3d7fe
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["Key"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["f"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["key"]],"type":{"tag":"rowId","path":[["TRealm"],["Key"]]}},{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["Key"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["f"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]},{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["f"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["f"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["key"]],[["a"],["value"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["Key"]]},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Key"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.ts
new file mode 100644
index 00000000..822be1ed
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.ts
@@ -0,0 +1,55 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      Key: (new runtime.RowIdSet.View(store, "TRealm.Key", [])),
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.f", [a]));
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      Key: (new runtime.RowIdSet.Transaction(
+        store,
+        "TRealm.Key",
+        [],
+        transaction
+      )),
+      f: (a: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.f",
+          [a],
+          transaction
+        ));
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-model.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-model.coln
index 69bf902a..8c10ef45 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-model.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-model.coln
@@ -2,10 +2,6 @@ theory Model := sig
   X : Set
 end
 
-def Payload : Set := sig
-  name : String
-end
-
 def Box (M : Model) (Y : Set) : Set := sig
   modelValue : M.X
   value : Y
@@ -13,7 +9,7 @@ end
 
 theory T := sig
   model : Model
-  boxed : Box model Payload -> Set
+  boxed : Box model String -> Set
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-model.output b/packages/coln-compiler/test/golden/basic-ir/param-record-model.output
index 0f4b510f..e149916e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-model.output
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-model.output
@@ -4,11 +4,6 @@ type: Theory
 value: sig
   X : Set
 end
-global entry named Payload
-type: Set
-value: sig
-  name : String
-end
 global entry named Box
 type: (M : Model) -> (Y : Set) -> Set
 value: M => Y => sig
@@ -19,25 +14,25 @@ global entry named T
 type: Theory
 value: sig
   model : Model
-  boxed : Box model Payload -> Set
+  boxed : Box model String -> Set
 end
 realm named TRealm
 generators: node
   model = node
     X = rel []
   end
-  boxed = rel [a : Box [X := TRealm.model.X []] Payload]
+  boxed = rel [a : Box [X := TRealm.model.X []] String]
 end
 lowered: flatrealm
   entities
     table ℜ.model.X := []
-    table ℜ.boxed := [.a.modelValue : ℜ.model.X, .a.value.name : String]
+    table ℜ.boxed := [.a.modelValue : ℜ.model.X, .a.value : String]
   end
   rules
     enforced ℜ.model.X.foreignKey := ℜ.model.X [] ⊢ ⊤
-    enforced ℜ.boxed.foreignKey a.modelValue a.value.name := ℜ.boxed [
+    enforced ℜ.boxed.foreignKey a.modelValue a.value := ℜ.boxed [
       .a.modelValue ↦ a.modelValue,
-      .a.value.name ↦ a.value.name
+      .a.value ↦ a.value
     ] ⊢ a.modelValue ∈ ℜ.model.X []
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.json
index 3857e386..b763f87f 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["model"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["modelValue"]],"type":{"tag":"rowId","path":[["TRealm"],["model"],["X"]]}},{"path":[["a"],["value"],["name"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["model"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["modelValue"]],[["a"],["value"],["name"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["model"],["X"]]},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["model"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["modelValue"]],"type":{"tag":"rowId","path":[["TRealm"],["model"],["X"]]}},{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["model"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["modelValue"]],[["a"],["value"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["model"],["X"]]},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["model"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.coln
index bced53d0..e2a2e6a2 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.coln
@@ -4,13 +4,11 @@ end
 
 def Nested (X : Set) : Set := sig
   inner : Box X
-  sibling : X
 end
 
 theory T := sig
   X : Set
   nested : Nested X -> Set
-  selected : Nested X -> X
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.output b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.output
index 43af4248..767977eb 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.output
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.output
@@ -8,46 +8,28 @@ global entry named Nested
 type: (X : Set) -> Set
 value: X => sig
   inner : Box X
-  sibling : X
 end
 global entry named T
 type: Theory
 value: sig
   X : Set
   nested : Nested X -> Set
-  selected : Nested X -> X
 end
 realm named TRealm
 generators: node
   X = rel []
   nested = rel [a : Nested (TRealm.X [])]
-  selected = (fun [a : Nested (TRealm.X [])] -> TRealm.X [])
 end
 lowered: flatrealm
   entities
     table ℜ.X := []
-    table ℜ.nested := [.a.inner.value : ℜ.X, .a.sibling : ℜ.X]
-    table ℜ.selected := [
-      .a.inner.value : ℜ.X,
-      .a.sibling : ℜ.X,
-      .b : ℜ.X
-    ] primarykey [.a.sibling, .a.inner.value]
+    table ℜ.nested := [.a.inner.value : ℜ.X]
   end
   rules
     enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
-    enforced ℜ.nested.foreignKey a.inner.value a.sibling := ℜ.nested [
-      .a.inner.value ↦ a.inner.value,
-      .a.sibling ↦ a.sibling
-    ] ⊢ a.inner.value ∈ ℜ.X [] ∧ a.sibling ∈ ℜ.X []
-    enforced ℜ.selected.foreignKey a.inner.value a.sibling b := ℜ.selected [
-      .a.inner.value ↦ a.inner.value,
-      .a.sibling ↦ a.sibling,
-      .b ↦ b
-    ] ⊢ a.inner.value ∈ ℜ.X [] ∧ a.sibling ∈ ℜ.X [] ∧ b ∈ ℜ.X []
-    monitored ℜ.selected.total a.inner.value a.sibling := a.inner.value ∈ ℜ.X [] ∧ a.sibling ∈ ℜ.X [] ⊢ ℜ.selected [
-      .a.inner.value ↦ a.inner.value,
-      .a.sibling ↦ a.sibling
-    ]
+    enforced ℜ.nested.foreignKey a.inner.value := ℜ.nested [
+      .a.inner.value ↦ a.inner.value
+    ] ⊢ a.inner.value ∈ ℜ.X []
   end
 end
 
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/T.ts
index ec08ec40..1a7337de 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/T.ts
@@ -3,11 +3,9 @@ import * as runtime from "@coln-project/runtime";
 export interface View {
   X: runtime.ColnSet.View;
   nested: (x: runtime.Value) => runtime.ColnSet.View;
-  selected: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   X: runtime.ColnSet.Transaction;
   nested: (x: runtime.Value) => runtime.ColnSet.Transaction;
-  selected: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.json
index 80357910..d9534daf 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["nested"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["inner"],["value"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["sibling"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["selected"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["inner"],["value"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["sibling"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":[[["a"],["sibling"]],[["a"],["inner"],["value"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["nested"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["inner"],["value"]],[["a"],["sibling"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nested"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["selected"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["inner"],["value"]],[["a"],["sibling"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["selected"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}}]}},{"path":[["TRealm"],["selected"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"],["inner"],["value"]],[["a"],["sibling"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["selected"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["nested"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["inner"],["value"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["nested"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["inner"],["value"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nested"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts
index 5870a915..6e14e4ed 100644
--- a/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts
@@ -11,9 +11,6 @@ export class View {
       X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
       nested: (a: runtime.Value) => {
         return (new runtime.RowIdSet.View(store, "TRealm.nested", [a]));
-      },
-      selected: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.selected", [a]));
       }
     };
   }
@@ -36,14 +33,6 @@ export class Transaction extends View {
           [a],
           transaction
         ));
-      },
-      selected: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.Transaction(
-          store,
-          "TRealm.selected",
-          [a],
-          transaction
-        ));
       }
     };
   }
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.coln
new file mode 100644
index 00000000..ea5046de
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.coln
@@ -0,0 +1,12 @@
+def Shadowed (X : Set) (X : Set) : Set := sig
+  value : X
+end
+
+theory T := sig
+  A : Set
+  B : Set
+  shadowed : Shadowed A B -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.output b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.output
new file mode 100644
index 00000000..3508fd40
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.output
@@ -0,0 +1,35 @@
+-- elaborated
+global entry named Shadowed
+type: (X : Set) -> (X : Set) -> Set
+value: X => X => sig
+  value : X
+end
+global entry named T
+type: Theory
+value: sig
+  A : Set
+  B : Set
+  shadowed : Shadowed A B -> Set
+end
+realm named TRealm
+generators: node
+  A = rel []
+  B = rel []
+  shadowed = rel [a : Shadowed (TRealm.A []) (TRealm.B [])]
+end
+lowered: flatrealm
+  entities
+    table ℜ.A := []
+    table ℜ.B := []
+    table ℜ.shadowed := [.a.value : ℜ.B]
+  end
+  rules
+    enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
+    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
+    enforced ℜ.shadowed.foreignKey a.value := ℜ.shadowed [
+      .a.value ↦ a.value
+    ] ⊢ a.value ∈ ℜ.B []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/T.ts
new file mode 100644
index 00000000..3c259686
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  A: runtime.ColnSet.View;
+  B: runtime.ColnSet.View;
+  shadowed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  A: runtime.ColnSet.Transaction;
+  B: runtime.ColnSet.Transaction;
+  shadowed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.json
new file mode 100644
index 00000000..d63a2d00
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["shadowed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["value"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["shadowed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["value"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["shadowed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.ts
new file mode 100644
index 00000000..1da46dc5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.ts
@@ -0,0 +1,41 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
+      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
+      shadowed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.shadowed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
+      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
+      shadowed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.shadowed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.coln
new file mode 100644
index 00000000..2d863e62
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.coln
@@ -0,0 +1,10 @@
+def Box (X : Set) (x : X) (E : X -> Set) : Set := sig
+  value : E x
+end
+
+theory T := sig
+  boxed : (x : Int) -> Box Int x (y => String) -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.output b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.output
new file mode 100644
index 00000000..6d68c872
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.output
@@ -0,0 +1,28 @@
+-- elaborated
+global entry named Box
+type: (X : Set) -> (x : X) -> (E : X -> Set) -> Set
+value: X => x => E => sig
+  value : E x
+end
+global entry named T
+type: Theory
+value: sig
+  boxed : (x : Int) -> Box Int x (y => String) -> Set
+end
+realm named TRealm
+generators: node
+  boxed = rel [x : Int, a : Box Int x (y => String)]
+end
+lowered: flatrealm
+  entities
+    table ℜ.boxed := [.x : Int, .a.value : String]
+  end
+  rules
+    enforced ℜ.boxed.foreignKey x a.value := ℜ.boxed [
+      .x ↦ x,
+      .a.value ↦ a.value
+    ] ⊢ ⊤
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/T.ts
new file mode 100644
index 00000000..be00308c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/T.ts
@@ -0,0 +1,9 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  boxed: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  boxed: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.json
new file mode 100644
index 00000000..39d0d8e8
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"builtin","type":"builtinInt"}},{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinString"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"],["value"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"},{"tag":"builtin","type":"builtinString"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.ts
new file mode 100644
index 00000000..beab66d7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.ts
@@ -0,0 +1,41 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      boxed: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.boxed", [x, a]));
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      boxed: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.boxed",
+            [x, a],
+            transaction
+          ));
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.coln
new file mode 100644
index 00000000..a240d226
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.coln
@@ -0,0 +1,13 @@
+def Cell (X : Set) (Y : Set) (R : X -> Y -> Set) (x : X) (y : Y) : Set := sig
+  entry : R x y
+end
+
+theory T := sig
+  X : Set
+  Y : Set
+  R : X -> Y -> Set
+  cells : (x : X) -> (y : Y) -> Cell X Y R x y -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.output b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.output
new file mode 100644
index 00000000..0fdf01d6
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.output
@@ -0,0 +1,51 @@
+-- elaborated
+global entry named Cell
+type: (X : Set) -> (Y : Set) -> (R : X -> Y -> Set) -> (x : X) -> (y : Y) -> Set
+value: X => Y => R => x => y => sig
+  entry : R x y
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  Y : Set
+  R : X -> Y -> Set
+  cells : (x : X) -> (y : Y) -> Cell X Y R x y -> Set
+end
+realm named TRealm
+generators: node
+  X = rel []
+  Y = rel []
+  R = rel [a : TRealm.X [], b : TRealm.Y []]
+  cells = rel [
+    x : TRealm.X [],
+    y : TRealm.Y [],
+    a : Cell (TRealm.X []) (TRealm.Y []) (a => b => TRealm.R [
+      a := a,
+      b := b
+    ]) x y
+  ]
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.Y := []
+    table ℜ.R := [.a : ℜ.X, .b : ℜ.Y]
+    table ℜ.cells := [.x : ℜ.X, .y : ℜ.Y, .a.entry : ℜ.R]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.Y.foreignKey := ℜ.Y [] ⊢ ⊤
+    enforced ℜ.R.foreignKey a b := ℜ.R [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.X [] ∧ b ∈ ℜ.Y []
+    enforced ℜ.cells.foreignKey x y a.entry := ℜ.cells [
+      .x ↦ x,
+      .y ↦ y,
+      .a.entry ↦ a.entry
+    ] ⊢ x ∈ ℜ.X [] ∧ y ∈ ℜ.Y [] ∧ a.entry ∈ ℜ.R [.a ↦ x, .b ↦ y]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/T.ts
new file mode 100644
index 00000000..56e70124
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  Y: runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  cells: (x: runtime.Value) => (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  Y: runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  cells: (x: runtime.Value) => (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.json
new file mode 100644
index 00000000..1ba8743f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Y"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["Y"]]}}],"primaryKey":null}},{"path":[["TRealm"],["cells"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["y"]],"type":{"tag":"rowId","path":[["TRealm"],["Y"]]}},{"path":[["a"],["entry"]],"type":{"tag":"rowId","path":[["TRealm"],["R"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Y"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["Y"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["cells"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["y"]],[["a"],["entry"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["Y"]]},{"tag":"rowId","path":[["TRealm"],["R"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["cells"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.ts
similarity index 53%
rename from packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.ts
index 984ab33a..593bfdd6 100644
--- a/packages/coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.ts
@@ -9,15 +9,21 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
-      P: (new runtime.RowIdSet.View(store, "TRealm.P", [])),
       Y: (new runtime.RowIdSet.View(store, "TRealm.Y", [])),
-      choose: (a: runtime.Value) => {
+      R: (a: runtime.Value) => {
         return (b: runtime.Value) => {
-          return (new runtime.TableCellRef.View(
-            store,
-            "TRealm.choose",
-            [a, b]
-          ));
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      },
+      cells: (x: runtime.Value) => {
+        return (y: runtime.Value) => {
+          return (a: runtime.Value) => {
+            return (new runtime.RowIdSet.View(
+              store,
+              "TRealm.cells",
+              [x, y, a]
+            ));
+          };
         };
       }
     };
@@ -34,17 +40,28 @@ export class Transaction extends View {
     super(store);
     this.root = {
       X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
-      P: (new runtime.RowIdSet.Transaction(store, "TRealm.P", [], transaction)),
       Y: (new runtime.RowIdSet.Transaction(store, "TRealm.Y", [], transaction)),
-      choose: (a: runtime.Value) => {
+      R: (a: runtime.Value) => {
         return (b: runtime.Value) => {
-          return (new runtime.TableCellRef.Transaction(
+          return (new runtime.RowIdSet.Transaction(
             store,
-            "TRealm.choose",
+            "TRealm.R",
             [a, b],
             transaction
           ));
         };
+      },
+      cells: (x: runtime.Value) => {
+        return (y: runtime.Value) => {
+          return (a: runtime.Value) => {
+            return (new runtime.RowIdSet.Transaction(
+              store,
+              "TRealm.cells",
+              [x, y, a],
+              transaction
+            ));
+          };
+        };
       }
     };
   }
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.coln
new file mode 100644
index 00000000..4f435691
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.coln
@@ -0,0 +1,13 @@
+def Slice (Y : Set) (S : Y -> Set) (y : Y) : Set := sig
+  entry : S y
+end
+
+theory T := sig
+  X : Set
+  Y : Set
+  R : X -> Y -> Set
+  slices : (x : X) -> (y : Y) -> Slice Y (R x) y -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.output b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.output
new file mode 100644
index 00000000..dbf7f62e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named Slice
+type: (Y : Set) -> (S : Y -> Set) -> (y : Y) -> Set
+value: Y => S => y => sig
+  entry : S y
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  Y : Set
+  R : X -> Y -> Set
+  slices : (x : X) -> (y : Y) -> Slice Y (R x) y -> Set
+end
+realm named TRealm
+generators: node
+  X = rel []
+  Y = rel []
+  R = rel [a : TRealm.X [], b : TRealm.Y []]
+  slices = rel [
+    x : TRealm.X [],
+    y : TRealm.Y [],
+    a : Slice (TRealm.Y []) (b => TRealm.R [a := x, b := b]) y
+  ]
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.Y := []
+    table ℜ.R := [.a : ℜ.X, .b : ℜ.Y]
+    table ℜ.slices := [.x : ℜ.X, .y : ℜ.Y, .a.entry : ℜ.R]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.Y.foreignKey := ℜ.Y [] ⊢ ⊤
+    enforced ℜ.R.foreignKey a b := ℜ.R [
+      .a ↦ a,
+      .b ↦ b
+    ] ⊢ a ∈ ℜ.X [] ∧ b ∈ ℜ.Y []
+    enforced ℜ.slices.foreignKey x y a.entry := ℜ.slices [
+      .x ↦ x,
+      .y ↦ y,
+      .a.entry ↦ a.entry
+    ] ⊢ x ∈ ℜ.X [] ∧ y ∈ ℜ.Y [] ∧ a.entry ∈ ℜ.R [.a ↦ x, .b ↦ y]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/T.ts
new file mode 100644
index 00000000..4862097f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  Y: runtime.ColnSet.View;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+  slices: (x: runtime.Value) => (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  Y: runtime.ColnSet.Transaction;
+  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+  slices: (x: runtime.Value) => (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.json
new file mode 100644
index 00000000..b8e6992a
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Y"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["Y"]]}}],"primaryKey":null}},{"path":[["TRealm"],["slices"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["y"]],"type":{"tag":"rowId","path":[["TRealm"],["Y"]]}},{"path":[["a"],["entry"]],"type":{"tag":"rowId","path":[["TRealm"],["R"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Y"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["Y"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["slices"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["y"]],[["a"],["entry"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["Y"]]},{"tag":"rowId","path":[["TRealm"],["R"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["slices"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Y"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.ts
new file mode 100644
index 00000000..44a9a5a3
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.ts
@@ -0,0 +1,68 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      Y: (new runtime.RowIdSet.View(store, "TRealm.Y", [])),
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.R", [a, b]));
+        };
+      },
+      slices: (x: runtime.Value) => {
+        return (y: runtime.Value) => {
+          return (a: runtime.Value) => {
+            return (new runtime.RowIdSet.View(
+              store,
+              "TRealm.slices",
+              [x, y, a]
+            ));
+          };
+        };
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      Y: (new runtime.RowIdSet.Transaction(store, "TRealm.Y", [], transaction)),
+      R: (a: runtime.Value) => {
+        return (b: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.R",
+            [a, b],
+            transaction
+          ));
+        };
+      },
+      slices: (x: runtime.Value) => {
+        return (y: runtime.Value) => {
+          return (a: runtime.Value) => {
+            return (new runtime.RowIdSet.Transaction(
+              store,
+              "TRealm.slices",
+              [x, y, a],
+              transaction
+            ));
+          };
+        };
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.coln
new file mode 100644
index 00000000..ddc76a4c
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.coln
@@ -0,0 +1,12 @@
+def Evidence (X : Set) (P : X -> Prop) (x : X) : Set := sig
+  proof : P x
+end
+
+theory T := sig
+  X : Set
+  P : X -> Prop
+  evidence : (x : X) -> Evidence X P x -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.output b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.output
new file mode 100644
index 00000000..b4304465
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.output
@@ -0,0 +1,39 @@
+-- elaborated
+global entry named Evidence
+type: (X : Set) -> (P : X -> Prop) -> (x : X) -> Set
+value: X => P => x => sig
+  proof : P x
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  P : X -> Prop
+  evidence : (x : X) -> Evidence X P x -> Set
+end
+realm named TRealm
+generators: node
+  X = rel []
+  P = rel [a : TRealm.X []]
+  evidence = rel [
+    x : TRealm.X [],
+    a : Evidence (TRealm.X []) (a => TRealm.P [a := a]) x
+  ]
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.P := [.a : ℜ.X]
+    table ℜ.evidence := [.x : ℜ.X, .a.proof : ℜ.P]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.P.foreignKey a := ℜ.P [.a ↦ a] ⊢ a ∈ ℜ.X []
+    enforced ℜ.evidence.foreignKey x a.proof := ℜ.evidence [
+      .x ↦ x,
+      .a.proof ↦ a.proof
+    ] ⊢ x ∈ ℜ.X [] ∧ a.proof ∈ ℜ.P [.a ↦ x]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/T.ts
new file mode 100644
index 00000000..b91204c6
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/T.ts
@@ -0,0 +1,13 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  P: (x: runtime.Value) => runtime.ColnSet.View;
+  evidence: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  P: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  evidence: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..6faf9b27
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["evidence"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["proof"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["evidence"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"],["proof"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["evidence"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.ts
similarity index 52%
rename from packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.ts
index 23c86773..354ac7b5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.ts
@@ -9,11 +9,12 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
-      P: (new runtime.RowIdSet.View(store, "TRealm.P", [])),
-      Q: (new runtime.RowIdSet.View(store, "TRealm.Q", [])),
-      f: (a: runtime.Value) => {
-        return (b: runtime.Value) => {
-          return (new runtime.TableCellRef.View(store, "TRealm.f", [a, b]));
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.P", [a]));
+      },
+      evidence: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.evidence", [x, a]));
         };
       }
     };
@@ -30,14 +31,20 @@ export class Transaction extends View {
     super(store);
     this.root = {
       X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
-      P: (new runtime.RowIdSet.Transaction(store, "TRealm.P", [], transaction)),
-      Q: (new runtime.RowIdSet.Transaction(store, "TRealm.Q", [], transaction)),
-      f: (a: runtime.Value) => {
-        return (b: runtime.Value) => {
-          return (new runtime.TableCellRef.Transaction(
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.P",
+          [a],
+          transaction
+        ));
+      },
+      evidence: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
             store,
-            "TRealm.f",
-            [a, b],
+            "TRealm.evidence",
+            [x, a],
             transaction
           ));
         };
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.coln b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.coln
new file mode 100644
index 00000000..863b1cef
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.coln
@@ -0,0 +1,11 @@
+def Box (X : Set) (E : X -> Set) : Set := sig
+  value : X
+end
+
+theory T := sig
+  E : Int -> Set
+  boxed : Box Int E -> Set
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.output b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.output
new file mode 100644
index 00000000..cb079a8b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.output
@@ -0,0 +1,29 @@
+-- elaborated
+global entry named Box
+type: (X : Set) -> (E : X -> Set) -> Set
+value: X => E => sig
+  value : X
+end
+global entry named T
+type: Theory
+value: sig
+  E : Int -> Set
+  boxed : Box Int E -> Set
+end
+realm named TRealm
+generators: node
+  E = rel [a : Int]
+  boxed = rel [a : Box Int (a => TRealm.E [a := a])]
+end
+lowered: flatrealm
+  entities
+    table ℜ.E := [.a : Int]
+    table ℜ.boxed := [.a.value : Int]
+  end
+  rules
+    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ ⊤
+    enforced ℜ.boxed.foreignKey a.value := ℜ.boxed [.a.value ↦ a.value] ⊢ ⊤
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/T.ts
new file mode 100644
index 00000000..71faf34d
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  E: (x: runtime.Value) => runtime.ColnSet.View;
+  boxed: (x: runtime.Value) => runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  boxed: (x: runtime.Value) => runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.json
new file mode 100644
index 00000000..33bf4c2b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"builtin","type":"builtinInt"}}],"primaryKey":null}},{"path":[["TRealm"],["boxed"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinInt"}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[]}},{"path":[["TRealm"],["boxed"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["value"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["boxed"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.ts
new file mode 100644
index 00000000..8c561f59
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.ts
@@ -0,0 +1,48 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.boxed", [a]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      E: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.E",
+          [a],
+          transaction
+        ));
+      },
+      boxed: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.boxed",
+          [a],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.coln
similarity index 86%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.coln
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.coln
index d3ff28bd..9768bd4f 100644
--- a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.coln
@@ -8,7 +8,6 @@ end
 theory T := sig
   X : Set
   Accepted : EqualTriple X -> Prop
-  select : EqualTriple X -> X
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.output
similarity index 50%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.output
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.output
index 82de7ce1..7f904066 100644
--- a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.output
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.output
@@ -12,24 +12,16 @@ type: Theory
 value: sig
   X : Set
   Accepted : EqualTriple X -> Prop
-  select : EqualTriple X -> X
 end
 realm named TRealm
 generators: node
   X = rel []
   Accepted = rel [a : EqualTriple (TRealm.X [])]
-  select = (fun [a : EqualTriple (TRealm.X [])] -> TRealm.X [])
 end
 lowered: flatrealm
   entities
     table ℜ.X := []
     table ℜ.Accepted := [.a.first : ℜ.X, .a.second : ℜ.X, .a.trailing : ℜ.X]
-    table ℜ.select := [
-      .a.first : ℜ.X,
-      .a.second : ℜ.X,
-      .a.trailing : ℜ.X,
-      .b : ℜ.X
-    ] primarykey [.a.first, .a.second, .a.trailing]
   end
   rules
     enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
@@ -38,17 +30,6 @@ lowered: flatrealm
       .a.second ↦ a.second,
       .a.trailing ↦ a.trailing
     ] ⊢ a.first ∈ ℜ.X [] ∧ a.second ∈ ℜ.X [] ∧ a.first = a.second ∧ a.trailing ∈ ℜ.X []
-    enforced ℜ.select.foreignKey a.first a.second a.trailing b := ℜ.select [
-      .a.first ↦ a.first,
-      .a.second ↦ a.second,
-      .a.trailing ↦ a.trailing,
-      .b ↦ b
-    ] ⊢ a.first ∈ ℜ.X [] ∧ a.second ∈ ℜ.X [] ∧ a.first = a.second ∧ a.trailing ∈ ℜ.X [] ∧ b ∈ ℜ.X []
-    monitored ℜ.select.total a.first a.second a.trailing := a.first ∈ ℜ.X [] ∧ a.second ∈ ℜ.X [] ∧ a.first = a.second ∧ a.trailing ∈ ℜ.X [] ⊢ ℜ.select [
-      .a.first ↦ a.first,
-      .a.second ↦ a.second,
-      .a.trailing ↦ a.trailing
-    ]
   end
 end
 
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/T.ts
similarity index 72%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/T.ts
index c2b18964..69069613 100644
--- a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/T.ts
@@ -3,11 +3,9 @@ import * as runtime from "@coln-project/runtime";
 export interface View {
   X: runtime.ColnSet.View;
   Accepted: (x: runtime.Value) => runtime.ColnSet.View;
-  select: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   X: runtime.ColnSet.Transaction;
   Accepted: (x: runtime.Value) => runtime.ColnSet.Transaction;
-  select: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.json
new file mode 100644
index 00000000..f39628a3
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Accepted"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["first"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["second"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["trailing"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Accepted"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["first"]],[["a"],["second"]],[["a"],["trailing"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Accepted"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":1}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.ts
similarity index 74%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.ts
index 91ed30e4..14a1cbf8 100644
--- a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.ts
@@ -11,9 +11,6 @@ export class View {
       X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
       Accepted: (a: runtime.Value) => {
         return (new runtime.RowIdSet.View(store, "TRealm.Accepted", [a]));
-      },
-      select: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.select", [a]));
       }
     };
   }
@@ -36,14 +33,6 @@ export class Transaction extends View {
           [a],
           transaction
         ));
-      },
-      select: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.Transaction(
-          store,
-          "TRealm.select",
-          [a],
-          transaction
-        ));
       }
     };
   }
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.coln
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.coln
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.coln
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.output
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.output
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.output
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/T.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/T.ts
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/T.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.json
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/TRealm.json
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.json
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.ts
similarity index 100%
rename from packages/coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/TRealm.ts
rename to packages/coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.ts
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.coln
new file mode 100644
index 00000000..7c7a6de9
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.coln
@@ -0,0 +1,16 @@
+def Evidence (X : Set) (actual : X) (expected : X) : Set := sig
+  proof : actual = expected
+end
+
+def Result (X : Set) (expected : X) : Set := sig
+  actual : X
+  evidence : Evidence X actual expected
+end
+
+theory T := sig
+  X : Set
+  result : (expected : X) -> Result X expected
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.output
new file mode 100644
index 00000000..e7a8ead7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.output
@@ -0,0 +1,41 @@
+-- elaborated
+global entry named Evidence
+type: (X : Set) -> (actual : X) -> (expected : X) -> Set
+value: X => actual => expected => sig
+  proof : actual = expected
+end
+global entry named Result
+type: (X : Set) -> (expected : X) -> Set
+value: X => expected => sig
+  actual : X
+  evidence : Evidence X actual expected
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  result : (expected : X) -> Result X expected
+end
+realm named TRealm
+generators: node
+  X = rel []
+  result = (fun [expected : TRealm.X []] -> Result (TRealm.X []) expected)
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.result := [.expected : ℜ.X, .a.actual : ℜ.X] primarykey [.expected]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.result.foreignKey expected a.actual := ℜ.result [
+      .expected ↦ expected,
+      .a.actual ↦ a.actual
+    ] ⊢ expected ∈ ℜ.X [] ∧ a.actual ∈ ℜ.X [] ∧ a.actual = expected
+    monitored ℜ.result.total expected := expected ∈ ℜ.X [] ⊢ ℜ.result [
+      .expected ↦ expected
+    ]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/T.ts
new file mode 100644
index 00000000..4b0bc9f1
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  result: (x: runtime.Value) => Result.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  result: (x: runtime.Value) => Result.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.json
new file mode 100644
index 00000000..ae9c23bb
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["result"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["expected"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["actual"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":[[["expected"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["result"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["expected"]],[["a"],["actual"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["result"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":1},"right":{"tag":"var","index":0}}]}},{"path":[["TRealm"],["result"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["expected"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["result"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.ts
new file mode 100644
index 00000000..37aca1f8
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.ts
@@ -0,0 +1,43 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      result: (expected: runtime.Value) => {
+        return (new runtime.TableCellRef.View(
+          store,
+          "TRealm.result",
+          [expected]
+        ));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      result: (expected: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.result",
+          [expected],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.coln
new file mode 100644
index 00000000..9c9d3a52
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.coln
@@ -0,0 +1,16 @@
+def Evidence (P : Prop) : Set := sig
+  proof : P
+end
+
+def Package (P : Int -> Prop) : Set := sig
+  value : Int
+  evidence : Evidence (P value)
+end
+
+theory T := sig
+  P : Int -> Prop
+  package : Package P
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.output
new file mode 100644
index 00000000..102b8740
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.output
@@ -0,0 +1,39 @@
+-- elaborated
+global entry named Evidence
+type: (P : Prop) -> Set
+value: P => sig
+  proof : P
+end
+global entry named Package
+type: (P : Int -> Prop) -> Set
+value: P => sig
+  value : Int
+  evidence : Evidence (P value)
+end
+global entry named T
+type: Theory
+value: sig
+  P : Int -> Prop
+  package : Package P
+end
+realm named TRealm
+generators: node
+  P = rel [a : Int]
+  package = (fun [] -> Package (a => TRealm.P [a := a]))
+end
+lowered: flatrealm
+  entities
+    table ℜ.P := [.a : Int]
+    table ℜ.package := [.a.value : Int, .a.evidence.proof : ℜ.P] primarykey []
+  end
+  rules
+    enforced ℜ.P.foreignKey a := ℜ.P [.a ↦ a] ⊢ ⊤
+    enforced ℜ.package.foreignKey a.value a.evidence.proof := ℜ.package [
+      .a.value ↦ a.value,
+      .a.evidence.proof ↦ a.evidence.proof
+    ] ⊢ a.evidence.proof ∈ ℜ.P [.a ↦ a.value]
+    monitored ℜ.package.total := ⊤ ⊢ ℜ.package []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/T.ts
new file mode 100644
index 00000000..f36c9d64
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  P: (x: runtime.Value) => runtime.ColnSet.View;
+  package: Package.View;
+}
+
+export interface Transaction extends View {
+  P: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  package: Package.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.json
new file mode 100644
index 00000000..df51631e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"builtin","type":"builtinInt"}}],"primaryKey":null}},{"path":[["TRealm"],["package"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["value"]],"type":{"tag":"builtin","type":"builtinInt"}},{"path":[["a"],["evidence"],["proof"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[]}},{"path":[["TRealm"],["package"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["value"]],[["a"],["evidence"],["proof"]]],"varTypes":[{"tag":"builtin","type":"builtinInt"},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["package"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["package"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["package"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.ts
new file mode 100644
index 00000000..5756c997
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.ts
@@ -0,0 +1,44 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.P", [a]));
+      },
+      package: (new runtime.TableCellRef.View(store, "TRealm.package", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.P",
+          [a],
+          transaction
+        ));
+      },
+      package: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.package",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.json
deleted file mode 100644
index 2c807669..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.json
+++ /dev/null
@@ -1 +0,0 @@
-{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["Accepted"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["first"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["second"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["trailing"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["select"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["first"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["second"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["trailing"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":[[["a"],["first"]],[["a"],["second"]],[["a"],["trailing"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["Accepted"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["first"]],[["a"],["second"]],[["a"],["trailing"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Accepted"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":1}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}}]}},{"path":[["TRealm"],["select"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["first"]],[["a"],["second"]],[["a"],["trailing"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["select"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}},{"column":3,"term":{"tag":"var","index":3}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":1}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":3},"values":[]}}]}},{"path":[["TRealm"],["select"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"],["first"]],[["a"],["second"]],[["a"],["trailing"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":1}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["select"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.coln
new file mode 100644
index 00000000..eaae8172
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.coln
@@ -0,0 +1,11 @@
+def Evidence (P : Prop) : Set := sig
+  proof : P
+end
+
+theory T := sig
+  P : Prop
+  evidence : Evidence P
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.output
new file mode 100644
index 00000000..4107a80b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.output
@@ -0,0 +1,32 @@
+-- elaborated
+global entry named Evidence
+type: (P : Prop) -> Set
+value: P => sig
+  proof : P
+end
+global entry named T
+type: Theory
+value: sig
+  P : Prop
+  evidence : Evidence P
+end
+realm named TRealm
+generators: node
+  P = rel []
+  evidence = (fun [] -> Evidence (TRealm.P []))
+end
+lowered: flatrealm
+  entities
+    table ℜ.P := []
+    table ℜ.evidence := [.a.proof : ℜ.P] primarykey []
+  end
+  rules
+    enforced ℜ.P.foreignKey := ℜ.P [] ⊢ ⊤
+    enforced ℜ.evidence.foreignKey a.proof := ℜ.evidence [
+      .a.proof ↦ a.proof
+    ] ⊢ a.proof ∈ ℜ.P []
+    monitored ℜ.evidence.total := ⊤ ⊢ ℜ.evidence []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/T.ts
new file mode 100644
index 00000000..76f5d21f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  P: runtime.ColnSet.View;
+  evidence: Evidence.View;
+}
+
+export interface Transaction extends View {
+  P: runtime.ColnSet.Transaction;
+  evidence: Evidence.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.json
new file mode 100644
index 00000000..db7bedf7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["evidence"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["proof"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["evidence"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["proof"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["evidence"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["evidence"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["evidence"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.ts
new file mode 100644
index 00000000..c0a628a5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.ts
@@ -0,0 +1,35 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      P: (new runtime.RowIdSet.View(store, "TRealm.P", [])),
+      evidence: (new runtime.TableCellRef.View(store, "TRealm.evidence", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      P: (new runtime.RowIdSet.Transaction(store, "TRealm.P", [], transaction)),
+      evidence: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.evidence",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.coln b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.coln
new file mode 100644
index 00000000..7846de2f
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.coln
@@ -0,0 +1,18 @@
+def Pair (X : Set) : Set := sig
+  left : X
+  right : X
+end
+
+def Comparison (X : Set) : Set := sig
+  first : Pair X
+  second : Pair X
+  same : first = second
+end
+
+theory T := sig
+  X : Set
+  comparison : Comparison X
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.output b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.output
new file mode 100644
index 00000000..1ba6d615
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.output
@@ -0,0 +1,48 @@
+-- elaborated
+global entry named Pair
+type: (X : Set) -> Set
+value: X => sig
+  left : X
+  right : X
+end
+global entry named Comparison
+type: (X : Set) -> Set
+value: X => sig
+  first : Pair X
+  second : Pair X
+  same : first = second
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  comparison : Comparison X
+end
+realm named TRealm
+generators: node
+  X = rel []
+  comparison = (fun [] -> Comparison (TRealm.X []))
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.comparison := [
+      .a.first.left : ℜ.X,
+      .a.first.right : ℜ.X,
+      .a.second.left : ℜ.X,
+      .a.second.right : ℜ.X
+    ] primarykey []
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.comparison.foreignKey a.first.left a.first.right a.second.left a.second.right := ℜ.comparison [
+      .a.first.left ↦ a.first.left,
+      .a.first.right ↦ a.first.right,
+      .a.second.left ↦ a.second.left,
+      .a.second.right ↦ a.second.right
+    ] ⊢ a.first.left ∈ ℜ.X [] ∧ a.first.right ∈ ℜ.X [] ∧ a.second.left ∈ ℜ.X [] ∧ a.second.right ∈ ℜ.X [] ∧ a.first.left = a.second.left ∧ a.first.right = a.second.right
+    monitored ℜ.comparison.total := ⊤ ⊢ ℜ.comparison []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/T.ts
new file mode 100644
index 00000000..97ac7fce
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  comparison: Comparison.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  comparison: Comparison.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.json
new file mode 100644
index 00000000..87c4c6aa
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["comparison"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["first"],["left"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["first"],["right"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["second"],["left"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["second"],["right"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["comparison"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["first"],["left"]],[["a"],["first"],["right"]],[["a"],["second"],["left"]],[["a"],["second"],["right"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["comparison"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}},{"column":3,"term":{"tag":"var","index":3}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":2},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":3},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":2}},{"tag":"eq","left":{"tag":"var","index":1},"right":{"tag":"var","index":3}}]}},{"path":[["TRealm"],["comparison"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["comparison"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.ts
new file mode 100644
index 00000000..665e7d34
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.ts
@@ -0,0 +1,39 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      comparison: (new runtime.TableCellRef.View(
+        store,
+        "TRealm.comparison",
+        []
+      ))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      comparison: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.comparison",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.coln b/packages/coln-compiler/test/golden/basic-ir/prop-alias.coln
new file mode 100644
index 00000000..82dfe8cf
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.coln
@@ -0,0 +1,8 @@
+theory PropAlias := Prop
+
+theory T := sig
+  V : PropAlias
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.output b/packages/coln-compiler/test/golden/basic-ir/prop-alias.output
new file mode 100644
index 00000000..0e0ea4d7
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.output
@@ -0,0 +1,23 @@
+-- elaborated
+global entry named PropAlias
+type: Theory
+value: Prop
+global entry named T
+type: Theory
+value: sig
+  V : PropAlias
+end
+realm named TRealm
+generators: node
+  V = rel []
+end
+lowered: flatrealm
+  entities
+    table ℜ.V := []
+  end
+  rules
+    enforced ℜ.V.foreignKey := ℜ.V [] ⊢ ⊤
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/PropAlias.ts b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/PropAlias.ts
new file mode 100644
index 00000000..1fbce54e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/PropAlias.ts
@@ -0,0 +1,5 @@
+import * as runtime from "@coln-project/runtime";
+
+export type View = runtime.ColnSet.View;
+
+export type Transaction = runtime.ColnSet.Transaction;
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/T.ts
new file mode 100644
index 00000000..0e874d07
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/T.ts
@@ -0,0 +1,10 @@
+import * as runtime from "@coln-project/runtime";
+import * as PropAlias from "./PropAlias.ts";
+
+export interface View {
+  V: runtime.ColnSet.View;
+}
+
+export interface Transaction extends View {
+  V: runtime.ColnSet.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.json
new file mode 100644
index 00000000..6cbfda78
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["V"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}}],"rules":[{"path":[["TRealm"],["V"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["V"]],"rowId":null,"values":[]}}],"consequents":[]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.ts
new file mode 100644
index 00000000..ea15e199
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.ts
@@ -0,0 +1,27 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as PropAlias from "./PropAlias.ts";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = { V: (new runtime.RowIdSet.View(store, "TRealm.V", [])) };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      V: (new runtime.RowIdSet.Transaction(store, "TRealm.V", [], transaction))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.coln b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.coln
new file mode 100644
index 00000000..452fb164
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.coln
@@ -0,0 +1,13 @@
+def Witness (P : Prop) : Prop := sig
+  first : P
+  second : P
+  same : first = second
+end
+
+theory T := sig
+  P : Prop
+  witness : Witness P
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.output b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.output
new file mode 100644
index 00000000..9e90b7df
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.output
@@ -0,0 +1,35 @@
+-- elaborated
+global entry named Witness
+type: (P : Prop) -> Prop
+value: P => sig
+  first : P
+  second : P
+  same : first = second
+end
+global entry named T
+type: Theory
+value: sig
+  P : Prop
+  witness : Witness P
+end
+realm named TRealm
+generators: node
+  P = rel []
+  witness = (fun [] -> Witness (TRealm.P []))
+end
+lowered: flatrealm
+  entities
+    table ℜ.P := []
+    table ℜ.witness := [.a.first : ℜ.P, .a.second : ℜ.P] primarykey []
+  end
+  rules
+    enforced ℜ.P.foreignKey := ℜ.P [] ⊢ ⊤
+    enforced ℜ.witness.foreignKey a.first a.second := ℜ.witness [
+      .a.first ↦ a.first,
+      .a.second ↦ a.second
+    ] ⊢ a.first ∈ ℜ.P [] ∧ a.second ∈ ℜ.P [] ∧ a.first = a.second
+    monitored ℜ.witness.total := ⊤ ⊢ ℜ.witness []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/T.ts
new file mode 100644
index 00000000..cfc10962
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/T.ts
@@ -0,0 +1,11 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  P: runtime.ColnSet.View;
+  witness: Witness.View;
+}
+
+export interface Transaction extends View {
+  P: runtime.ColnSet.Transaction;
+  witness: Witness.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.json
new file mode 100644
index 00000000..b57dadf2
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["witness"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["first"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}},{"path":[["a"],["second"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["witness"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["first"]],[["a"],["second"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["P"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[]}},{"tag":"eq","left":{"tag":"var","index":0},"right":{"tag":"var","index":1}}]}},{"path":[["TRealm"],["witness"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.ts
new file mode 100644
index 00000000..72295060
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.ts
@@ -0,0 +1,35 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      P: (new runtime.RowIdSet.View(store, "TRealm.P", [])),
+      witness: (new runtime.TableCellRef.View(store, "TRealm.witness", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      P: (new runtime.RowIdSet.Transaction(store, "TRealm.P", [], transaction)),
+      witness: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.witness",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.coln b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.coln
new file mode 100644
index 00000000..96aeace5
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.coln
@@ -0,0 +1,18 @@
+def Inner (P : Prop) : Prop := sig
+  proof : P
+end
+
+def Outer (P : Prop) (Q : Prop) : Prop := sig
+  nested : Inner P
+  direct : Q
+end
+
+theory T := sig
+  X : Set
+  P : X -> Prop
+  Q : X -> Prop
+  make : (x : X) -> Outer (P x) (Q x)
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.output b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.output
new file mode 100644
index 00000000..2f61d2d2
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.output
@@ -0,0 +1,54 @@
+-- elaborated
+global entry named Inner
+type: (P : Prop) -> Prop
+value: P => sig
+  proof : P
+end
+global entry named Outer
+type: (P : Prop) -> (Q : Prop) -> Prop
+value: P => Q => sig
+  nested : Inner P
+  direct : Q
+end
+global entry named T
+type: Theory
+value: sig
+  X : Set
+  P : X -> Prop
+  Q : X -> Prop
+  make : (x : X) -> Outer (P x) (Q x)
+end
+realm named TRealm
+generators: node
+  X = rel []
+  P = rel [a : TRealm.X []]
+  Q = rel [a : TRealm.X []]
+  make = (fun [x : TRealm.X []] -> Outer (TRealm.P [a := x]) (TRealm.Q [
+    a := x
+  ]))
+end
+lowered: flatrealm
+  entities
+    table ℜ.X := []
+    table ℜ.P := [.a : ℜ.X]
+    table ℜ.Q := [.a : ℜ.X]
+    table ℜ.make := [
+      .x : ℜ.X,
+      .a.nested.proof : ℜ.P,
+      .a.direct : ℜ.Q
+    ] primarykey [.x]
+  end
+  rules
+    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
+    enforced ℜ.P.foreignKey a := ℜ.P [.a ↦ a] ⊢ a ∈ ℜ.X []
+    enforced ℜ.Q.foreignKey a := ℜ.Q [.a ↦ a] ⊢ a ∈ ℜ.X []
+    enforced ℜ.make.foreignKey x a.nested.proof a.direct := ℜ.make [
+      .x ↦ x,
+      .a.nested.proof ↦ a.nested.proof,
+      .a.direct ↦ a.direct
+    ] ⊢ x ∈ ℜ.X [] ∧ a.nested.proof ∈ ℜ.P [.a ↦ x] ∧ a.direct ∈ ℜ.Q [.a ↦ x]
+    monitored ℜ.make.total x := x ∈ ℜ.X [] ⊢ ℜ.make [.x ↦ x]
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/T.ts
new file mode 100644
index 00000000..4d22d8e3
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/T.ts
@@ -0,0 +1,15 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  X: runtime.ColnSet.View;
+  P: (x: runtime.Value) => runtime.ColnSet.View;
+  Q: (x: runtime.Value) => runtime.ColnSet.View;
+  make: (x: runtime.Value) => Outer.View;
+}
+
+export interface Transaction extends View {
+  X: runtime.ColnSet.Transaction;
+  P: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  Q: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  make: (x: runtime.Value) => Outer.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.json
new file mode 100644
index 00000000..a9912967
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["Q"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["make"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"],["nested"],["proof"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}},{"path":[["a"],["direct"]],"type":{"tag":"rowId","path":[["TRealm"],["Q"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["Q"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["Q"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["make"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"],["nested"],["proof"]],[["a"],["direct"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]},{"tag":"rowId","path":[["TRealm"],["Q"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["make"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}},{"column":2,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["Q"]],"rowId":{"tag":"var","index":2},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["make"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["make"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.ts
new file mode 100644
index 00000000..0f53a2f0
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.ts
@@ -0,0 +1,61 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.P", [a]));
+      },
+      Q: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.Q", [a]));
+      },
+      make: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.make", [x]));
+      }
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
+      P: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.P",
+          [a],
+          transaction
+        ));
+      },
+      Q: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.Transaction(
+          store,
+          "TRealm.Q",
+          [a],
+          transaction
+        ));
+      },
+      make: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.Transaction(
+          store,
+          "TRealm.make",
+          [x],
+          transaction
+        ));
+      }
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/record-nested.coln b/packages/coln-compiler/test/golden/basic-ir/record-nested.coln
new file mode 100644
index 00000000..f656b11b
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/record-nested.coln
@@ -0,0 +1,15 @@
+def Inner : Set := sig
+  rank : Int
+end
+
+def Outer : Set := sig
+  name : String
+  inner : Inner
+end
+
+theory T := sig
+  payload : Outer
+end
+
+realm TRealm @ T
+end
diff --git a/packages/coln-compiler/test/golden/basic-ir/record-nested.output b/packages/coln-compiler/test/golden/basic-ir/record-nested.output
new file mode 100644
index 00000000..080c0639
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/record-nested.output
@@ -0,0 +1,35 @@
+-- elaborated
+global entry named Inner
+type: Set
+value: sig
+  rank : Int
+end
+global entry named Outer
+type: Set
+value: sig
+  name : String
+  inner : Inner
+end
+global entry named T
+type: Theory
+value: sig
+  payload : Outer
+end
+realm named TRealm
+generators: node
+  payload = (fun [] -> Outer)
+end
+lowered: flatrealm
+  entities
+    table ℜ.payload := [.a.name : String, .a.inner.rank : Int] primarykey []
+  end
+  rules
+    enforced ℜ.payload.foreignKey a.name a.inner.rank := ℜ.payload [
+      .a.name ↦ a.name,
+      .a.inner.rank ↦ a.inner.rank
+    ] ⊢ ⊤
+    monitored ℜ.payload.total := ⊤ ⊢ ℜ.payload []
+  end
+end
+
+-- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/T.ts
new file mode 100644
index 00000000..5926016e
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/T.ts
@@ -0,0 +1,9 @@
+import * as runtime from "@coln-project/runtime";
+
+export interface View {
+  payload: Outer.View;
+}
+
+export interface Transaction extends View {
+  payload: Outer.Transaction;
+}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.json
new file mode 100644
index 00000000..fcfc69fd
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.json
@@ -0,0 +1 @@
+{"entities":[{"path":[["TRealm"],["payload"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"],["name"]],"type":{"tag":"builtin","type":"builtinString"}},{"path":[["a"],["inner"],["rank"]],"type":{"tag":"builtin","type":"builtinInt"}}],"primaryKey":[]}}],"rules":[{"path":[["TRealm"],["payload"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"],["name"]],[["a"],["inner"],["rank"]]],"varTypes":[{"tag":"builtin","type":"builtinString"},{"tag":"builtin","type":"builtinInt"}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["payload"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[]}},{"path":[["TRealm"],["payload"],["total"]],"value":{"ruleVariant":"monitored","varNames":[],"varTypes":[],"antecedents":[],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["payload"]],"rowId":null,"values":[]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.ts
new file mode 100644
index 00000000..5d80b8e8
--- /dev/null
+++ b/packages/coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.ts
@@ -0,0 +1,33 @@
+import schema from "./TRealm.json";
+export {schema};
+import * as runtime from "@coln-project/runtime";
+import * as T from "./T.ts";
+
+export class View {
+  root: T.View;
+
+  constructor(store: runtime.StoreHandle) {
+    this.root = {
+      payload: (new runtime.TableCellRef.View(store, "TRealm.payload", []))
+    };
+  }
+}
+
+export class Transaction extends View {
+  root: T.Transaction;
+
+  constructor(
+    store: runtime.StoreHandle,
+    transaction: runtime.TransactionHandle
+  ) {
+    super(store);
+    this.root = {
+      payload: (new runtime.TableCellRef.Transaction(
+        store,
+        "TRealm.payload",
+        [],
+        transaction
+      ))
+    };
+  }
+}
\ No newline at end of file
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-prop.test.ts
new file mode 100644
index 00000000..29682f06
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-prop.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-prop-prop-prop", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropPropPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-set.test.ts
new file mode 100644
index 00000000..d108efd4
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-prop-set.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentPropPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-prop-prop-set", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropPropSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
new file mode 100644
index 00000000..a4e4db76
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
@@ -0,0 +1,45 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentPropSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-prop-set-prop", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
+
+test("dependent-function-argument-prop-set-prop is vacuous when its proof domain is empty", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
+
+  realm.commit();
+});
+
+test("dependent-function-argument-prop-set-prop requires an output when its codomain is uninhabited", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
+  const a = realm.root.A.add();
+  realm.root.B(a).add();
+
+  assert.throws(() => realm.commit(), /rule TRealm\.f/);
+});
+
+test("dependent-function-argument-prop-set-prop infers its output from an inhabited codomain", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-set.test.ts
new file mode 100644
index 00000000..606d413e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-set.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentPropSetSetRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-prop-set-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-prop-set-set", () => {
+  const realm = beginRealm(DependentFunctionArgumentPropSetSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-prop.test.ts
new file mode 100644
index 00000000..bb73346c
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-prop.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentSetPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-set-prop-prop", () => {
+  const realm = beginRealm(DependentFunctionArgumentSetPropPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-set.test.ts
new file mode 100644
index 00000000..d634afbc
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-prop-set.test.ts
@@ -0,0 +1,28 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentSetPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-set-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-set-prop-set", () => {
+  const realm = beginRealm(DependentFunctionArgumentSetPropSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
+
+test("dependent-function-argument-set-prop-set is vacuous when its dependent proof domain is empty", () => {
+  const realm = beginRealm(DependentFunctionArgumentSetPropSetRealm);
+  realm.root.A.add();
+
+  realm.commit();
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-set-prop.test.ts
new file mode 100644
index 00000000..09e44bde
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-set-set-prop.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentSetSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument-set-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument-set-set-prop", () => {
+  const realm = beginRealm(DependentFunctionArgumentSetSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument.test.ts
new file mode 100644
index 00000000..f4f580f2
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-argument.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-argument", () => {
+  const realm = beginRealm(DependentFunctionArgumentRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const c = realm.root.C(a)(b).add();
+  realm.root.f(a)(b).set(c);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a)(b).get(), c), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-prop.test.ts
new file mode 100644
index 00000000..d0840aa1
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-prop.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-prop-prop", () => {
+  const realm = beginRealm(DependentFunctionPropPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  realm.root.f(a).set(b);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a).get(), b), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-set.test.ts
new file mode 100644
index 00000000..2b8a7418
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-prop-set.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-prop-set", () => {
+  const realm = beginRealm(DependentFunctionPropSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  realm.root.f(a).set(b);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a).get(), b), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-set-prop.test.ts
new file mode 100644
index 00000000..b7a9999a
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-set-prop.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function-set-prop", () => {
+  const realm = beginRealm(DependentFunctionSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  realm.root.f(a).set(b);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a).get(), b), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function.test.ts
new file mode 100644
index 00000000..48c78e45
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as DependentFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/dependent-function.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("dependent-function", () => {
+  const realm = beginRealm(DependentFunctionRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  realm.root.f(a).set(b);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.f(a).get(), b), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts
new file mode 100644
index 00000000..1196120d
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as EmptyPropRecordFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("empty-prop-record-function", () => {
+  const realm = beginRealm(EmptyPropRecordFunctionRealm);
+  const value = realm.root.X.add();
+
+  assert.deepEqual(realm.root.trivial(value), {});
+
+  const view = realm.commit();
+
+  assert.deepEqual(view.trivial(value), {});
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
index 69692306..9f4f688a 100644
--- a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
@@ -8,14 +8,7 @@ import test from "node:test";
 import * as EmptyPropRecordRealm from "../../../coln-compiler/test/golden/basic-ir/empty-prop-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "empty proposition records are exposed as table cells",
-    match: /Expected values to be strictly deep-equal/,
-  },
-};
-
-test("empty-prop-record", expectedFailure, () => {
+test("empty-prop-record", () => {
   const realm = beginRealm(EmptyPropRecordRealm);
 
   assert.deepEqual(realm.root.truth, {});
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
index a9e2f2be..3664d3ef 100644
--- a/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
@@ -5,75 +5,11 @@
 import assert from "node:assert/strict";
 import test from "node:test";
 
-import { valueEqual } from "@coln-project/runtime";
 import * as EmptyRecordRealm from "../../../coln-compiler/test/golden/basic-ir/empty-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "empty records are emitted as table cells rather than sets",
-    match: /realm\.root\.unit\.add is not a function/,
-  },
-};
-
-const expectedImplicitInhabitantFailure = {
-  expectFailure: {
-    label: "the empty record is not inhabited automatically",
-    match: /\.unit\.total/,
-  },
-};
-
-test("empty-record is inhabited without add", expectedImplicitInhabitantFailure, () => {
-  const realm = beginRealm(EmptyRecordRealm);
-  const view = realm.commit();
-  const values = view.unit.values();
-
-  assert.equal(values.next().done, false);
-  assert.equal(values.next().done, true);
-});
-
-test("empty-record", expectedFailure, () => {
-  const realm = beginRealm(EmptyRecordRealm);
-  const value = realm.root.unit.add();
-  const view = realm.commit();
-
-  assert.equal(view.unit.has(value), true);
-});
-
-test("empty-record canonicalizes values", expectedFailure, () => {
-  const realm = beginRealm(EmptyRecordRealm);
-  const first = realm.root.unit.add();
-  const second = realm.root.unit.add();
-  realm.commit();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("empty-record canonicalizes pending values", expectedFailure, () => {
-  const realm = beginRealm(EmptyRecordRealm);
-  const first = realm.root.unit.add();
-  const second = realm.root.unit.add();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("empty-record keeps canonical value handles valid", expectedFailure, () => {
+test("empty-record is inhabited without a write", () => {
   const realm = beginRealm(EmptyRecordRealm);
-  const first = realm.root.unit.add();
-  const second = realm.root.unit.add();
   const view = realm.commit();
-
-  assert.equal(view.unit.has(first), true);
-  assert.equal(view.unit.has(second), true);
-});
-
-test("empty-record has exactly one value", expectedFailure, () => {
-  const realm = beginRealm(EmptyRecordRealm);
-  realm.root.unit.add();
-  realm.root.unit.add();
-  const view = realm.commit();
-  const values = view.unit.values();
-
-  assert.equal(values.next().done, false);
-  assert.equal(values.next().done, true);
+  assert.deepEqual(view.unit, {});
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-prop.pending.ts b/packages/coln-js-runtime/tests/basic-ir/equality-prop.pending.ts
deleted file mode 100644
index c8e1b4c0..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/equality-prop.pending.ts
+++ /dev/null
@@ -1,86 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as EqualityPropRealm from "../../../coln-compiler/test/golden/basic-ir/equality-prop.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-test("equality-prop is inhabited without add", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const firstProof = realm.root.P.add();
-  const secondProof = realm.root.P.add();
-  realm.root.x.set(firstProof);
-  realm.root.y.set(secondProof);
-  const view = realm.commit();
-  const equalityProofs = view.eq.values();
-
-  assert.equal(equalityProofs.next().done, false);
-  assert.equal(equalityProofs.next().done, true);
-});
-
-test("equality-prop accepts equality between proof handles", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const firstProof = realm.root.P.add();
-  const secondProof = realm.root.P.add();
-  realm.root.x.set(firstProof);
-  realm.root.y.set(secondProof);
-  const equalityProof = realm.root.eq.add();
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.x.get(), view.y.get()), true);
-  assert.equal(view.eq.has(equalityProof), true);
-});
-
-test("equality-prop canonicalizes equality proofs", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const proof = realm.root.P.add();
-  realm.root.x.set(proof);
-  realm.root.y.set(proof);
-  const first = realm.root.eq.add();
-  const second = realm.root.eq.add();
-  realm.commit();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("equality-prop canonicalizes pending equality proofs", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const proof = realm.root.P.add();
-  realm.root.x.set(proof);
-  realm.root.y.set(proof);
-  const first = realm.root.eq.add();
-  const second = realm.root.eq.add();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("equality-prop keeps canonical equality proof handles valid", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const proof = realm.root.P.add();
-  realm.root.x.set(proof);
-  realm.root.y.set(proof);
-  const first = realm.root.eq.add();
-  const second = realm.root.eq.add();
-  const view = realm.commit();
-
-  assert.equal(view.eq.has(first), true);
-  assert.equal(view.eq.has(second), true);
-});
-
-test("equality-prop has exactly one equality proof", () => {
-  const realm = beginRealm(EqualityPropRealm);
-  const proof = realm.root.P.add();
-  realm.root.x.set(proof);
-  realm.root.y.set(proof);
-  realm.root.eq.add();
-  realm.root.eq.add();
-  const view = realm.commit();
-  const equalityProofs = view.eq.values();
-
-  assert.equal(equalityProofs.next().done, false);
-  assert.equal(equalityProofs.next().done, true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-prop.test.ts
new file mode 100644
index 00000000..8fd1908a
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/equality-prop.test.ts
@@ -0,0 +1,18 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import test from "node:test";
+
+import * as EqualityPropRealm from "../../../coln-compiler/test/golden/basic-ir/equality-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("equality-prop compares erased proof operands", () => {
+  const realm = beginRealm(EqualityPropRealm);
+  const proof = realm.root.P.add();
+  realm.root.x.set(proof);
+  realm.root.y.set(proof);
+  const view = realm.commit();
+
+  view.eq.get();
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-record-nested.test.ts
new file mode 100644
index 00000000..854ad718
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/equality-record-nested.test.ts
@@ -0,0 +1,37 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as EqualityRecordNestedRealm from "../../../coln-compiler/test/golden/basic-ir/equality-record-nested.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("equality-record-nested compares empty, stored, and proof fields", () => {
+  const realm = beginRealm(EqualityRecordNestedRealm);
+  realm.root.P.add();
+  const inner = realm.root.X.add();
+  const trailing = realm.root.X.add();
+  realm.root.first.inner.value.set(inner);
+  realm.root.first.trailing.set(trailing);
+  realm.root.second.inner.value.set(inner);
+  realm.root.second.trailing.set(trailing);
+  const view = realm.commit();
+
+  view.same.get();
+});
+
+test("equality-record-nested rejects a nested stored difference", () => {
+  const realm = beginRealm(EqualityRecordNestedRealm);
+  realm.root.P.add();
+  const first = realm.root.X.add();
+  const second = realm.root.X.add();
+  const trailing = realm.root.X.add();
+  realm.root.first.inner.value.set(first);
+  realm.root.first.trailing.set(trailing);
+  realm.root.second.inner.value.set(second);
+  realm.root.second.trailing.set(trailing);
+
+  assert.throws(() => realm.commit(), /rule TRealm\.same/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-record.test.ts
new file mode 100644
index 00000000..11eb25c3
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/equality-record.test.ts
@@ -0,0 +1,34 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as EqualityRecordRealm from "../../../coln-compiler/test/golden/basic-ir/equality-record.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("equality-record compares every stored field", () => {
+  const realm = beginRealm(EqualityRecordRealm);
+  const left = realm.root.X.add();
+  const right = realm.root.X.add();
+  realm.root.first.left.set(left);
+  realm.root.first.right.set(right);
+  realm.root.second.left.set(left);
+  realm.root.second.right.set(right);
+  const view = realm.commit();
+
+  view.same.get();
+});
+
+test("equality-record rejects a difference in one field", () => {
+  const realm = beginRealm(EqualityRecordRealm);
+  const first = realm.root.X.add();
+  const second = realm.root.X.add();
+  realm.root.first.left.set(first);
+  realm.root.first.right.set(first);
+  realm.root.second.left.set(first);
+  realm.root.second.right.set(second);
+
+  assert.throws(() => realm.commit(), /rule TRealm\.same/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality.pending.ts b/packages/coln-js-runtime/tests/basic-ir/equality.pending.ts
deleted file mode 100644
index 3b3ce5f7..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/equality.pending.ts
+++ /dev/null
@@ -1,58 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as EqualityRealm from "../../../coln-compiler/test/golden/basic-ir/equality.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-test("equality is inhabited without add for equal values", () => {
-  const realm = beginRealm(EqualityRealm);
-  const value = realm.root.V.add();
-  realm.root.x.set(value);
-  realm.root.y.set(value);
-  const view = realm.commit();
-  const proofs = view.eq.values();
-
-  assert.equal(proofs.next().done, false);
-  assert.equal(proofs.next().done, true);
-});
-
-test("equality is not inhabited for unequal values", () => {
-  const realm = beginRealm(EqualityRealm);
-  const first = realm.root.V.add();
-  const second = realm.root.V.add();
-  realm.root.x.set(first);
-  realm.root.y.set(second);
-
-  assert.throws(() => realm.commit(), /\.eq\.total/);
-});
-
-test("equality canonicalizes proofs", () => {
-  const realm = beginRealm(EqualityRealm);
-  const value = realm.root.V.add();
-  realm.root.x.set(value);
-  realm.root.y.set(value);
-  const first = realm.root.eq.add();
-  const second = realm.root.eq.add();
-  const view = realm.commit();
-  const proofs = view.eq.values();
-
-  assert.equal(valueEqual(first, second), true);
-  assert.equal(proofs.next().done, false);
-  assert.equal(proofs.next().done, true);
-});
-
-test("equality rejects a proof of unequal values", () => {
-  const realm = beginRealm(EqualityRealm);
-  const first = realm.root.V.add();
-  const second = realm.root.V.add();
-  realm.root.x.set(first);
-  realm.root.y.set(second);
-  realm.root.eq.add();
-
-  assert.throws(() => realm.commit(), /\.eq\.foreignKey/);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality.test.ts
new file mode 100644
index 00000000..c82514cd
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/equality.test.ts
@@ -0,0 +1,29 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as EqualityRealm from "../../../coln-compiler/test/golden/basic-ir/equality.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("equality produces a proof for equal values", () => {
+  const realm = beginRealm(EqualityRealm);
+  const value = realm.root.V.add();
+  realm.root.x.set(value);
+  realm.root.y.set(value);
+  const view = realm.commit();
+
+  view.eq.get();
+});
+
+test("equality rejects unequal values", () => {
+  const realm = beginRealm(EqualityRealm);
+  const first = realm.root.V.add();
+  const second = realm.root.V.add();
+  realm.root.x.set(first);
+  realm.root.y.set(second);
+
+  assert.throws(() => realm.commit(), /rule TRealm\.eq/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-prop.test.ts
new file mode 100644
index 00000000..828765be
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-prop.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-prop-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-prop-prop-prop", () => {
+  const realm = beginRealm(FamilyArgumentPropPropPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-set.test.ts
new file mode 100644
index 00000000..e705a06c
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-prop-set.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentPropPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-prop-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-prop-prop-set", () => {
+  const realm = beginRealm(FamilyArgumentPropPropSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-prop.test.ts
new file mode 100644
index 00000000..ff96dcc2
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-prop.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentPropSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-prop-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-prop-set-prop", () => {
+  const realm = beginRealm(FamilyArgumentPropSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-set.test.ts
new file mode 100644
index 00000000..376e0f1a
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-prop-set-set.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentPropSetSetRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-prop-set-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-prop-set-set", () => {
+  const realm = beginRealm(FamilyArgumentPropSetSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-prop.test.ts
new file mode 100644
index 00000000..55949ef3
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-prop.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentSetPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-set-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-set-prop-prop", () => {
+  const realm = beginRealm(FamilyArgumentSetPropPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-set.test.ts
new file mode 100644
index 00000000..ab01c9b2
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-prop-set.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentSetPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-set-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-set-prop-set", () => {
+  const realm = beginRealm(FamilyArgumentSetPropSetRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-set-prop.test.ts
new file mode 100644
index 00000000..e2ce076e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument-set-set-prop.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentSetSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument-set-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument-set-set-prop", () => {
+  const realm = beginRealm(FamilyArgumentSetSetPropRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/family-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/family-argument.test.ts
new file mode 100644
index 00000000..3134043e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/family-argument.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as FamilyArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/family-argument.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("family-argument", () => {
+  const realm = beginRealm(FamilyArgumentRealm);
+  const a = realm.root.A.add();
+  const b = realm.root.B(a).add();
+  const r = realm.root.R(a)(b).add();
+  const view = realm.commit();
+
+  assert.equal(view.R(a)(b).has(r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-prop.test.ts
index 531327e4..815972c7 100644
--- a/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-prop.test.ts
@@ -5,43 +5,14 @@
 import assert from "node:assert/strict";
 import test from "node:test";
 
-import { valueEqual } from "@coln-project/runtime";
 import * as ForeignKeyPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/foreign-key-prop-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "proof parameters and results are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
 test("foreign-key-prop-prop", () => {
   const realm = beginRealm(ForeignKeyPropPropRealm);
   const vertex = realm.root.V.add();
   const edge = realm.root.E(vertex).add();
   const view = realm.commit();
 
-  assert.equal(view.V.has(vertex), true);
   assert.equal(view.E(vertex).has(edge), true);
 });
-
-test("foreign-key-prop-prop rejects a parameter from the wrong table", () => {
-  const realm = beginRealm(ForeignKeyPropPropRealm);
-  const vertex = realm.root.V.add();
-  const edge = realm.root.E(vertex).add();
-  realm.root.E(edge).add();
-
-  assert.throws(() => realm.commit(), /\.E\.foreignKey/);
-});
-
-test("foreign-key-prop-prop ignores proof identity in its parameter", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(ForeignKeyPropPropRealm);
-  const firstVertex = realm.root.V.add();
-  const secondVertex = realm.root.V.add();
-  const firstEdge = realm.root.E(firstVertex).add();
-  const secondEdge = realm.root.E(secondVertex).add();
-  realm.commit();
-
-  assert.equal(valueEqual(firstEdge, secondEdge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-set.test.ts
index 6661065a..cf4e7913 100644
--- a/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/foreign-key-prop-set.test.ts
@@ -8,38 +8,11 @@ import test from "node:test";
 import * as ForeignKeyPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/foreign-key-prop-set.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "sets indexed by equal proofs are treated as distinct",
-    match: /false !== true/,
-  },
-};
-
 test("foreign-key-prop-set", () => {
   const realm = beginRealm(ForeignKeyPropSetRealm);
   const vertex = realm.root.V.add();
   const edge = realm.root.E(vertex).add();
   const view = realm.commit();
 
-  assert.equal(view.V.has(vertex), true);
   assert.equal(view.E(vertex).has(edge), true);
 });
-
-test("foreign-key-prop-set rejects a parameter from the wrong table", () => {
-  const realm = beginRealm(ForeignKeyPropSetRealm);
-  const vertex = realm.root.V.add();
-  const edge = realm.root.E(vertex).add();
-  realm.root.E(edge).add();
-
-  assert.throws(() => realm.commit(), /\.E\.foreignKey/);
-});
-
-test("foreign-key-prop-set ignores proof identity in its parameter", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(ForeignKeyPropSetRealm);
-  const firstVertex = realm.root.V.add();
-  const secondVertex = realm.root.V.add();
-  const edge = realm.root.E(firstVertex).add();
-  const view = realm.commit();
-
-  assert.equal(view.E(secondVertex).has(edge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
index a5526023..b3158282 100644
--- a/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
@@ -9,76 +9,15 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ForeignKeySetPropRealm from "../../../coln-compiler/test/golden/basic-ir/foreign-key-set-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedCanonicalizationFailure = {
-  expectFailure: {
-    label: "multiple proofs with the same parameter tuple are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
-const expectedPendingCanonicalizationFailure = {
-  expectFailure: {
-    label: "pending proofs with the same parameter tuple are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
-const expectedCardinalityFailure = {
-  expectFailure: {
-    label: "a proposition can contain multiple proof rows for one parameter tuple",
-    match: /false !== true/,
-  },
-};
-
 test("foreign-key-set-prop", () => {
   const realm = beginRealm(ForeignKeySetPropRealm);
   const vertex = realm.root.V.add();
   const edge = realm.root.E(vertex).add();
   const view = realm.commit();
 
-  assert.equal(view.V.has(vertex), true);
   assert.equal(view.E(vertex).has(edge), true);
 });
 
-test("foreign-key-set-prop rejects a parameter from the wrong table", () => {
-  const realm = beginRealm(ForeignKeySetPropRealm);
-  const vertex = realm.root.V.add();
-  const edge = realm.root.E(vertex).add();
-  realm.root.E(edge).add();
-
-  assert.throws(() => realm.commit(), /\.E\.foreignKey/);
-});
-
-test("foreign-key-set-prop canonicalizes proofs with the same parameter tuple", expectedCanonicalizationFailure, () => {
-  const realm = beginRealm(ForeignKeySetPropRealm);
-  const vertex = realm.root.V.add();
-  const first = realm.root.E(vertex).add();
-  const second = realm.root.E(vertex).add();
-  realm.commit();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("foreign-key-set-prop canonicalizes pending proofs with the same parameter tuple", expectedPendingCanonicalizationFailure, () => {
-  const realm = beginRealm(ForeignKeySetPropRealm);
-  const vertex = realm.root.V.add();
-  const first = realm.root.E(vertex).add();
-  const second = realm.root.E(vertex).add();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
-test("foreign-key-set-prop keeps canonical proof handles valid", () => {
-  const realm = beginRealm(ForeignKeySetPropRealm);
-  const vertex = realm.root.V.add();
-  const first = realm.root.E(vertex).add();
-  const second = realm.root.E(vertex).add();
-  const view = realm.commit();
-
-  assert.equal(view.E(vertex).has(first), true);
-  assert.equal(view.E(vertex).has(second), true);
-});
-
 test("foreign-key-set-prop keeps proofs for different parameter tuples distinct", () => {
   const realm = beginRealm(ForeignKeySetPropRealm);
   const firstVertex = realm.root.V.add();
@@ -90,7 +29,7 @@ test("foreign-key-set-prop keeps proofs for different parameter tuples distinct"
   assert.equal(valueEqual(first, second), false);
 });
 
-test("foreign-key-set-prop has at most one proof per parameter tuple", expectedCardinalityFailure, () => {
+test("foreign-key-set-prop has at most one proof per parameter tuple", () => {
   const realm = beginRealm(ForeignKeySetPropRealm);
   const vertex = realm.root.V.add();
   realm.root.E(vertex).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/foreign-key.test.ts b/packages/coln-js-runtime/tests/basic-ir/foreign-key.test.ts
index cc0321f9..67dab518 100644
--- a/packages/coln-js-runtime/tests/basic-ir/foreign-key.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/foreign-key.test.ts
@@ -14,7 +14,6 @@ test("foreign-key", () => {
   const edge = realm.root.E(vertex).add();
   const view = realm.commit();
 
-  assert.equal(view.V.has(vertex), true);
   assert.equal(view.E(vertex).has(edge), true);
 });
 
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-mixed-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-mixed-prop-set.test.ts
deleted file mode 100644
index 71a2a22e..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/function-mixed-prop-set.test.ts
+++ /dev/null
@@ -1,49 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as FunctionMixedPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/function-mixed-prop-set.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedProofKeyFailure = {
-  expectFailure: {
-    label: "proof arguments remain part of material function keys",
-    match: /3 !== 2/,
-  },
-};
-
-test("function-mixed-prop-set", () => {
-  const realm = beginRealm(FunctionMixedPropSetRealm);
-  const input = realm.root.X.add();
-  const proof = realm.root.P.add();
-  const output = realm.root.Y.add();
-  realm.root.choose(input)(proof).set(output);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.choose(input)(proof).get(), output), true);
-});
-
-test("function-mixed-prop-set retains its erased proof premise", () => {
-  const realm = beginRealm(FunctionMixedPropSetRealm);
-  const input = realm.root.X.add();
-  const output = realm.root.Y.add();
-  realm.root.choose(input)(input).set(output);
-
-  assert.throws(() => realm.commit(), /\.choose\.foreignKey/);
-});
-
-test(
-  "function-mixed-prop-set erases its proof argument column",
-  expectedProofKeyFailure,
-  () => {
-    const choose = FunctionMixedPropSetRealm.schema.entities.find(
-      (entity) => entity.path.flat().join(".") === "TRealm.choose",
-    );
-
-    assert.equal(choose?.value.columns.length, 2);
-  },
-);
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-multi-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-multi-argument.test.ts
deleted file mode 100644
index ca0e1506..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/function-multi-argument.test.ts
+++ /dev/null
@@ -1,103 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as FunctionMultiArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/function-multi-argument.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedImplicitOutputFailure = {
-  expectFailure: {
-    label: "a multi-argument function into an inhabited proposition is not synthesized",
-    match: /\.f\.total/,
-  },
-};
-
-const expectedParameterFailure = {
-  expectFailure: {
-    label: "a function treats equal proof parameters as distinct",
-    match: /\.f\.total/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "a proof-valued function can return a noncanonical proof",
-    match: /false !== true/,
-  },
-};
-
-test("function-multi-argument", () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const inputProof = realm.root.P.add();
-  const outputProof = realm.root.Q.add();
-  realm.root.f(inputProof)(value).set(outputProof);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.f(inputProof)(value).get(), outputProof), true);
-});
-
-test("function-multi-argument rejects parameters in the wrong order", () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const inputProof = realm.root.P.add();
-  const outputProof = realm.root.Q.add();
-  realm.root.f(value)(inputProof).set(outputProof);
-
-  assert.throws(() => realm.commit(), /\.f\.foreignKey/);
-});
-
-test("function-multi-argument is vacuous when its proof domain is empty", () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  realm.root.X.add();
-  const view = realm.commit();
-
-  assert.equal(view.P.values().next().done, true);
-  assert.equal(view.Q.values().next().done, true);
-});
-
-test("function-multi-argument requires an output when its codomain is uninhabited", () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  realm.root.X.add();
-  realm.root.P.add();
-
-  assert.throws(() => realm.commit(), /\.f\.total/);
-});
-
-test("function-multi-argument infers its output from an inhabited codomain", expectedImplicitOutputFailure, () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const inputProof = realm.root.P.add();
-  const outputProof = realm.root.Q.add();
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.f(inputProof)(value).get(), outputProof), true);
-});
-
-test("function-multi-argument ignores proof identity in its parameter", expectedParameterFailure, () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const firstInputProof = realm.root.P.add();
-  const secondInputProof = realm.root.P.add();
-  const outputProof = realm.root.Q.add();
-  realm.root.f(firstInputProof)(value).set(outputProof);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.f(secondInputProof)(value).get(), outputProof), true);
-});
-
-test("function-multi-argument returns a canonical proof", expectedOutputFailure, () => {
-  const realm = beginRealm(FunctionMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const inputProof = realm.root.P.add();
-  const firstOutputProof = realm.root.Q.add();
-  const secondOutputProof = realm.root.Q.add();
-  realm.root.f(inputProof)(value).set(firstOutputProof);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.f(inputProof)(value).get(), secondOutputProof), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
index f5ec6ac4..4eb708d7 100644
--- a/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
@@ -9,28 +9,6 @@ import { valueEqual } from "@coln-project/runtime";
 import * as FunctionPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/function-prop-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "a function can return distinct proofs of the same proposition",
-    match: /false !== true/,
-  },
-};
-
-const expectedImplicitOutputFailure = {
-  expectFailure: {
-    label: "a function into an inhabited proposition is not synthesized",
-    match: /\.next\.total/,
-  },
-};
-
-test("function-prop-prop is vacuous when its domain is empty", () => {
-  const realm = beginRealm(FunctionPropPropRealm);
-  const view = realm.commit();
-
-  assert.equal(view.X.values().next().done, true);
-  assert.equal(view.Y.values().next().done, true);
-});
-
 test("function-prop-prop", () => {
   const realm = beginRealm(FunctionPropPropRealm);
   const input = realm.root.X.add();
@@ -41,42 +19,25 @@ test("function-prop-prop", () => {
   assert.equal(valueEqual(view.next(input).get(), output), true);
 });
 
-test("function-prop-prop requires an output when its codomain is uninhabited", () => {
+test("function-prop-prop is vacuous when its domain is empty", () => {
   const realm = beginRealm(FunctionPropPropRealm);
-  realm.root.X.add();
+  const view = realm.commit();
 
-  assert.throws(() => realm.commit(), /\.next\.total/);
+  assert.equal(view.Y.values().next().done, true);
 });
 
-test("function-prop-prop infers its output from an inhabited codomain", expectedImplicitOutputFailure, () => {
+test("function-prop-prop requires an output when its codomain is uninhabited", () => {
   const realm = beginRealm(FunctionPropPropRealm);
-  const input = realm.root.X.add();
-  const output = realm.root.Y.add();
-  const view = realm.commit();
+  realm.root.X.add();
 
-  assert.equal(valueEqual(view.next(input).get(), output), true);
+  assert.throws(() => realm.commit(), /rule TRealm\.next/);
 });
 
-test("function-prop-prop rejects an output from the wrong table", () => {
+test("function-prop-prop infers its output from an inhabited codomain", () => {
   const realm = beginRealm(FunctionPropPropRealm);
   const input = realm.root.X.add();
-  const wrongOutput = realm.root.X.add();
   const output = realm.root.Y.add();
-  realm.root.next(input).set(wrongOutput);
-  realm.root.next(wrongOutput).set(output);
-
-  assert.throws(() => realm.commit(), /\.next\.foreignKey/);
-});
-
-test("function-prop-prop returns equal proofs for equal proof inputs", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(FunctionPropPropRealm);
-  const firstInput = realm.root.X.add();
-  const secondInput = realm.root.X.add();
-  const firstOutput = realm.root.Y.add();
-  const secondOutput = realm.root.Y.add();
-  realm.root.next(firstInput).set(firstOutput);
-  realm.root.next(secondInput).set(secondOutput);
   const view = realm.commit();
 
-  assert.equal(valueEqual(view.next(firstInput).get(), view.next(secondInput).get()), true);
+  assert.equal(valueEqual(view.next(input).get(), output), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-prop-set.test.ts
index 8ffc6e36..a14d548d 100644
--- a/packages/coln-js-runtime/tests/basic-ir/function-prop-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/function-prop-set.test.ts
@@ -9,13 +9,6 @@ import { valueEqual } from "@coln-project/runtime";
 import * as FunctionPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/function-prop-set.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "a function treats equal proof inputs as distinct",
-    match: /\.next\.total/,
-  },
-};
-
 test("function-prop-set", () => {
   const realm = beginRealm(FunctionPropSetRealm);
   const input = realm.root.X.add();
@@ -32,25 +25,3 @@ test("function-prop-set requires an output for every input", () => {
 
   assert.throws(() => realm.commit(), /\.next\.total/);
 });
-
-test("function-prop-set rejects an output from the wrong table", () => {
-  const realm = beginRealm(FunctionPropSetRealm);
-  const input = realm.root.X.add();
-  const wrongOutput = realm.root.X.add();
-  const output = realm.root.Y.add();
-  realm.root.next(input).set(wrongOutput);
-  realm.root.next(wrongOutput).set(output);
-
-  assert.throws(() => realm.commit(), /\.next\.foreignKey/);
-});
-
-test("function-prop-set ignores proof identity in its input", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(FunctionPropSetRealm);
-  const firstInput = realm.root.X.add();
-  const secondInput = realm.root.X.add();
-  const output = realm.root.Y.add();
-  realm.root.next(firstInput).set(output);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(secondInput).get(), output), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
index f9810a2c..53a62735 100644
--- a/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
@@ -9,27 +9,6 @@ import { valueEqual } from "@coln-project/runtime";
 import * as FunctionSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/function-set-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedCanonicalizationFailure = {
-  expectFailure: {
-    label: "a function can return distinct proofs of the same proposition",
-    match: /false !== true/,
-  },
-};
-
-const expectedCardinalityFailure = {
-  expectFailure: {
-    label: "the proposition codomain can contain multiple proof rows",
-    match: /false !== true/,
-  },
-};
-
-const expectedImplicitOutputFailure = {
-  expectFailure: {
-    label: "a function into an inhabited proposition is not synthesized",
-    match: /\.next\.total/,
-  },
-};
-
 test("function-set-prop", () => {
   const realm = beginRealm(FunctionSetPropRealm);
   const input = realm.root.X.add();
@@ -44,10 +23,10 @@ test("function-set-prop requires an output when its codomain is uninhabited", ()
   const realm = beginRealm(FunctionSetPropRealm);
   realm.root.X.add();
 
-  assert.throws(() => realm.commit(), /\.next\.total/);
+  assert.throws(() => realm.commit(), /rule TRealm\.next/);
 });
 
-test("function-set-prop infers its output from an inhabited codomain", expectedImplicitOutputFailure, () => {
+test("function-set-prop infers its output from an inhabited codomain", () => {
   const realm = beginRealm(FunctionSetPropRealm);
   const input = realm.root.X.add();
   const output = realm.root.Y.add();
@@ -56,18 +35,7 @@ test("function-set-prop infers its output from an inhabited codomain", expectedI
   assert.equal(valueEqual(view.next(input).get(), output), true);
 });
 
-test("function-set-prop rejects an output from the wrong table", () => {
-  const realm = beginRealm(FunctionSetPropRealm);
-  const input = realm.root.X.add();
-  const wrongOutput = realm.root.X.add();
-  const output = realm.root.Y.add();
-  realm.root.next(input).set(wrongOutput);
-  realm.root.next(wrongOutput).set(output);
-
-  assert.throws(() => realm.commit(), /\.next\.foreignKey/);
-});
-
-test("function-set-prop returns equal proofs for different inputs", expectedCanonicalizationFailure, () => {
+test("function-set-prop returns equal proofs for different inputs", () => {
   const realm = beginRealm(FunctionSetPropRealm);
   const firstInput = realm.root.X.add();
   const secondInput = realm.root.X.add();
@@ -79,14 +47,3 @@ test("function-set-prop returns equal proofs for different inputs", expectedCano
 
   assert.equal(valueEqual(view.next(firstInput).get(), view.next(secondInput).get()), true);
 });
-
-test("function-set-prop codomain has at most one proof", expectedCardinalityFailure, () => {
-  const realm = beginRealm(FunctionSetPropRealm);
-  realm.root.Y.add();
-  realm.root.Y.add();
-  const view = realm.commit();
-  const proofs = view.Y.values();
-
-  assert.equal(proofs.next().done, false);
-  assert.equal(proofs.next().done, true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts b/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
index 345375e1..74c4ebe3 100644
--- a/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
@@ -13,11 +13,6 @@ const goldenDirectory = resolve(
   here,
   "../../../coln-compiler/test/golden/basic-ir",
 );
-const missingRealms = [
-  "equality",
-  "equality-prop",
-  "rule-literals",
-];
 const testSuffix = /\.(?:pending|test)\.ts$/;
 
 test("every realm has an integration test", () => {
@@ -30,5 +25,5 @@ test("every realm has an integration test", () => {
     .map((path) => path.replace(testSuffix, ""))
     .sort();
 
-  assert.deepEqual(integrationTests, [...realms, ...missingRealms].sort());
+  assert.deepEqual(integrationTests, realms.sort());
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts
new file mode 100644
index 00000000..5f29983e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-prop-prop-prop", () => {
+  const realm = beginRealm(LookupArgumentProjectionPropPropPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts
new file mode 100644
index 00000000..966ae80d
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionPropPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-prop-prop-set", () => {
+  const realm = beginRealm(LookupArgumentProjectionPropPropSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts
new file mode 100644
index 00000000..262e0d2e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionPropSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-prop-set-prop", () => {
+  const realm = beginRealm(LookupArgumentProjectionPropSetPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts
new file mode 100644
index 00000000..68f34866
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionPropSetSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-prop-set-set", () => {
+  const realm = beginRealm(LookupArgumentProjectionPropSetSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts
new file mode 100644
index 00000000..6f70b9ca
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionSetPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-set-prop-prop", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetPropPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts
new file mode 100644
index 00000000..8775b27a
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupArgumentProjectionSetPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-argument-projection-set-prop-set", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetPropSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.next(source).set(target);
+  realm.root.nextedge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
similarity index 59%
rename from packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-set-prop.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
index 407a5484..b5986393 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
@@ -6,25 +6,11 @@ import assert from "node:assert/strict";
 import test from "node:test";
 
 import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionSetSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-set-set-prop.ts.output/TRealm.ts";
+import * as LookupArgumentProjectionSetSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "lookups can return distinct proofs of the same proposition",
-    match: /false !== true/,
-  },
-};
-
-const expectedImplicitOutputFailure = {
-  expectFailure: {
-    label: "a dependent function into an inhabited proposition is not synthesized",
-    match: /\.nextedge\.total/,
-  },
-};
-
-test("lookup-projection-set-set-prop", () => {
-  const realm = beginRealm(LookupProjectionSetSetPropRealm);
+test("lookup-argument-projection-set-set-prop", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
   const target = realm.root.B.add();
   const edge = realm.root.E(target).add();
@@ -32,15 +18,11 @@ test("lookup-projection-set-set-prop", () => {
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
   assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
 });
 
-test("lookup-projection-set-set-prop rejects an edge at a different target", () => {
-  const realm = beginRealm(LookupProjectionSetSetPropRealm);
+test("lookup-argument-projection-set-set-prop rejects an edge at a different target", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
   const target = realm.root.B.add();
   const otherTarget = realm.root.B.add();
@@ -48,11 +30,11 @@ test("lookup-projection-set-set-prop rejects an edge at a different target", ()
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
 
-  assert.throws(() => realm.commit(), /\.nextedge\.foreignKey/);
+  assert.throws(() => realm.commit(), /rule TRealm\.nextedge/);
 });
 
-test("lookup-projection-set-set-prop infers its output from an inhabited proposition", expectedImplicitOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionSetSetPropRealm);
+test("lookup-argument-projection-set-set-prop infers its output from an inhabited proposition", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
   const target = realm.root.B.add();
   const edge = realm.root.E(target).add();
@@ -62,8 +44,8 @@ test("lookup-projection-set-set-prop infers its output from an inhabited proposi
   assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
 });
 
-test("lookup-projection-set-set-prop returns equal proofs for equal lookup results", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(LookupProjectionSetSetPropRealm);
+test("lookup-argument-projection-set-set-prop returns equal proofs for equal lookup results", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const firstSource = realm.root.A.add();
   const secondSource = realm.root.A.add();
   const target = realm.root.B.add();
@@ -78,8 +60,8 @@ test("lookup-projection-set-set-prop returns equal proofs for equal lookup resul
   assert.equal(valueEqual(view.nextedge(firstSource).get(), view.nextedge(secondSource).get()), true);
 });
 
-test("lookup-projection-set-set-prop keeps proofs for different lookup results distinct", () => {
-  const realm = beginRealm(LookupProjectionSetSetPropRealm);
+test("lookup-argument-projection-set-set-prop keeps proofs for different lookup results distinct", () => {
+  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const firstSource = realm.root.A.add();
   const secondSource = realm.root.A.add();
   const firstTarget = realm.root.B.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
similarity index 62%
rename from packages/coln-js-runtime/tests/basic-ir/lookup-projection.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
index afc11432..49604434 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
@@ -6,11 +6,11 @@ import assert from "node:assert/strict";
 import test from "node:test";
 
 import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection.ts.output/TRealm.ts";
+import * as LookupArgumentProjectionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("lookup-projection", () => {
-  const realm = beginRealm(LookupProjectionRealm);
+test("lookup-argument-projection", () => {
+  const realm = beginRealm(LookupArgumentProjectionRealm);
   const source = realm.root.A.add();
   const target = realm.root.B.add();
   const edge = realm.root.E(target).add();
@@ -18,15 +18,11 @@ test("lookup-projection", () => {
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
   assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
 });
 
-test("lookup-projection rejects an edge at a different target", () => {
-  const realm = beginRealm(LookupProjectionRealm);
+test("lookup-argument-projection rejects an edge at a different target", () => {
+  const realm = beginRealm(LookupArgumentProjectionRealm);
   const source = realm.root.A.add();
   const target = realm.root.B.add();
   const otherTarget = realm.root.B.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-builtin.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-builtin.test.ts
index 5e9a2108..006e2c65 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-builtin.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-builtin.test.ts
@@ -18,9 +18,6 @@ test("lookup-builtin", () => {
   realm.root.edge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(view.X.has(source), true);
-  assert.equal(view.E(rank).has(edge), true);
-  assert.equal(valueEqual(view.rank(source).get(), rank), true);
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
 
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts
new file mode 100644
index 00000000..cf3f92bc
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts
@@ -0,0 +1,35 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupCompositionPropPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-composition-prop-prop-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-composition-prop-prop-prop-prop", () => {
+  const realm = beginRealm(LookupCompositionPropPropPropPropRealm);
+  const source = realm.root.A.add();
+  const intermediate = realm.root.B.add();
+  const target = realm.root.C.add();
+  const edge = realm.root.E(target).add();
+  realm.root.first(source).set(intermediate);
+  realm.root.second(intermediate).set(target);
+  realm.root.edge(source).set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge(source).get(), edge), true);
+});
+
+test("lookup-composition-prop-prop-prop-prop infers an inhabited composition", () => {
+  const realm = beginRealm(LookupCompositionPropPropPropPropRealm);
+  const source = realm.root.A.add();
+  const intermediate = realm.root.B.add();
+  const target = realm.root.C.add();
+  const edge = realm.root.E(target).add();
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge(source).get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop.test.ts
deleted file mode 100644
index fe720277..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop.test.ts
+++ /dev/null
@@ -1,140 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupCompositionPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-composition-prop.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedInputFailure = {
-  expectFailure: {
-    label: "composition treats equal source proofs as distinct",
-    match: /\.first\.total/,
-  },
-};
-
-const expectedIntermediateFailure = {
-  expectFailure: {
-    label: "composition treats equal intermediate proofs as distinct",
-    match: /\.second\.total/,
-  },
-};
-
-const expectedEqualTargetFailure = {
-  expectFailure: {
-    label: "equal composed target proofs identify different propositions",
-    match: /\.edge\.foreignKey/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "proof-valued composition can return a distinct proof",
-    match: /false !== true/,
-  },
-};
-
-const expectedImplicitCompositionFailure = {
-  expectFailure: {
-    label: "composition through inhabited propositions is not synthesized",
-    match: /\.first\.total/,
-  },
-};
-
-test("lookup-composition-prop", () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const source = realm.root.A.add();
-  const intermediate = realm.root.B.add();
-  const target = realm.root.C.add();
-  const edge = realm.root.E(target).add();
-  realm.root.first(source).set(intermediate);
-  realm.root.second(intermediate).set(target);
-  realm.root.edge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(intermediate), true);
-  assert.equal(view.C.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.first(source).get(), intermediate), true);
-  assert.equal(valueEqual(view.second(intermediate).get(), target), true);
-  assert.equal(valueEqual(view.edge(source).get(), edge), true);
-});
-
-test("lookup-composition-prop ignores proof identity in its source", expectedInputFailure, () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const intermediate = realm.root.B.add();
-  const target = realm.root.C.add();
-  const edge = realm.root.E(target).add();
-  realm.root.first(firstSource).set(intermediate);
-  realm.root.second(intermediate).set(target);
-  realm.root.edge(firstSource).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.first(secondSource).get(), intermediate), true);
-  assert.equal(valueEqual(view.edge(secondSource).get(), edge), true);
-});
-
-test("lookup-composition-prop ignores proof identity at its intermediate lookup", expectedIntermediateFailure, () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const source = realm.root.A.add();
-  const firstIntermediate = realm.root.B.add();
-  const secondIntermediate = realm.root.B.add();
-  const target = realm.root.C.add();
-  const edge = realm.root.E(target).add();
-  realm.root.first(source).set(firstIntermediate);
-  realm.root.second(secondIntermediate).set(target);
-  realm.root.edge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.second(firstIntermediate).get(), target), true);
-  assert.equal(valueEqual(view.edge(source).get(), edge), true);
-});
-
-test("lookup-composition-prop accepts an edge at an equal composed target", expectedEqualTargetFailure, () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const source = realm.root.A.add();
-  const intermediate = realm.root.B.add();
-  const firstTarget = realm.root.C.add();
-  const secondTarget = realm.root.C.add();
-  const edge = realm.root.E(secondTarget).add();
-  realm.root.first(source).set(intermediate);
-  realm.root.second(intermediate).set(firstTarget);
-  realm.root.edge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.E(firstTarget).has(edge), true);
-});
-
-test("lookup-composition-prop returns a canonical edge proof", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const source = realm.root.A.add();
-  const intermediate = realm.root.B.add();
-  const target = realm.root.C.add();
-  const firstEdge = realm.root.E(target).add();
-  const secondEdge = realm.root.E(target).add();
-  realm.root.first(source).set(intermediate);
-  realm.root.second(intermediate).set(target);
-  realm.root.edge(source).set(firstEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.edge(source).get(), secondEdge), true);
-});
-
-test("lookup-composition-prop infers an inhabited composition", expectedImplicitCompositionFailure, () => {
-  const realm = beginRealm(LookupCompositionPropRealm);
-  const source = realm.root.A.add();
-  const intermediate = realm.root.B.add();
-  const target = realm.root.C.add();
-  const edge = realm.root.E(target).add();
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.first(source).get(), intermediate), true);
-  assert.equal(valueEqual(view.second(intermediate).get(), target), true);
-  assert.equal(valueEqual(view.edge(source).get(), edge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-composition.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-composition.test.ts
index a984ac0d..1fd56d3b 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-composition.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-composition.test.ts
@@ -20,12 +20,6 @@ test("lookup-composition", () => {
   realm.root.edge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(intermediate), true);
-  assert.equal(view.C.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.first(source).get(), intermediate), true);
-  assert.equal(valueEqual(view.second(intermediate).get(), target), true);
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
 
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-prop.test.ts
new file mode 100644
index 00000000..32c2def2
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-prop.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-prop-prop-prop", () => {
+  const realm = beginRealm(LookupFieldProjectionPropPropPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-set.test.ts
new file mode 100644
index 00000000..fc2cb1d4
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-prop-set.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionPropPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-prop-prop-set", () => {
+  const realm = beginRealm(LookupFieldProjectionPropPropSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-prop.test.ts
new file mode 100644
index 00000000..4a94268f
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-prop.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionPropSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-prop-set-prop", () => {
+  const realm = beginRealm(LookupFieldProjectionPropSetPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-set.test.ts
new file mode 100644
index 00000000..beb6a394
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-prop-set-set.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionPropSetSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-prop-set-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-prop-set-set", () => {
+  const realm = beginRealm(LookupFieldProjectionPropSetSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-prop.test.ts
new file mode 100644
index 00000000..37b3b2b7
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-prop.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionSetPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-set-prop-prop", () => {
+  const realm = beginRealm(LookupFieldProjectionSetPropPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-set.test.ts
new file mode 100644
index 00000000..e17aa087
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-prop-set.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionSetPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-set-prop-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-set-prop-set", () => {
+  const realm = beginRealm(LookupFieldProjectionSetPropSetRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-set-prop.test.ts
new file mode 100644
index 00000000..4ff4faac
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection-set-set-prop.test.ts
@@ -0,0 +1,36 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionSetSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection-set-set-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection-set-set-prop", () => {
+  const realm = beginRealm(LookupFieldProjectionSetSetPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
+
+test("lookup-field-projection-set-set-prop rejects an edge at a different target", () => {
+  const realm = beginRealm(LookupFieldProjectionSetSetPropRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const otherTarget = realm.root.B.add();
+  const edge = realm.root.E(otherTarget).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+
+  assert.throws(() => realm.commit(), /rule TRealm\.edge/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection.test.ts
new file mode 100644
index 00000000..5a5a7fc4
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-field-projection.test.ts
@@ -0,0 +1,23 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupFieldProjectionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-field-projection.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-field-projection", () => {
+  const realm = beginRealm(LookupFieldProjectionRealm);
+  const source = realm.root.A.add();
+  const target = realm.root.B.add();
+  const edge = realm.root.E(target).add();
+  realm.root.x.set(source);
+  realm.root.next(source).set(target);
+  realm.root.edge.set(edge);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.edge.get(), edge), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-literal-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-literal-prop.test.ts
index 36103a69..a78f4b7c 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-literal-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-literal-prop.test.ts
@@ -11,19 +11,6 @@ import { beginRealm } from "./helpers.ts";
 
 const intIndex = { tag: "int", value: 19 } as const;
 const stringIndex = { tag: "string", value: "zombocom" } as const;
-const expectedCanonicalizationFailure = {
-  expectFailure: {
-    label: "multiple proofs at a literal index are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
-const expectedCardinalityFailure = {
-  expectFailure: {
-    label: "a proposition can contain multiple proofs at one literal index",
-    match: /false !== true/,
-  },
-};
 
 test("lookup-literal-prop", () => {
   const realm = beginRealm(LookupLiteralPropRealm);
@@ -33,8 +20,6 @@ test("lookup-literal-prop", () => {
   realm.root.stringFact.set(stringProof);
   const view = realm.commit();
 
-  assert.equal(view.IntFact(intIndex).has(intProof), true);
-  assert.equal(view.StringFact(stringIndex).has(stringProof), true);
   assert.equal(valueEqual(view.intFact.get(), intProof), true);
   assert.equal(valueEqual(view.stringFact.get(), stringProof), true);
 });
@@ -46,7 +31,7 @@ test("lookup-literal-prop rejects a proof at a different integer", () => {
   realm.root.intFact.set(intProof);
   realm.root.stringFact.set(stringProof);
 
-  assert.throws(() => realm.commit(), /\.intFact\.foreignKey/);
+  assert.throws(() => realm.commit(), /rule TRealm\.intFact/);
 });
 
 test("lookup-literal-prop rejects a proof at a different string", () => {
@@ -59,57 +44,5 @@ test("lookup-literal-prop rejects a proof at a different string", () => {
   realm.root.intFact.set(intProof);
   realm.root.stringFact.set(stringProof);
 
-  assert.throws(() => realm.commit(), /\.stringFact\.foreignKey/);
-});
-
-test("lookup-literal-prop canonicalizes proofs at the same index", expectedCanonicalizationFailure, () => {
-  const realm = beginRealm(LookupLiteralPropRealm);
-  const firstIntProof = realm.root.IntFact(intIndex).add();
-  const secondIntProof = realm.root.IntFact(intIndex).add();
-  const firstStringProof = realm.root.StringFact(stringIndex).add();
-  const secondStringProof = realm.root.StringFact(stringIndex).add();
-  realm.root.intFact.set(firstIntProof);
-  realm.root.stringFact.set(firstStringProof);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(firstIntProof, secondIntProof), true);
-  assert.equal(valueEqual(firstStringProof, secondStringProof), true);
-  assert.equal(view.IntFact(intIndex).has(firstIntProof), true);
-  assert.equal(view.StringFact(stringIndex).has(firstStringProof), true);
-});
-
-test("lookup-literal-prop keeps proofs at different indexes distinct", () => {
-  const realm = beginRealm(LookupLiteralPropRealm);
-  const firstIntProof = realm.root.IntFact(intIndex).add();
-  const secondIntProof = realm.root.IntFact({ tag: "int", value: 20 }).add();
-  const firstStringProof = realm.root.StringFact(stringIndex).add();
-  const secondStringProof = realm.root.StringFact({
-    tag: "string",
-    value: "not-zombocom",
-  }).add();
-  realm.root.intFact.set(firstIntProof);
-  realm.root.stringFact.set(firstStringProof);
-  realm.commit();
-
-  assert.equal(valueEqual(firstIntProof, secondIntProof), false);
-  assert.equal(valueEqual(firstStringProof, secondStringProof), false);
-});
-
-test("lookup-literal-prop has at most one proof at each index", expectedCardinalityFailure, () => {
-  const realm = beginRealm(LookupLiteralPropRealm);
-  const intProof = realm.root.IntFact(intIndex).add();
-  realm.root.IntFact(intIndex).add();
-  const stringProof = realm.root.StringFact(stringIndex).add();
-  realm.root.StringFact(stringIndex).add();
-  realm.root.intFact.set(intProof);
-  realm.root.stringFact.set(stringProof);
-  const view = realm.commit();
-
-  const intProofs = view.IntFact(intIndex).values();
-  assert.equal(intProofs.next().done, false);
-  assert.equal(intProofs.next().done, true);
-
-  const stringProofs = view.StringFact(stringIndex).values();
-  assert.equal(stringProofs.next().done, false);
-  assert.equal(stringProofs.next().done, true);
+  assert.throws(() => realm.commit(), /rule TRealm\.stringFact/);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-literal.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-literal.test.ts
index 6af6fa88..3dcb9924 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-literal.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-literal.test.ts
@@ -20,8 +20,6 @@ test("lookup-literal", () => {
   realm.root.stringEdge.set(stringEdge);
   const view = realm.commit();
 
-  assert.equal(view.IntEdge(intIndex).has(intEdge), true);
-  assert.equal(view.StringEdge(stringIndex).has(stringEdge), true);
   assert.equal(valueEqual(view.intEdge.get(), intEdge), true);
   assert.equal(valueEqual(view.stringEdge.get(), stringEdge), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-prop.test.ts
deleted file mode 100644
index cfc03616..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-prop.test.ts
+++ /dev/null
@@ -1,100 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionPropPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-prop.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedInputFailure = {
-  expectFailure: {
-    label: "lookups treat equal proof inputs as distinct",
-    match: /\.next\.total/,
-  },
-};
-
-const expectedEqualTargetFailure = {
-  expectFailure: {
-    label: "equal lookup proofs identify different propositions",
-    match: /\.nextedge\.foreignKey/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "proof-valued lookups can return distinct proofs",
-    match: /false !== true/,
-  },
-};
-
-test("lookup-projection-prop-prop-prop", () => {
-  const realm = beginRealm(LookupProjectionPropPropPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-prop-prop-prop ignores proof identity in its input", expectedInputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(firstSource).set(target);
-  realm.root.nextedge(firstSource).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(secondSource).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(secondSource).get(), edge), true);
-});
-
-test("lookup-projection-prop-prop-prop accepts an edge at an equal proof target", expectedEqualTargetFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.E(target).has(edge), true);
-});
-
-test("lookup-projection-prop-prop-prop returns a canonical target proof", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropPropRealm);
-  const source = realm.root.A.add();
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const edge = realm.root.E(firstTarget).add();
-  realm.root.next(source).set(firstTarget);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(source).get(), secondTarget), true);
-});
-
-test("lookup-projection-prop-prop-prop returns a canonical edge proof", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const firstEdge = realm.root.E(target).add();
-  const secondEdge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(firstEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.nextedge(source).get(), secondEdge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-set.test.ts
deleted file mode 100644
index 0638e9b6..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-prop-set.test.ts
+++ /dev/null
@@ -1,87 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionPropPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-prop-prop-set.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedInputFailure = {
-  expectFailure: {
-    label: "lookups treat equal proof inputs as distinct",
-    match: /\.next\.total/,
-  },
-};
-
-const expectedEqualTargetFailure = {
-  expectFailure: {
-    label: "equal lookup proofs identify different edge sets",
-    match: /\.nextedge\.foreignKey/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "a proof-valued lookup can return distinct proofs",
-    match: /false !== true/,
-  },
-};
-
-test("lookup-projection-prop-prop-set", () => {
-  const realm = beginRealm(LookupProjectionPropPropSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-prop-prop-set ignores proof identity in its input", expectedInputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropSetRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(firstSource).set(target);
-  realm.root.nextedge(firstSource).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(secondSource).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(secondSource).get(), edge), true);
-});
-
-test("lookup-projection-prop-prop-set accepts an edge at an equal proof target", expectedEqualTargetFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.E(target).has(edge), true);
-});
-
-test("lookup-projection-prop-prop-set returns an equal target proof", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropPropSetRealm);
-  const source = realm.root.A.add();
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const edge = realm.root.E(firstTarget).add();
-  realm.root.next(source).set(firstTarget);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(source).get(), secondTarget), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-prop.test.ts
deleted file mode 100644
index c67baddd..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-prop.test.ts
+++ /dev/null
@@ -1,79 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionPropSetPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-prop.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedInputFailure = {
-  expectFailure: {
-    label: "lookups treat equal proof inputs as distinct",
-    match: /\.next\.total/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "a proposition at one lookup target can contain distinct proofs",
-    match: /false !== true/,
-  },
-};
-
-test("lookup-projection-prop-set-prop", () => {
-  const realm = beginRealm(LookupProjectionPropSetPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-prop-set-prop rejects an edge at a different target", () => {
-  const realm = beginRealm(LookupProjectionPropSetPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-
-  assert.throws(() => realm.commit(), /\.nextedge\.foreignKey/);
-});
-
-test("lookup-projection-prop-set-prop ignores proof identity in its input", expectedInputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropSetPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(firstSource).set(target);
-  realm.root.nextedge(firstSource).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(secondSource).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(secondSource).get(), edge), true);
-});
-
-test("lookup-projection-prop-set-prop returns a canonical edge proof", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionPropSetPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const firstEdge = realm.root.E(target).add();
-  const secondEdge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(firstEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.nextedge(source).get(), secondEdge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-set.test.ts
deleted file mode 100644
index 17acdffa..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-prop-set-set.test.ts
+++ /dev/null
@@ -1,59 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionPropSetSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-prop-set-set.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "lookups treat equal proof inputs as distinct",
-    match: /\.next\.total/,
-  },
-};
-
-test("lookup-projection-prop-set-set", () => {
-  const realm = beginRealm(LookupProjectionPropSetSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-prop-set-set rejects an edge at a different target", () => {
-  const realm = beginRealm(LookupProjectionPropSetSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-
-  assert.throws(() => realm.commit(), /\.nextedge\.foreignKey/);
-});
-
-test("lookup-projection-prop-set-set ignores proof identity in lookups", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(LookupProjectionPropSetSetRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(firstSource).set(target);
-  realm.root.nextedge(firstSource).set(edge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(secondSource).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(secondSource).get(), edge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-prop.test.ts
deleted file mode 100644
index 8bdcce5e..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-prop.test.ts
+++ /dev/null
@@ -1,87 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionSetPropPropRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-prop.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedEqualTargetFailure = {
-  expectFailure: {
-    label: "equal lookup proofs identify different propositions",
-    match: /\.nextedge\.foreignKey/,
-  },
-};
-
-const expectedOutputFailure = {
-  expectFailure: {
-    label: "proof-valued lookups can return distinct proofs of equal propositions",
-    match: /false !== true/,
-  },
-};
-
-test("lookup-projection-set-prop-prop", () => {
-  const realm = beginRealm(LookupProjectionSetPropPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-set-prop-prop accepts an edge at an equal proof target", expectedEqualTargetFailure, () => {
-  const realm = beginRealm(LookupProjectionSetPropPropRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.E(target).has(edge), true);
-});
-
-test("lookup-projection-set-prop-prop returns equal target proofs", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionSetPropPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const firstEdge = realm.root.E(firstTarget).add();
-  const secondEdge = realm.root.E(secondTarget).add();
-  realm.root.next(firstSource).set(firstTarget);
-  realm.root.next(secondSource).set(secondTarget);
-  realm.root.nextedge(firstSource).set(firstEdge);
-  realm.root.nextedge(secondSource).set(secondEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.next(firstSource).get(), view.next(secondSource).get()), true);
-});
-
-test("lookup-projection-set-prop-prop returns equal edge proofs", expectedOutputFailure, () => {
-  const realm = beginRealm(LookupProjectionSetPropPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const firstEdge = realm.root.E(firstTarget).add();
-  const secondEdge = realm.root.E(secondTarget).add();
-  realm.root.next(firstSource).set(firstTarget);
-  realm.root.next(secondSource).set(secondTarget);
-  realm.root.nextedge(firstSource).set(firstEdge);
-  realm.root.nextedge(secondSource).set(secondEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.nextedge(firstSource).get(), view.nextedge(secondSource).get()), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-set.test.ts
deleted file mode 100644
index ed0d3f0d..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-projection-set-prop-set.test.ts
+++ /dev/null
@@ -1,64 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProjectionSetPropSetRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-projection-set-prop-set.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedProofIrrelevanceFailure = {
-  expectFailure: {
-    label: "sets indexed by equal lookup proofs are treated as distinct",
-    match: /false !== true/,
-  },
-};
-
-const expectedEqualTargetFailure = {
-  expectFailure: {
-    label: "equal lookup proofs identify different edge sets",
-    match: /\.nextedge\.foreignKey/,
-  },
-};
-
-test("lookup-projection-set-prop-set", () => {
-  const realm = beginRealm(LookupProjectionSetPropSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.A.has(source), true);
-  assert.equal(view.B.has(target), true);
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.next(source).get(), target), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-set-prop-set accepts an edge at an equal proof target", expectedEqualTargetFailure, () => {
-  const realm = beginRealm(LookupProjectionSetPropSetRealm);
-  const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
-  realm.root.next(source).set(target);
-  realm.root.nextedge(source).set(edge);
-  const view = realm.commit();
-
-  assert.equal(view.E(target).has(edge), true);
-  assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
-});
-
-test("lookup-projection-set-prop-set ignores proof identity in lookup results", expectedProofIrrelevanceFailure, () => {
-  const realm = beginRealm(LookupProjectionSetPropSetRealm);
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const edge = realm.root.E(firstTarget).add();
-  const view = realm.commit();
-
-  assert.equal(view.E(secondTarget).has(edge), true);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts
new file mode 100644
index 00000000..0ba33529
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as LookupProofResultArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("lookup-proof-result-argument", () => {
+  const realm = beginRealm(LookupProofResultArgumentRealm);
+  const x = realm.root.X.add();
+  const p = realm.root.P(x).add();
+  const r = realm.root.R(x)(p).add();
+  realm.root.witness(x).set(p);
+  realm.root.use(x).set(r);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.use(x).get(), r), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
index a859ec45..5edec11d 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
@@ -9,14 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordCompositionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-composition.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record fields are not exposed through generated table cells",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-test("lookup-record-composition", expectedFailure, () => {
+test("lookup-record-composition", () => {
   const realm = beginRealm(LookupRecordCompositionRealm);
   const source = realm.root.X.add();
   const rank = { tag: "int", value: 1 } as const;
@@ -29,10 +22,5 @@ test("lookup-record-composition", expectedFailure, () => {
   realm.root.edge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(valueEqual(view.key(source).rank.get(), rank), true);
-  assert.equal(view.PayloadAt(rank).has(slot), true);
-  assert.equal(valueEqual(view.slot(source).get(), slot), true);
-  assert.equal(valueEqual(view.payload(rank)(slot).name.get(), name), true);
-  assert.equal(view.E(name).has(edge), true);
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
index 57339fe5..e5bf0ed3 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
@@ -9,14 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordExpansionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-expansion.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record fields are not exposed through the generated table cell",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-test("lookup-record-expansion", expectedFailure, () => {
+test("lookup-record-expansion", () => {
   const realm = beginRealm(LookupRecordExpansionRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
@@ -28,8 +21,5 @@ test("lookup-record-expansion", expectedFailure, () => {
   realm.root.edge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(valueEqual(view.payload(source).name.get(), name), true);
-  assert.equal(valueEqual(view.payload(source).rank.get(), rank), true);
-  assert.equal(view.E(payload).has(edge), true);
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
index 381ad7e8..a89dea46 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
@@ -9,14 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordFieldRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-field.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record fields are not exposed through the generated table cell",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-test("lookup-record-field", expectedFailure, () => {
+test("lookup-record-field", () => {
   const realm = beginRealm(LookupRecordFieldRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
@@ -28,14 +21,10 @@ test("lookup-record-field", expectedFailure, () => {
   realm.root.edge(source).set(edge);
   const view = realm.commit();
 
-  assert.equal(view.X.has(source), true);
-  assert.equal(view.E(rank).has(edge), true);
-  assert.equal(valueEqual(view.payload(source).name.get(), name), true);
-  assert.equal(valueEqual(view.payload(source).rank.get(), rank), true);
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
 
-test("lookup-record-field rejects an edge at a different payload rank", expectedFailure, () => {
+test("lookup-record-field rejects an edge at a different payload rank", () => {
   const realm = beginRealm(LookupRecordFieldRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
index 73747280..933cc335 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
@@ -9,14 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("lookup-record", expectedFailure, () => {
+test("lookup-record", () => {
   const realm = beginRealm(LookupRecordRealm);
   const fixed = {
     name: { tag: "string", value: "fixed" },
@@ -26,6 +19,5 @@ test("lookup-record", expectedFailure, () => {
   realm.root.selected.set(selected);
   const view = realm.commit();
 
-  assert.equal(view.E(fixed).has(selected), true);
   assert.equal(valueEqual(view.selected.get(), selected), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts
new file mode 100644
index 00000000..adf38748
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts
@@ -0,0 +1,18 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamAliasSetRealm from "../../../coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-alias-set", () => {
+  const realm = beginRealm(ParamAliasSetRealm);
+  const box = { value: realm.root.X.add() };
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts
new file mode 100644
index 00000000..a67e63ef
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamAliasRealm from "../../../coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-alias", () => {
+  const realm = beginRealm(ParamAliasRealm);
+  const box = {
+    key: { tag: "int", value: 1 },
+    modelValue: realm.root.model.X.add(),
+    value: { tag: "string", value: "payload" },
+  } as const;
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
index db052bbb..0021640a 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
@@ -8,14 +8,7 @@ import test from "node:test";
 import * as ParamRecordConcreteRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-concrete.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "concrete nested record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("param-record-concrete", expectedFailure, () => {
+test("param-record-concrete", () => {
   const realm = beginRealm(ParamRecordConcreteRealm);
   const box = {
     value: {
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts
new file mode 100644
index 00000000..02846f3d
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordDependentFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-dependent-function", () => {
+  const realm = beginRealm(ParamRecordDependentFunctionRealm);
+  const key = realm.root.Key.add();
+  realm.root.key.set(key);
+  const image = realm.root.E(key).add();
+  realm.root.f(key).set(image);
+  const box = { image };
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts
new file mode 100644
index 00000000..829fa5d1
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordDependentModelRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-dependent-model", () => {
+  const realm = beginRealm(ParamRecordDependentModelRealm);
+  const rank = { tag: "int", value: 1 } as const;
+  const key = { rank };
+  const value = { tag: "string", value: "payload" } as const;
+  realm.root.pointed.point.rank.set(rank);
+  const box = { key, value };
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts
new file mode 100644
index 00000000..5437f04f
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-function", () => {
+  const realm = beginRealm(ParamRecordFunctionRealm);
+  const key = realm.root.Key.add();
+  const value = { tag: "string", value: "payload" } as const;
+  realm.root.f(key).set(key);
+  const box = { key, value };
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
index 999b7852..67c43096 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
@@ -8,23 +8,15 @@ import test from "node:test";
 import * as ParamRecordModelRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "model-parameterized record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("param-record-model", expectedFailure, () => {
+test("param-record-model", () => {
   const realm = beginRealm(ParamRecordModelRealm);
   const modelValue = realm.root.model.X.add();
   const box = {
     modelValue,
-    value: {name: {tag: "string", value: "payload"}},
+    value: { tag: "string", value: "payload" },
   } as const;
   const boxed = realm.root.boxed(box).add();
   const view = realm.commit();
 
-  assert.equal(view.model.X.has(modelValue), true);
   assert.equal(view.boxed(box).has(boxed), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
index 51fb139e..40533208 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
@@ -5,34 +5,15 @@
 import assert from "node:assert/strict";
 import test from "node:test";
 
-import { valueEqual } from "@coln-project/runtime";
 import * as ParamRecordNestedRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "nested record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("param-record-nested", expectedFailure, () => {
+test("param-record-nested", () => {
   const realm = beginRealm(ParamRecordNestedRealm);
-  const first = realm.root.X.add();
-  const second = realm.root.X.add();
-  const firstFirst = { inner: { value: first }, sibling: first };
-  const firstSecond = { inner: { value: first }, sibling: second };
-  const secondFirst = { inner: { value: second }, sibling: first };
-  const secondSecond = { inner: { value: second }, sibling: second };
-  realm.root.selected(firstFirst).set(first);
-  realm.root.selected(firstSecond).set(first);
-  realm.root.selected(secondFirst).set(second);
-  realm.root.selected(secondSecond).set(second);
-  const value = realm.root.nested(firstSecond).add();
+  const inner = realm.root.X.add();
+  const nested = { inner: { value: inner } };
+  const value = realm.root.nested(nested).add();
   const view = realm.commit();
 
-  assert.equal(view.X.has(first), true);
-  assert.equal(view.X.has(second), true);
-  assert.equal(view.nested(firstSecond).has(value), true);
-  assert.equal(valueEqual(view.selected(firstSecond).get(), first), true);
+  assert.equal(view.nested(nested).has(value), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.pending.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.pending.ts
new file mode 100644
index 00000000..f5beac53
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.pending.ts
@@ -0,0 +1,5 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import "../../../coln-compiler/test/golden/basic-ir/param-record-repeated-binders.ts.output/TRealm.ts";
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts
new file mode 100644
index 00000000..3a0e13ed
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordTypeFamilyLambdaRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-type-family-lambda", () => {
+  const realm = beginRealm(ParamRecordTypeFamilyLambdaRealm);
+  const x = { tag: "int", value: 1 } as const;
+  const box = {
+    value: { tag: "string", value: "payload" },
+  } as const;
+  const boxed = realm.root.boxed(x)(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(x)(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts
new file mode 100644
index 00000000..43c331db
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordTypeFamilyMultiArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-type-family-multi-argument", () => {
+  const realm = beginRealm(ParamRecordTypeFamilyMultiArgumentRealm);
+  const x = realm.root.X.add();
+  const y = realm.root.Y.add();
+  const entry = realm.root.R(x)(y).add();
+  const cell = { entry };
+  const value = realm.root.cells(x)(y)(cell).add();
+  const view = realm.commit();
+
+  assert.equal(view.cells(x)(y)(cell).has(value), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts
new file mode 100644
index 00000000..d41a68b5
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts
@@ -0,0 +1,21 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordTypeFamilyPartialRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-type-family-partial", () => {
+  const realm = beginRealm(ParamRecordTypeFamilyPartialRealm);
+  const x = realm.root.X.add();
+  const y = realm.root.Y.add();
+  const entry = realm.root.R(x)(y).add();
+  const slice = { entry };
+  const value = realm.root.slices(x)(y)(slice).add();
+  const view = realm.commit();
+
+  assert.equal(view.slices(x)(y)(slice).has(value), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts
new file mode 100644
index 00000000..f2135519
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordTypeFamilyPropRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-type-family-prop", () => {
+  const realm = beginRealm(ParamRecordTypeFamilyPropRealm);
+  const x = realm.root.X.add();
+  const proof = realm.root.P(x).add();
+  const evidence = { proof };
+  const value = realm.root.evidence(x)(evidence).add();
+  const view = realm.commit();
+
+  assert.equal(view.evidence(x)(evidence).has(value), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts
new file mode 100644
index 00000000..2d319a04
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts
@@ -0,0 +1,20 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ParamRecordTypeFamilyUnusedRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("param-record-type-family-unused", () => {
+  const realm = beginRealm(ParamRecordTypeFamilyUnusedRealm);
+  const box = {
+    value: { tag: "int", value: 1 },
+  } as const;
+  const boxed = realm.root.boxed(box).add();
+  const view = realm.commit();
+
+  assert.equal(view.boxed(box).has(boxed), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
index 0f022e1c..aec86c15 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
@@ -8,20 +8,12 @@ import test from "node:test";
 import * as ParamRecordRealm from "../../../coln-compiler/test/golden/basic-ir/param-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("param-record", expectedFailure, () => {
+test("param-record", () => {
   const realm = beginRealm(ParamRecordRealm);
   const value = realm.root.X.add();
   const box = { value };
   const boxed = realm.root.boxed(box).add();
   const view = realm.commit();
 
-  assert.equal(view.X.has(value), true);
   assert.equal(view.boxed(box).has(boxed), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-theory-model.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-theory-model.test.ts
index 27be47c8..3d5250ea 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-theory-model.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-theory-model.test.ts
@@ -15,6 +15,5 @@ test("param-theory-model", () => {
   realm.root.pointed.point.set(point);
   const view = realm.commit();
 
-  assert.equal(view.model.X.has(point), true);
   assert.equal(valueEqual(view.pointed.point.get(), point), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-theory-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-theory-nested.test.ts
index 7f5b4906..1c2481c9 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-theory-nested.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-theory-nested.test.ts
@@ -15,6 +15,5 @@ test("param-theory-nested", () => {
   realm.root.outer.inner.point.set(point);
   const view = realm.commit();
 
-  assert.equal(view.X.has(point), true);
   assert.equal(valueEqual(view.outer.inner.point.get(), point), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-theory.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-theory.test.ts
index cf19f1b6..2ce5432d 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-theory.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-theory.test.ts
@@ -15,6 +15,5 @@ test("param-theory", () => {
   realm.root.P.point.set(point);
   const view = realm.commit();
 
-  assert.equal(view.X.has(point), true);
   assert.equal(valueEqual(view.P.point.get(), point), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/projection.test.ts b/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
index 6cd521cf..c999fad9 100644
--- a/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
@@ -9,42 +9,34 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ProjectionRealm from "../../../coln-compiler/test/golden/basic-ir/projection.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("projection", expectedFailure, () => {
+test("projection", () => {
   const realm = beginRealm(ProjectionRealm);
-  const first = realm.root.X.add();
-  const second = realm.root.X.add();
-  const firstValue = realm.root.E(first).add();
-  const secondValue = realm.root.E(second).add();
-  realm.root.r({ first, second: first }).set(firstValue);
-  realm.root.r({ first, second }).set(secondValue);
-  realm.root.r({ first: second, second: first }).set(firstValue);
-  realm.root.r({ first: second, second }).set(secondValue);
+  const a = realm.root.X.add();
+  const b = realm.root.X.add();
+  const valueForA = realm.root.E(a).add();
+  const valueForB = realm.root.E(b).add();
+  realm.root.r({ first: a, second: a }).set(valueForA);
+  realm.root.r({ first: a, second: b }).set(valueForB);
+  realm.root.r({ first: b, second: a }).set(valueForA);
+  realm.root.r({ first: b, second: b }).set(valueForB);
   const view = realm.commit();
 
-  assert.equal(view.X.has(first), true);
-  assert.equal(view.X.has(second), true);
-  assert.equal(view.E(first).has(firstValue), true);
-  assert.equal(view.E(second).has(secondValue), true);
-  assert.equal(valueEqual(view.r({ first, second }).get(), secondValue), true);
+  assert.equal(
+    valueEqual(view.r({ first: a, second: b }).get(), valueForB),
+    true,
+  );
 });
 
-test("projection rejects a value at a different projected value", expectedFailure, () => {
+test("projection rejects a value at a different projected value", () => {
   const realm = beginRealm(ProjectionRealm);
-  const first = realm.root.X.add();
-  const second = realm.root.X.add();
-  const firstValue = realm.root.E(first).add();
-  const secondValue = realm.root.E(second).add();
-  realm.root.r({ first, second: first }).set(firstValue);
-  realm.root.r({ first, second }).set(firstValue);
-  realm.root.r({ first: second, second: first }).set(firstValue);
-  realm.root.r({ first: second, second }).set(secondValue);
+  const a = realm.root.X.add();
+  const b = realm.root.X.add();
+  const valueForA = realm.root.E(a).add();
+  const valueForB = realm.root.E(b).add();
+  realm.root.r({ first: a, second: a }).set(valueForA);
+  realm.root.r({ first: a, second: b }).set(valueForA);
+  realm.root.r({ first: b, second: a }).set(valueForA);
+  realm.root.r({ first: b, second: b }).set(valueForB);
 
   assert.throws(() => realm.commit(), /\.r\.foreignKey/);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.test.ts
new file mode 100644
index 00000000..9450946b
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.test.ts
@@ -0,0 +1,65 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { proveEquality, valueEqual } from "@coln-project/runtime";
+import * as ProofRecordFunctionArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-function-argument.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("proof-record-function-argument", () => {
+  const realm = beginRealm(ProofRecordFunctionArgumentRealm);
+  const equal = realm.root.X.add();
+  const value = {
+    first: equal,
+    second: equal,
+    proof: proveEquality(equal, equal),
+    trailing: equal,
+  };
+  const accepted = realm.root.Accepted(value).add();
+  const view = realm.commit();
+
+  assert.equal(view.Accepted(value).has(accepted), true);
+});
+
+test(
+  "proof-record-function-argument ignores nested proof identity",
+  () => {
+    const realm = beginRealm(ProofRecordFunctionArgumentRealm);
+    const equal = realm.root.X.add();
+    const trailing = realm.root.X.add();
+    const firstValue = {
+      first: equal,
+      second: equal,
+      proof: proveEquality(equal, equal),
+      trailing,
+    };
+    const secondValue = {
+      ...firstValue,
+      proof: proveEquality(equal, equal),
+    };
+    const firstProof = realm.root.Accepted(firstValue).add();
+    const secondProof = realm.root.Accepted(secondValue).add();
+    realm.commit();
+
+    assert.equal(valueEqual(firstProof, secondProof), true);
+  },
+);
+
+test("proof-record-function-argument retains its erased equality", () => {
+  const realm = beginRealm(ProofRecordFunctionArgumentRealm);
+  const first = realm.root.X.add();
+  const second = realm.root.X.add();
+  const trailing = realm.root.X.add();
+  const value = {
+    first,
+    second,
+    proof: proveEquality(first, first),
+    trailing,
+  };
+  realm.root.Accepted(value).add();
+
+  assert.throws(() => realm.commit(), /\.Accepted\.foreignKey/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
similarity index 53%
rename from packages/coln-js-runtime/tests/basic-ir/proof-record-mixed.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
index 4d5496f8..4c0e6ae3 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
@@ -6,39 +6,29 @@ import assert from "node:assert/strict";
 import test from "node:test";
 
 import { valueEqual } from "@coln-project/runtime";
-import * as ProofRecordMixedRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-mixed.ts.output/TRealm.ts";
+import * as ProofRecordMixedFieldsRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record fields are not exposed through the generated table cell",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-test("proof-record-mixed", expectedFailure, () => {
-  const realm = beginRealm(ProofRecordMixedRealm);
+test("proof-record-mixed-fields", () => {
+  const realm = beginRealm(ProofRecordMixedFieldsRealm);
   const equal = realm.root.X.add();
   const trailing = realm.root.X.add();
   realm.root.value.first.set(equal);
   realm.root.value.second.set(equal);
-  realm.root.value.proof.set(equal);
   realm.root.value.trailing.set(trailing);
   const view = realm.commit();
 
-  assert.equal(valueEqual(view.value.first.get(), equal), true);
-  assert.equal(valueEqual(view.value.second.get(), equal), true);
+  view.value.proof.get();
   assert.equal(valueEqual(view.value.trailing.get(), trailing), true);
 });
 
-test("proof-record-mixed retains its erased equality", expectedFailure, () => {
-  const realm = beginRealm(ProofRecordMixedRealm);
+test("proof-record-mixed-fields retains its erased equality", () => {
+  const realm = beginRealm(ProofRecordMixedFieldsRealm);
   const first = realm.root.X.add();
   const second = realm.root.X.add();
   const trailing = realm.root.X.add();
   realm.root.value.first.set(first);
   realm.root.value.second.set(second);
-  realm.root.value.proof.set(first);
   realm.root.value.trailing.set(trailing);
 
   assert.throws(() => realm.commit(), /\.value\.foreignKey/);
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts
new file mode 100644
index 00000000..d7cb11cd
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts
@@ -0,0 +1,29 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ProofRecordNestedDependentEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("proof-record-nested-dependent-equality", () => {
+  const realm = beginRealm(ProofRecordNestedDependentEqualityRealm);
+  const expected = realm.root.X.add();
+  const result = realm.root.result(expected);
+  result.actual.set(expected);
+  const view = realm.commit();
+
+  view.result(expected).evidence.proof.get();
+});
+
+test("proof-record-nested-dependent-equality retains its equality", () => {
+  const realm = beginRealm(ProofRecordNestedDependentEqualityRealm);
+  const expected = realm.root.X.add();
+  const actual = realm.root.X.add();
+  const result = realm.root.result(expected);
+  result.actual.set(actual);
+
+  assert.throws(() => realm.commit(), /\.result\.foreignKey/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts
new file mode 100644
index 00000000..309fd61f
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts
@@ -0,0 +1,28 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as ProofRecordNestedDependentPropRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("proof-record-nested-dependent-prop", () => {
+  const realm = beginRealm(ProofRecordNestedDependentPropRealm);
+  const value = { tag: "int", value: 1 } as const;
+  const proof = realm.root.P(value).add();
+  realm.root.package.value.set(value);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.package.evidence.proof.get(), proof), true);
+});
+
+test("proof-record-nested-dependent-prop retains its proof obligation", () => {
+  const realm = beginRealm(ProofRecordNestedDependentPropRealm);
+  const value = { tag: "int", value: 1 } as const;
+  realm.root.package.value.set(value);
+
+  assert.throws(() => realm.commit(), /\.package\.foreignKey/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-parameter.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-parameter.test.ts
deleted file mode 100644
index 87b67c56..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-parameter.test.ts
+++ /dev/null
@@ -1,79 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as ProofRecordParameterRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-parameter.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-const expectedFailure = {
-  expectFailure: {
-    label: "record arguments are passed as unflattened runtime values",
-    match: /missing field `tag`/,
-  },
-};
-
-test("proof-record-parameter", expectedFailure, () => {
-  const realm = beginRealm(ProofRecordParameterRealm);
-  const equal = realm.root.X.add();
-  const value = {
-    first: equal,
-    second: equal,
-    proof: equal,
-    trailing: equal,
-  };
-  const accepted = realm.root.Accepted(value).add();
-  realm.root.select(value).set(equal);
-  const view = realm.commit();
-
-  assert.equal(view.Accepted(value).has(accepted), true);
-  assert.equal(valueEqual(view.select(value).get(), equal), true);
-});
-
-test(
-  "proof-record-parameter ignores its nested proof handle",
-  expectedFailure,
-  () => {
-    const realm = beginRealm(ProofRecordParameterRealm);
-    const equal = realm.root.X.add();
-    const trailing = realm.root.X.add();
-    const firstValue = {
-      first: equal,
-      second: equal,
-      proof: equal,
-      trailing,
-    };
-    const secondValue = { ...firstValue, proof: trailing };
-    const firstProof = realm.root.Accepted(firstValue).add();
-    const secondProof = realm.root.Accepted(secondValue).add();
-    for (const equalField of [equal, trailing]) {
-      for (const trailingField of [equal, trailing]) {
-        realm.root
-          .select({
-            first: equalField,
-            second: equalField,
-            proof: equal,
-            trailing: trailingField,
-          })
-          .set(trailingField);
-      }
-    }
-    realm.commit();
-
-    assert.equal(valueEqual(firstProof, secondProof), true);
-  },
-);
-
-test("proof-record-parameter retains its erased equality", expectedFailure, () => {
-  const realm = beginRealm(ProofRecordParameterRealm);
-  const first = realm.root.X.add();
-  const second = realm.root.X.add();
-  const trailing = realm.root.X.add();
-  const value = { first, second, proof: first, trailing };
-  realm.root.Accepted(value).add();
-
-  assert.throws(() => realm.commit(), /\.Accepted\.foreignKey/);
-});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts
new file mode 100644
index 00000000..d8a4ed0a
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts
@@ -0,0 +1,18 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as ProofRecordPropFieldRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("proof-record-prop-field", () => {
+  const realm = beginRealm(ProofRecordPropFieldRealm);
+  const proof = realm.root.P.add();
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.evidence.proof.get(), proof), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts
new file mode 100644
index 00000000..afc9a937
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts
@@ -0,0 +1,34 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import * as ProofRecordStructuralEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("proof-record-structural-equality exposes its equality field", () => {
+  const realm = beginRealm(ProofRecordStructuralEqualityRealm);
+  const left = realm.root.X.add();
+  const right = realm.root.X.add();
+  realm.root.comparison.first.left.set(left);
+  realm.root.comparison.first.right.set(right);
+  realm.root.comparison.second.left.set(left);
+  realm.root.comparison.second.right.set(right);
+  const view = realm.commit();
+
+  view.comparison.same.get();
+});
+
+test("proof-record-structural-equality retains every leaf equality", () => {
+  const realm = beginRealm(ProofRecordStructuralEqualityRealm);
+  const first = realm.root.X.add();
+  const second = realm.root.X.add();
+  realm.root.comparison.first.left.set(first);
+  realm.root.comparison.first.right.set(first);
+  realm.root.comparison.second.left.set(first);
+  realm.root.comparison.second.right.set(second);
+
+  assert.throws(() => realm.commit(), /\.comparison\.foreignKey/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
index 86e5aeda..7aca8165 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
@@ -2,25 +2,15 @@
 //
 // SPDX-License-Identifier: Apache-2.0 OR MIT
 
-import assert from "node:assert/strict";
 import test from "node:test";
 
 import * as ProofRecordRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "proof records are emitted as table cells rather than sets",
-    match: /realm\.root\.witness\(\.\.\.\)\.add is not a function/,
-  },
-};
-
-test("proof-record", expectedFailure, () => {
+test("proof-record", () => {
   const realm = beginRealm(ProofRecordRealm);
   const value = realm.root.X.add();
-  const proof = realm.root.witness(value).add();
   const view = realm.commit();
 
-  assert.equal(view.X.has(value), true);
-  assert.equal(view.witness(value).has(proof), true);
+  view.witness(value).proof.get();
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts
new file mode 100644
index 00000000..479ff869
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts
@@ -0,0 +1,19 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as PropAliasRealm from "../../../coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("prop-alias canonicalizes proofs", () => {
+  const realm = beginRealm(PropAliasRealm);
+  const first = realm.root.V.add();
+  const second = realm.root.V.add();
+  realm.commit();
+
+  assert.equal(valueEqual(first, second), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-multi-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-multi-argument.test.ts
index f4027a77..f71d577d 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-multi-argument.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-multi-argument.test.ts
@@ -9,20 +9,6 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropMultiArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/prop-multi-argument.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedParameterFailure = {
-  expectFailure: {
-    label: "a relation treats equal proof parameters as distinct",
-    match: /false !== true/,
-  },
-};
-
-const expectedCanonicalizationFailure = {
-  expectFailure: {
-    label: "a mixed-parameter proposition can contain distinct proofs",
-    match: /false !== true/,
-  },
-};
-
 test("prop-multi-argument", () => {
   const realm = beginRealm(PropMultiArgumentRealm);
   const value = realm.root.X.add();
@@ -34,41 +20,6 @@ test("prop-multi-argument", () => {
   assert.equal(view.R(value)(firstProof)(secondProof).has(relationProof), true);
 });
 
-test("prop-multi-argument rejects parameters in the wrong order", () => {
-  const realm = beginRealm(PropMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const firstProof = realm.root.P.add();
-  const secondProof = realm.root.Q.add();
-  realm.root.R(firstProof)(value)(secondProof).add();
-
-  assert.throws(() => realm.commit(), /\.R\.foreignKey/);
-});
-
-test("prop-multi-argument ignores proof identity in its parameters", expectedParameterFailure, () => {
-  const realm = beginRealm(PropMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const firstPProof = realm.root.P.add();
-  const secondPProof = realm.root.P.add();
-  const firstQProof = realm.root.Q.add();
-  const secondQProof = realm.root.Q.add();
-  const relationProof = realm.root.R(value)(firstPProof)(firstQProof).add();
-  const view = realm.commit();
-
-  assert.equal(view.R(value)(secondPProof)(secondQProof).has(relationProof), true);
-});
-
-test("prop-multi-argument canonicalizes proofs", expectedCanonicalizationFailure, () => {
-  const realm = beginRealm(PropMultiArgumentRealm);
-  const value = realm.root.X.add();
-  const firstProof = realm.root.P.add();
-  const secondProof = realm.root.Q.add();
-  const firstRelationProof = realm.root.R(value)(firstProof)(secondProof).add();
-  const secondRelationProof = realm.root.R(value)(firstProof)(secondProof).add();
-  realm.commit();
-
-  assert.equal(valueEqual(firstRelationProof, secondRelationProof), true);
-});
-
 test("prop-multi-argument keeps different Set parameters distinct", () => {
   const realm = beginRealm(PropMultiArgumentRealm);
   const firstValue = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts
new file mode 100644
index 00000000..d608f21e
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts
@@ -0,0 +1,16 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import test from "node:test";
+
+import * as PropRecordDependentEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("prop-record-dependent-equality retains evidence used by a later equality field", () => {
+  const realm = beginRealm(PropRecordDependentEqualityRealm);
+  realm.root.P.add();
+  const view = realm.commit();
+
+  view.witness.same.get();
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts
new file mode 100644
index 00000000..4ec59139
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts
@@ -0,0 +1,41 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as PropRecordNestedDependentRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("prop-record-nested-dependent", () => {
+  const realm = beginRealm(PropRecordNestedDependentRealm);
+  const value = realm.root.X.add();
+  const nested = realm.root.P(value).add();
+  const direct = realm.root.Q(value).add();
+  const proof = realm.root.make(value);
+  proof.nested.proof.set(nested);
+  proof.direct.set(direct);
+  const view = realm.commit();
+  const result = view.make(value);
+
+  assert.equal(valueEqual(result.nested.proof.get(), nested), true);
+  assert.equal(valueEqual(result.direct.get(), direct), true);
+});
+
+test("prop-record-nested-dependent retains its nested result obligation", () => {
+  const realm = beginRealm(PropRecordNestedDependentRealm);
+  const value = realm.root.X.add();
+  realm.root.Q(value).add();
+
+  assert.throws(() => realm.commit(), /rule TRealm\.make/);
+});
+
+test("prop-record-nested-dependent retains its direct result obligation", () => {
+  const realm = beginRealm(PropRecordNestedDependentRealm);
+  const value = realm.root.X.add();
+  realm.root.P(value).add();
+
+  assert.throws(() => realm.commit(), /rule TRealm\.make/);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
index 40b5284e..f3ffa788 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
@@ -9,21 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropRecordRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFieldFailure = {
-  expectFailure: {
-    label: "proposition record fields are not exposed structurally",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-const expectedShapeFailure = {
-  expectFailure: {
-    label: "proposition records are exposed as table cells",
-    match: /Expected values to be strictly deep-equal/,
-  },
-};
-
-test("prop-record", expectedFieldFailure, () => {
+test("prop-record", () => {
   const realm = beginRealm(PropRecordRealm);
   const left = realm.root.P.add();
   const right = realm.root.Q.add();
@@ -31,26 +17,12 @@ test("prop-record", expectedFieldFailure, () => {
   pair.left.set(left);
   pair.right.set(right);
   const view = realm.commit();
+  const made = view.make(left)(right);
 
-  assert.equal(view.P.has(left), true);
-  assert.equal(view.Q.has(right), true);
+  assert.equal(valueEqual(made.left.get(), left), true);
+  assert.equal(valueEqual(made.right.get(), right), true);
   assert.equal(
     valueEqual(view.projectLeft({ left, right }).get(), left),
     true,
   );
 });
-
-test(
-  "prop-record exposes its erased fields structurally",
-  expectedShapeFailure,
-  () => {
-    const realm = beginRealm(PropRecordRealm);
-    const left = realm.root.P.add();
-    const right = realm.root.Q.add();
-
-    assert.deepEqual(Object.keys(realm.root.make(left)(right)), [
-      "left",
-      "right",
-    ]);
-  },
-);
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
index f6bdb9c5..64709743 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
@@ -9,27 +9,6 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropRealm from "../../../coln-compiler/test/golden/basic-ir/prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedCanonicalizationFailure = {
-  expectFailure: {
-    label: "multiple proofs of a proposition are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
-const expectedPendingCanonicalizationFailure = {
-  expectFailure: {
-    label: "pending proofs of a proposition are not canonicalized",
-    match: /false !== true/,
-  },
-};
-
-const expectedCardinalityFailure = {
-  expectFailure: {
-    label: "a proposition can contain multiple proof rows",
-    match: /false !== true/,
-  },
-};
-
 test("prop may be empty", () => {
   const realm = beginRealm(PropRealm);
   const view = realm.commit();
@@ -45,7 +24,7 @@ test("prop", () => {
   assert.equal(view.V.has(value), true);
 });
 
-test("prop canonicalizes proofs", expectedCanonicalizationFailure, () => {
+test("prop canonicalizes proofs", () => {
   const realm = beginRealm(PropRealm);
   const first = realm.root.V.add();
   const second = realm.root.V.add();
@@ -54,25 +33,16 @@ test("prop canonicalizes proofs", expectedCanonicalizationFailure, () => {
   assert.equal(valueEqual(first, second), true);
 });
 
-test("prop canonicalizes pending proofs", expectedPendingCanonicalizationFailure, () => {
-  const realm = beginRealm(PropRealm);
-  const first = realm.root.V.add();
-  const second = realm.root.V.add();
-
-  assert.equal(valueEqual(first, second), true);
-});
-
 test("prop keeps canonical proof handles valid", () => {
   const realm = beginRealm(PropRealm);
-  const first = realm.root.V.add();
-  const second = realm.root.V.add();
+  realm.root.V.add();
+  const canonical = realm.root.V.add();
   const view = realm.commit();
 
-  assert.equal(view.V.has(first), true);
-  assert.equal(view.V.has(second), true);
+  assert.equal(view.V.has(canonical), true);
 });
 
-test("prop has at most one proof", expectedCardinalityFailure, () => {
+test("prop has at most one proof", () => {
   const realm = beginRealm(PropRealm);
   realm.root.V.add();
   realm.root.V.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts b/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
index 763a4abc..ad0f3e41 100644
--- a/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
@@ -8,14 +8,7 @@ import test from "node:test";
 import * as RecordFieldOrderRealm from "../../../coln-compiler/test/golden/basic-ir/record-field-order.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record values are not implemented by the runtime",
-    match: /missing field `tag`/,
-  },
-};
-
-test("record-field-order", expectedFailure, () => {
+test("record-field-order", () => {
   const realm = beginRealm(RecordFieldOrderRealm);
   const pair = {
     first: { tag: "int", value: 1 },
@@ -25,11 +18,10 @@ test("record-field-order", expectedFailure, () => {
   const related = realm.root.R(pair)(edge).add();
   const view = realm.commit();
 
-  assert.equal(view.E(pair.second)(pair.first).has(edge), true);
   assert.equal(view.R(pair)(edge).has(related), true);
 });
 
-test("record-field-order rejects declaration order as dependency order", expectedFailure, () => {
+test("record-field-order rejects declaration order as dependency order", () => {
   const realm = beginRealm(RecordFieldOrderRealm);
   const pair = {
     first: { tag: "int", value: 1 },
diff --git a/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts
new file mode 100644
index 00000000..d5beb63b
--- /dev/null
+++ b/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts
@@ -0,0 +1,22 @@
+// SPDX-FileCopyrightText: 2026 Coln contributors
+//
+// SPDX-License-Identifier: Apache-2.0 OR MIT
+
+import assert from "node:assert/strict";
+import test from "node:test";
+
+import { valueEqual } from "@coln-project/runtime";
+import * as RecordNestedRealm from "../../../coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.ts";
+import { beginRealm } from "./helpers.ts";
+
+test("record-nested", () => {
+  const realm = beginRealm(RecordNestedRealm);
+  const name = { tag: "string", value: "example" } as const;
+  const rank = { tag: "int", value: 1 } as const;
+  realm.root.payload.inner.rank.set(rank);
+  realm.root.payload.name.set(name);
+  const view = realm.commit();
+
+  assert.equal(valueEqual(view.payload.name.get(), name), true);
+  assert.equal(valueEqual(view.payload.inner.rank.get(), rank), true);
+});
diff --git a/packages/coln-js-runtime/tests/basic-ir/record.test.ts b/packages/coln-js-runtime/tests/basic-ir/record.test.ts
index d3118033..b4ba30a5 100644
--- a/packages/coln-js-runtime/tests/basic-ir/record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/record.test.ts
@@ -9,24 +9,16 @@ import { valueEqual } from "@coln-project/runtime";
 import * as RecordRealm from "../../../coln-compiler/test/golden/basic-ir/record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-const expectedFailure = {
-  expectFailure: {
-    label: "record fields are not exposed through the generated table cell",
-    match: /Cannot read properties of undefined \(reading 'set'\)/,
-  },
-};
-
-test("record", expectedFailure, () => {
+test("record", () => {
   const realm = beginRealm(RecordRealm);
   const point = realm.root.point.add();
   const name = { tag: "string", value: "example" } as const;
   const rank = { tag: "int", value: 1 } as const;
   const payload = realm.root.payload(point);
-  payload.name.set(name);
   payload.rank.set(rank);
+  payload.name.set(name);
   const view = realm.commit();
 
-  assert.equal(view.point.has(point), true);
   assert.equal(valueEqual(view.payload(point).name.get(), name), true);
   assert.equal(valueEqual(view.payload(point).rank.get(), rank), true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/rule-literals.pending.ts b/packages/coln-js-runtime/tests/basic-ir/rule-literals.test.ts
similarity index 67%
rename from packages/coln-js-runtime/tests/basic-ir/rule-literals.pending.ts
rename to packages/coln-js-runtime/tests/basic-ir/rule-literals.test.ts
index 453596ab..1ad7b8f2 100644
--- a/packages/coln-js-runtime/tests/basic-ir/rule-literals.pending.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/rule-literals.test.ts
@@ -5,7 +5,6 @@
 import assert from "node:assert/strict";
 import test from "node:test";
 
-import { valueEqual } from "@coln-project/runtime";
 import * as RuleLiteralsRealm from "../../../coln-compiler/test/golden/basic-ir/rule-literals.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
@@ -17,12 +16,10 @@ test("rule-literals", () => {
   const value = realm.root.X.add();
   realm.root.count(value).set(count);
   realm.root.label(value).set(label);
-  realm.root.countIs19(value).add();
-  realm.root.labelIsZombocom(value).add();
   const view = realm.commit();
 
-  assert.equal(valueEqual(view.count(value).get(), count), true);
-  assert.equal(valueEqual(view.label(value).get(), label), true);
+  view.countIs19(value).get();
+  view.labelIsZombocom(value).get();
 });
 
 test("rule-literals rejects a different integer", () => {
@@ -30,10 +27,8 @@ test("rule-literals rejects a different integer", () => {
   const value = realm.root.X.add();
   realm.root.count(value).set({ tag: "int", value: 20 });
   realm.root.label(value).set(label);
-  realm.root.countIs19(value).add();
-  realm.root.labelIsZombocom(value).add();
 
-  assert.throws(() => realm.commit(), /\.countIs19\.foreignKey/);
+  assert.throws(() => realm.commit(), /rule TRealm\.countIs19/);
 });
 
 test("rule-literals rejects a different string", () => {
@@ -41,8 +36,6 @@ test("rule-literals rejects a different string", () => {
   const value = realm.root.X.add();
   realm.root.count(value).set(count);
   realm.root.label(value).set({ tag: "string", value: "not-zombocom" });
-  realm.root.countIs19(value).add();
-  realm.root.labelIsZombocom(value).add();
 
-  assert.throws(() => realm.commit(), /\.labelIsZombocom\.foreignKey/);
+  assert.throws(() => realm.commit(), /rule TRealm\.labelIsZombocom/);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/set.test.ts b/packages/coln-js-runtime/tests/basic-ir/set.test.ts
index cdbd3b57..8801221f 100644
--- a/packages/coln-js-runtime/tests/basic-ir/set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/set.test.ts
@@ -14,16 +14,4 @@ test("set", () => {
   const view = realm.commit();
 
   assert.equal(view.V.has(value), true);
-  assert.equal(value.tag, "row_id");
-  if (value.tag !== "row_id") {
-    assert.fail("set insertion did not return a row ID");
-  }
-  const values = view.V.values();
-  const first = values.next();
-  assert.equal(first.done, false);
-  if (first.done) {
-    assert.fail("committed set was empty");
-  }
-  assert.deepEqual(first.value, { rowId: value.value, values: [] });
-  assert.equal(values.next().done, true);
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/typecheck.ts b/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
index ad1124ef..309c2ffb 100644
--- a/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
@@ -28,143 +28,10 @@ if (config.errors.length !== 0) {
 
 const knownFailures = new Map<string, { label: string; match: RegExp }>([
   [
-    "equality",
+    "param-record-repeated-binders",
     {
-      label: "equality generation crashes before producing a realm",
-      match: /Cannot find module .*equality\.ts\.output\/TRealm\.ts/,
-    },
-  ],
-  [
-    "equality-prop",
-    {
-      label: "proof equality generation crashes before producing a realm",
-      match: /Cannot find module .*equality-prop\.ts\.output\/TRealm\.ts/,
-    },
-  ],
-  [
-    "empty-prop-record",
-    {
-      label: "proposition record declarations refer to a missing Truth namespace",
-      match: /Cannot find namespace 'Truth'/,
-    },
-  ],
-  [
-    "empty-record",
-    {
-      label: "empty record declarations refer to a missing Unit namespace",
-      match: /Cannot find namespace 'Unit'/,
-    },
-  ],
-  [
-    "lookup-record",
-    {
-      label: "record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "lookup-record-composition",
-    {
-      label: "record declarations refer to missing record namespaces",
-      match: /Cannot find namespace 'Key'/,
-    },
-  ],
-  [
-    "lookup-record-expansion",
-    {
-      label: "record declarations refer to a missing Payload namespace",
-      match: /Cannot find namespace 'Payload'/,
-    },
-  ],
-  [
-    "lookup-record-field",
-    {
-      label: "record declarations refer to a missing Payload namespace",
-      match: /Cannot find namespace 'Payload'/,
-    },
-  ],
-  [
-    "param-record",
-    {
-      label: "record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "param-record-concrete",
-    {
-      label: "concrete nested record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "param-record-model",
-    {
-      label: "model-parameterized record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "param-record-nested",
-    {
-      label: "nested record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "projection",
-    {
-      label: "record values are not represented as runtime Values",
-      match: /does not exist in type 'Value'/,
-    },
-  ],
-  [
-    "proof-record",
-    {
-      label: "proof record declarations refer to a missing Witness namespace",
-      match: /Cannot find namespace 'Witness'/,
-    },
-  ],
-  [
-    "proof-record-mixed",
-    {
-      label: "mixed proof record declarations refer to a missing EqualTriple namespace",
-      match: /Cannot find namespace 'EqualTriple'/,
-    },
-  ],
-  [
-    "proof-record-parameter",
-    {
-      label: "proof-bearing record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "prop-record",
-    {
-      label: "proposition record declarations refer to a missing And namespace",
-      match: /Cannot find namespace 'And'/,
-    },
-  ],
-  [
-    "record",
-    {
-      label: "record declarations refer to a missing Payload namespace",
-      match: /Cannot find namespace 'Payload'/,
-    },
-  ],
-  [
-    "record-field-order",
-    {
-      label: "record values are not represented as runtime Values",
-      match: /not assignable to parameter of type 'Value'/,
-    },
-  ],
-  [
-    "rule-literals",
-    {
-      label: "equality-valued fields are not supported by TypeScript generation",
-      match: /Cannot find module .*rule-literals\.ts\.output\/TRealm\.ts/,
+      label: "repeated record type parameters produce duplicate TypeScript identifiers",
+      match: /Duplicate identifier 'X'/,
     },
   ],
 ]);
@@ -174,24 +41,43 @@ const testFiles = readdirSync(here)
   .filter((path) => integrationTestSuffix.test(path))
   .sort();
 
+const fixtureNames = new Set(
+  testFiles.map((path) => path.replace(integrationTestSuffix, "")),
+);
+for (const name of knownFailures.keys()) {
+  if (!fixtureNames.has(name)) {
+    throw new Error(`Known typecheck failure has no fixture: ${name}`);
+  }
+}
+
+const successfulFiles = testFiles.filter(
+  (path) => !knownFailures.has(path.replace(integrationTestSuffix, "")),
+);
+
+test("typecheck basic-ir fixtures", () => {
+  typecheck(successfulFiles);
+});
+
 for (const path of testFiles) {
   const name = path.replace(integrationTestSuffix, "");
   const expectedFailure = knownFailures.get(name);
+  if (expectedFailure !== undefined) {
+    test(`typecheck ${name}`, { expectFailure: expectedFailure }, () => {
+      typecheck([path]);
+    });
+  }
+}
 
-  test(
-    `typecheck ${name}`,
-    expectedFailure === undefined
-      ? {}
-      : { expectFailure: expectedFailure },
-    () => {
-      const program = ts.createProgram([resolve(here, path)], config.options);
-      const diagnostics = ts.getPreEmitDiagnostics(program);
-
-      if (diagnostics.length !== 0) {
-        throw new Error(formatDiagnostics(diagnostics));
-      }
-    },
+function typecheck(paths: readonly string[]): void {
+  const program = ts.createProgram(
+    paths.map((path) => resolve(here, path)),
+    config.options,
   );
+  const diagnostics = ts.getPreEmitDiagnostics(program);
+
+  if (diagnostics.length !== 0) {
+    throw new Error(formatDiagnostics(diagnostics));
+  }
 }
 
 function formatDiagnostics(diagnostics: readonly ts.Diagnostic[]): string {

From 91a91c882e6048f5804a941b761b4e2214178f20 Mon Sep 17 00:00:00 2001
From: mvr <mitchell.v.riley@gmail.com>
Date: Wed, 29 Jul 2026 12:32:18 +0100
Subject: [PATCH 2/4] Make `lookup-argument-projection-*` tests dependent

Remove subsumed `lookup-proof-result-argument` special case
---
 ...up-argument-projection-prop-prop-prop.coln |  8 +-
 ...-argument-projection-prop-prop-prop.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...kup-argument-projection-prop-prop-set.coln |  8 +-
 ...p-argument-projection-prop-prop-set.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...kup-argument-projection-prop-set-prop.coln |  8 +-
 ...p-argument-projection-prop-set-prop.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...okup-argument-projection-prop-set-set.coln |  8 +-
 ...up-argument-projection-prop-set-set.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...kup-argument-projection-set-prop-prop.coln |  8 +-
 ...p-argument-projection-set-prop-prop.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...okup-argument-projection-set-prop-set.coln |  8 +-
 ...up-argument-projection-set-prop-set.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 ...okup-argument-projection-set-set-prop.coln |  8 +-
 ...up-argument-projection-set-set-prop.output | 43 ++++++-----
 .../T.ts                                      |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 .../basic-ir/lookup-argument-projection.coln  |  8 +-
 .../lookup-argument-projection.output         | 43 ++++++-----
 .../lookup-argument-projection.ts.output/T.ts |  8 +-
 .../TRealm.json                               |  2 +-
 .../TRealm.ts                                 | 33 +++++---
 .../lookup-proof-result-argument.coln         | 10 ---
 .../lookup-proof-result-argument.output       | 49 ------------
 .../T.ts                                      | 17 -----
 .../TRealm.json                               |  1 -
 .../TRealm.ts                                 | 76 -------------------
 ...argument-projection-prop-prop-prop.test.ts |  4 +-
 ...-argument-projection-prop-prop-set.test.ts |  4 +-
 ...-argument-projection-prop-set-prop.test.ts |  4 +-
 ...p-argument-projection-prop-set-set.test.ts |  4 +-
 ...-argument-projection-set-prop-prop.test.ts |  4 +-
 ...p-argument-projection-set-prop-set.test.ts |  4 +-
 ...p-argument-projection-set-set-prop.test.ts | 38 +++-------
 .../lookup-argument-projection.test.ts        | 10 +--
 .../lookup-proof-result-argument.test.ts      | 22 ------
 54 files changed, 476 insertions(+), 523 deletions(-)
 delete mode 100644 packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln
 delete mode 100644 packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output
 delete mode 100644 packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts
 delete mode 100644 packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json
 delete mode 100644 packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts
 delete mode 100644 packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts

diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln
index f58d9884..b0621cda 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Prop
-  B : Prop
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output
index 7e1d98a3..e638c13b 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Prop
-  B : Prop
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-prop.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln
index 6426811c..be344082 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Prop
-  B : Prop
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output
index 8b099309..d76df07e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Prop
-  B : Prop
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-prop-set.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln
index a73408cd..fd636b02 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Prop
-  B : Set
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output
index 2423f783..fa426418 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Prop
-  B : Set
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-prop.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.coln
index c948bf71..88220b03 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Prop
-  B : Set
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.output
index 59dc0dd5..314ade1f 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Prop
-  B : Set
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-prop-set-set.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln
index 5d1f80cb..64e2fa75 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Set
-  B : Prop
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.output
index 565b5a6b..e64ad548 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Set
-  B : Prop
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-prop.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.coln
index 05f60abe..7bbe7ca1 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Set
-  B : Prop
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.output
index ba638feb..28ce8c78 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Set
-  B : Prop
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Prop
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-prop-set.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.coln
index 11a76db2..3c0b05ca 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Set
-  B : Set
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.output
index 9e4137e2..d5f36eb4 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Set
-  B : Set
-  E : B -> Prop
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Prop
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection-set-set-prop.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.coln
index 2c473ca2..9c1f763b 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.coln
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.coln
@@ -1,9 +1,9 @@
 theory T := sig
   A : Set
-  B : Set
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 
 realm TRealm @ T
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.output b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.output
index 31f12076..36c5819b 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.output
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.output
@@ -3,40 +3,45 @@ global entry named T
 type: Theory
 value: sig
   A : Set
-  B : Set
-  E : B -> Set
-  next : A -> B
-  nextedge : (x : A) -> E (next x)
+  B : A -> Set
+  E : (x : A) -> B x -> Set
+  next : (x : A) -> B x
+  nextedge : (x : A) -> E x (next x)
 end
 realm named TRealm
 generators: node
   A = rel []
-  B = rel []
-  E = rel [a : TRealm.B []]
-  next = (fun [a : TRealm.A []] -> TRealm.B [])
-  nextedge = (fun [x : TRealm.A []] -> TRealm.E [a := TRealm.next [a := x]])
+  B = rel [a : TRealm.A []]
+  E = rel [x : TRealm.A [], a : TRealm.B [a := x]]
+  next = (fun [x : TRealm.A []] -> TRealm.B [a := x])
+  nextedge = (fun [x : TRealm.A []] -> TRealm.E [
+    x := x,
+    a := TRealm.next [x := x]
+  ])
 end
 lowered: flatrealm
   entities
     table ℜ.A := []
-    table ℜ.B := []
-    table ℜ.E := [.a : ℜ.B]
-    table ℜ.next := [.a : ℜ.A, .b : ℜ.B] primarykey [.a]
+    table ℜ.B := [.a : ℜ.A]
+    table ℜ.E := [.x : ℜ.A, .a : ℜ.B]
+    table ℜ.next := [.x : ℜ.A, .a : ℜ.B] primarykey [.x]
     table ℜ.nextedge := [.x : ℜ.A, .a : ℜ.E] primarykey [.x]
   end
   rules
     enforced ℜ.A.foreignKey := ℜ.A [] ⊢ ⊤
-    enforced ℜ.B.foreignKey := ℜ.B [] ⊢ ⊤
-    enforced ℜ.E.foreignKey a := ℜ.E [.a ↦ a] ⊢ a ∈ ℜ.B []
-    enforced ℜ.next.foreignKey a b := ℜ.next [
-      .a ↦ a,
-      .b ↦ b
-    ] ⊢ a ∈ ℜ.A [] ∧ b ∈ ℜ.B []
-    monitored ℜ.next.total a := a ∈ ℜ.A [] ⊢ ℜ.next [.a ↦ a]
+    enforced ℜ.B.foreignKey a := ℜ.B [.a ↦ a] ⊢ a ∈ ℜ.A []
+    enforced ℜ.E.foreignKey x a := ℜ.E [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [
+      .a ↦ x
+    ]
+    enforced ℜ.next.foreignKey x a := ℜ.next [
+      .x ↦ x,
+      .a ↦ a
+    ] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.B [.a ↦ x]
+    monitored ℜ.next.total x := x ∈ ℜ.A [] ⊢ ℜ.next [.x ↦ x]
     enforced ℜ.nextedge.foreignKey x a a.a := ℜ.nextedge [
       .x ↦ x,
       .a ↦ a
-    ] ∧ ℜ.next [.a ↦ x, .b ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.a ↦ a.a]
+    ] ∧ ℜ.next [.x ↦ x, .a ↦ a.a] ⊢ x ∈ ℜ.A [] ∧ a ∈ ℜ.E [.x ↦ x, .a ↦ a.a]
     monitored ℜ.nextedge.total x := x ∈ ℜ.A [] ⊢ ℜ.nextedge [.x ↦ x]
   end
 end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/T.ts
index 9325f06c..84e31f4e 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/T.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/T.ts
@@ -2,16 +2,16 @@ import * as runtime from "@coln-project/runtime";
 
 export interface View {
   A: runtime.ColnSet.View;
-  B: runtime.ColnSet.View;
-  E: (x: runtime.Value) => runtime.ColnSet.View;
+  B: (x: runtime.Value) => runtime.ColnSet.View;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
   next: (x: runtime.Value) => runtime.ColnRef.View;
   nextedge: (x: runtime.Value) => runtime.ColnRef.View;
 }
 
 export interface Transaction extends View {
   A: runtime.ColnSet.Transaction;
-  B: runtime.ColnSet.Transaction;
-  E: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  B: (x: runtime.Value) => runtime.ColnSet.Transaction;
+  E: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
   next: (x: runtime.Value) => runtime.ColnRef.Transaction;
   nextedge: (x: runtime.Value) => runtime.ColnRef.Transaction;
 }
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.json
index 6be3fdae..fb828798 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.json
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.json
@@ -1 +1 @@
-{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["b"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["a"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]],[["b"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
+{"entities":[{"path":[["TRealm"],["A"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["B"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}}],"primaryKey":null}},{"path":[["TRealm"],["E"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":null}},{"path":[["TRealm"],["next"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["B"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["nextedge"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["A"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["E"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["A"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["B"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["E"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["B"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["next"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["nextedge"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]},{"tag":"rowId","path":[["TRealm"],["E"]]},{"tag":"rowId","path":[["TRealm"],["B"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["next"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["E"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["nextedge"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["A"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["A"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["nextedge"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts
index a09d0576..04305db5 100644
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts
+++ b/packages/coln-compiler/test/golden/basic-ir/lookup-argument-projection.ts.output/TRealm.ts
@@ -9,12 +9,16 @@ export class View {
   constructor(store: runtime.StoreHandle) {
     this.root = {
       A: (new runtime.RowIdSet.View(store, "TRealm.A", [])),
-      B: (new runtime.RowIdSet.View(store, "TRealm.B", [])),
-      E: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.E", [a]));
+      B: (a: runtime.Value) => {
+        return (new runtime.RowIdSet.View(store, "TRealm.B", [a]));
       },
-      next: (a: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.next", [a]));
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.View(store, "TRealm.E", [x, a]));
+        };
+      },
+      next: (x: runtime.Value) => {
+        return (new runtime.TableCellRef.View(store, "TRealm.next", [x]));
       },
       nextedge: (x: runtime.Value) => {
         return (new runtime.TableCellRef.View(store, "TRealm.nextedge", [x]));
@@ -33,20 +37,29 @@ export class Transaction extends View {
     super(store);
     this.root = {
       A: (new runtime.RowIdSet.Transaction(store, "TRealm.A", [], transaction)),
-      B: (new runtime.RowIdSet.Transaction(store, "TRealm.B", [], transaction)),
-      E: (a: runtime.Value) => {
+      B: (a: runtime.Value) => {
         return (new runtime.RowIdSet.Transaction(
           store,
-          "TRealm.E",
+          "TRealm.B",
           [a],
           transaction
         ));
       },
-      next: (a: runtime.Value) => {
+      E: (x: runtime.Value) => {
+        return (a: runtime.Value) => {
+          return (new runtime.RowIdSet.Transaction(
+            store,
+            "TRealm.E",
+            [x, a],
+            transaction
+          ));
+        };
+      },
+      next: (x: runtime.Value) => {
         return (new runtime.TableCellRef.Transaction(
           store,
           "TRealm.next",
-          [a],
+          [x],
           transaction
         ));
       },
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln
deleted file mode 100644
index f875c020..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.coln
+++ /dev/null
@@ -1,10 +0,0 @@
-theory T := sig
-  X : Set
-  P : X -> Prop
-  witness : (x : X) -> P x
-  R : (x : X) -> P x -> Prop
-  use : (x : X) -> R x (witness x)
-end
-
-realm TRealm @ T
-end
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output
deleted file mode 100644
index da1ec05a..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.output
+++ /dev/null
@@ -1,49 +0,0 @@
--- elaborated
-global entry named T
-type: Theory
-value: sig
-  X : Set
-  P : X -> Prop
-  witness : (x : X) -> P x
-  R : (x : X) -> P x -> Prop
-  use : (x : X) -> R x (witness x)
-end
-realm named TRealm
-generators: node
-  X = rel []
-  P = rel [a : TRealm.X []]
-  witness = (fun [x : TRealm.X []] -> TRealm.P [a := x])
-  R = rel [x : TRealm.X [], a : TRealm.P [a := x]]
-  use = (fun [x : TRealm.X []] -> TRealm.R [
-    x := x,
-    a := TRealm.witness [x := x]
-  ])
-end
-lowered: flatrealm
-  entities
-    table ℜ.X := []
-    table ℜ.P := [.a : ℜ.X]
-    table ℜ.witness := [.x : ℜ.X, .a : ℜ.P] primarykey [.x]
-    table ℜ.R := [.x : ℜ.X, .a : ℜ.P]
-    table ℜ.use := [.x : ℜ.X, .a : ℜ.R] primarykey [.x]
-  end
-  rules
-    enforced ℜ.X.foreignKey := ℜ.X [] ⊢ ⊤
-    enforced ℜ.P.foreignKey a := ℜ.P [.a ↦ a] ⊢ a ∈ ℜ.X []
-    enforced ℜ.witness.foreignKey x a := ℜ.witness [
-      .x ↦ x,
-      .a ↦ a
-    ] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.P [.a ↦ x]
-    monitored ℜ.witness.total x := x ∈ ℜ.X [] ⊢ ℜ.witness [.x ↦ x]
-    enforced ℜ.R.foreignKey x a := ℜ.R [.x ↦ x, .a ↦ a] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.P [
-      .a ↦ x
-    ]
-    enforced ℜ.use.foreignKey x a a.a := ℜ.use [.x ↦ x, .a ↦ a] ∧ ℜ.witness [
-      .x ↦ x,
-      .a ↦ a.a
-    ] ⊢ x ∈ ℜ.X [] ∧ a ∈ ℜ.R [.x ↦ x, .a ↦ a.a]
-    monitored ℜ.use.total x := x ∈ ℜ.X [] ⊢ ℜ.use [.x ↦ x]
-  end
-end
-
--- messages
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts
deleted file mode 100644
index b860e498..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/T.ts
+++ /dev/null
@@ -1,17 +0,0 @@
-import * as runtime from "@coln-project/runtime";
-
-export interface View {
-  X: runtime.ColnSet.View;
-  P: (x: runtime.Value) => runtime.ColnSet.View;
-  witness: (x: runtime.Value) => runtime.ColnRef.View;
-  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.View;
-  use: (x: runtime.Value) => runtime.ColnRef.View;
-}
-
-export interface Transaction extends View {
-  X: runtime.ColnSet.Transaction;
-  P: (x: runtime.Value) => runtime.ColnSet.Transaction;
-  witness: (x: runtime.Value) => runtime.ColnRef.Transaction;
-  R: (x: runtime.Value) => (x: runtime.Value) => runtime.ColnSet.Transaction;
-  use: (x: runtime.Value) => runtime.ColnRef.Transaction;
-}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json
deleted file mode 100644
index edccfea3..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.json
+++ /dev/null
@@ -1 +0,0 @@
-{"entities":[{"path":[["TRealm"],["X"]],"value":{"entityVariant":{"tag":"table"},"columns":[],"primaryKey":null}},{"path":[["TRealm"],["P"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}}],"primaryKey":null}},{"path":[["TRealm"],["witness"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":[[["x"]]]}},{"path":[["TRealm"],["R"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["P"]]}}],"primaryKey":null}},{"path":[["TRealm"],["use"]],"value":{"entityVariant":{"tag":"table"},"columns":[{"path":[["x"]],"type":{"tag":"rowId","path":[["TRealm"],["X"]]}},{"path":[["a"]],"type":{"tag":"rowId","path":[["TRealm"],["R"]]}}],"primaryKey":[[["x"]]]}}],"rules":[{"path":[["TRealm"],["X"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[],"varTypes":[],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":null,"values":[]}}],"consequents":[]}},{"path":[["TRealm"],["P"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}]}},{"path":[["TRealm"],["witness"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["witness"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["R"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["P"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}},{"path":[["TRealm"],["use"],["foreignKey"]],"value":{"ruleVariant":"enforced","varNames":[[["x"]],[["a"]],[["a"],["a"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]},{"tag":"rowId","path":[["TRealm"],["R"]]},{"tag":"rowId","path":[["TRealm"],["P"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["use"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":1}}]}},{"tag":"atom","atom":{"entity":[["TRealm"],["witness"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}},{"tag":"atom","atom":{"entity":[["TRealm"],["R"]],"rowId":{"tag":"var","index":1},"values":[{"column":0,"term":{"tag":"var","index":0}},{"column":1,"term":{"tag":"var","index":2}}]}}]}},{"path":[["TRealm"],["use"],["total"]],"value":{"ruleVariant":"monitored","varNames":[[["x"]]],"varTypes":[{"tag":"rowId","path":[["TRealm"],["X"]]}],"antecedents":[{"tag":"atom","atom":{"entity":[["TRealm"],["X"]],"rowId":{"tag":"var","index":0},"values":[]}}],"consequents":[{"tag":"atom","atom":{"entity":[["TRealm"],["use"]],"rowId":null,"values":[{"column":0,"term":{"tag":"var","index":0}}]}}]}}]}
\ No newline at end of file
diff --git a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts b/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts
deleted file mode 100644
index 8f8754c3..00000000
--- a/packages/coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts
+++ /dev/null
@@ -1,76 +0,0 @@
-import schema from "./TRealm.json";
-export {schema};
-import * as runtime from "@coln-project/runtime";
-import * as T from "./T.ts";
-
-export class View {
-  root: T.View;
-
-  constructor(store: runtime.StoreHandle) {
-    this.root = {
-      X: (new runtime.RowIdSet.View(store, "TRealm.X", [])),
-      P: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.View(store, "TRealm.P", [a]));
-      },
-      witness: (x: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.witness", [x]));
-      },
-      R: (x: runtime.Value) => {
-        return (a: runtime.Value) => {
-          return (new runtime.RowIdSet.View(store, "TRealm.R", [x, a]));
-        };
-      },
-      use: (x: runtime.Value) => {
-        return (new runtime.TableCellRef.View(store, "TRealm.use", [x]));
-      }
-    };
-  }
-}
-
-export class Transaction extends View {
-  root: T.Transaction;
-
-  constructor(
-    store: runtime.StoreHandle,
-    transaction: runtime.TransactionHandle
-  ) {
-    super(store);
-    this.root = {
-      X: (new runtime.RowIdSet.Transaction(store, "TRealm.X", [], transaction)),
-      P: (a: runtime.Value) => {
-        return (new runtime.RowIdSet.Transaction(
-          store,
-          "TRealm.P",
-          [a],
-          transaction
-        ));
-      },
-      witness: (x: runtime.Value) => {
-        return (new runtime.TableCellRef.Transaction(
-          store,
-          "TRealm.witness",
-          [x],
-          transaction
-        ));
-      },
-      R: (x: runtime.Value) => {
-        return (a: runtime.Value) => {
-          return (new runtime.RowIdSet.Transaction(
-            store,
-            "TRealm.R",
-            [x, a],
-            transaction
-          ));
-        };
-      },
-      use: (x: runtime.Value) => {
-        return (new runtime.TableCellRef.Transaction(
-          store,
-          "TRealm.use",
-          [x],
-          transaction
-        ));
-      }
-    };
-  }
-}
\ No newline at end of file
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts
index 5f29983e..75a948b6 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-prop.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-prop-prop-prop", () => {
   const realm = beginRealm(LookupArgumentProjectionPropPropPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts
index 966ae80d..85c5794f 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-prop-set.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-prop-prop-set", () => {
   const realm = beginRealm(LookupArgumentProjectionPropPropSetRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts
index 262e0d2e..18447be3 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-prop.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-prop-set-prop", () => {
   const realm = beginRealm(LookupArgumentProjectionPropSetPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts
index 68f34866..101db3d6 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-prop-set-set.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-prop-set-set", () => {
   const realm = beginRealm(LookupArgumentProjectionPropSetSetRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts
index 6f70b9ca..85dfb184 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-prop.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-set-prop-prop", () => {
   const realm = beginRealm(LookupArgumentProjectionSetPropPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts
index 8775b27a..eecb1733 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-prop-set.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-set-prop-set", () => {
   const realm = beginRealm(LookupArgumentProjectionSetPropSetRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
index b5986393..b22edbd9 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection-set-set-prop", () => {
   const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
@@ -24,9 +24,9 @@ test("lookup-argument-projection-set-set-prop", () => {
 test("lookup-argument-projection-set-set-prop rejects an edge at a different target", () => {
   const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
+  const target = realm.root.B(source).add();
+  const otherTarget = realm.root.B(source).add();
+  const edge = realm.root.E(source)(otherTarget).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
 
@@ -36,38 +36,22 @@ test("lookup-argument-projection-set-set-prop rejects an edge at a different tar
 test("lookup-argument-projection-set-set-prop infers its output from an inhabited proposition", () => {
   const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   const view = realm.commit();
 
   assert.equal(valueEqual(view.nextedge(source).get(), edge), true);
 });
 
-test("lookup-argument-projection-set-set-prop returns equal proofs for equal lookup results", () => {
-  const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
-  const firstSource = realm.root.A.add();
-  const secondSource = realm.root.A.add();
-  const target = realm.root.B.add();
-  const firstEdge = realm.root.E(target).add();
-  const secondEdge = realm.root.E(target).add();
-  realm.root.next(firstSource).set(target);
-  realm.root.next(secondSource).set(target);
-  realm.root.nextedge(firstSource).set(firstEdge);
-  realm.root.nextedge(secondSource).set(secondEdge);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.nextedge(firstSource).get(), view.nextedge(secondSource).get()), true);
-});
-
 test("lookup-argument-projection-set-set-prop keeps proofs for different lookup results distinct", () => {
   const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const firstSource = realm.root.A.add();
   const secondSource = realm.root.A.add();
-  const firstTarget = realm.root.B.add();
-  const secondTarget = realm.root.B.add();
-  const firstEdge = realm.root.E(firstTarget).add();
-  const secondEdge = realm.root.E(secondTarget).add();
+  const firstTarget = realm.root.B(firstSource).add();
+  const secondTarget = realm.root.B(secondSource).add();
+  const firstEdge = realm.root.E(firstSource)(firstTarget).add();
+  const secondEdge = realm.root.E(secondSource)(secondTarget).add();
   realm.root.next(firstSource).set(firstTarget);
   realm.root.next(secondSource).set(secondTarget);
   realm.root.nextedge(firstSource).set(firstEdge);
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
index 49604434..51c52678 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection.test.ts
@@ -12,8 +12,8 @@ import { beginRealm } from "./helpers.ts";
 test("lookup-argument-projection", () => {
   const realm = beginRealm(LookupArgumentProjectionRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const edge = realm.root.E(target).add();
+  const target = realm.root.B(source).add();
+  const edge = realm.root.E(source)(target).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
   const view = realm.commit();
@@ -24,9 +24,9 @@ test("lookup-argument-projection", () => {
 test("lookup-argument-projection rejects an edge at a different target", () => {
   const realm = beginRealm(LookupArgumentProjectionRealm);
   const source = realm.root.A.add();
-  const target = realm.root.B.add();
-  const otherTarget = realm.root.B.add();
-  const edge = realm.root.E(otherTarget).add();
+  const target = realm.root.B(source).add();
+  const otherTarget = realm.root.B(source).add();
+  const edge = realm.root.E(source)(otherTarget).add();
   realm.root.next(source).set(target);
   realm.root.nextedge(source).set(edge);
 
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts
deleted file mode 100644
index 0ba33529..00000000
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-proof-result-argument.test.ts
+++ /dev/null
@@ -1,22 +0,0 @@
-// SPDX-FileCopyrightText: 2026 Coln contributors
-//
-// SPDX-License-Identifier: Apache-2.0 OR MIT
-
-import assert from "node:assert/strict";
-import test from "node:test";
-
-import { valueEqual } from "@coln-project/runtime";
-import * as LookupProofResultArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-proof-result-argument.ts.output/TRealm.ts";
-import { beginRealm } from "./helpers.ts";
-
-test("lookup-proof-result-argument", () => {
-  const realm = beginRealm(LookupProofResultArgumentRealm);
-  const x = realm.root.X.add();
-  const p = realm.root.P(x).add();
-  const r = realm.root.R(x)(p).add();
-  realm.root.witness(x).set(p);
-  realm.root.use(x).set(r);
-  const view = realm.commit();
-
-  assert.equal(valueEqual(view.use(x).get(), r), true);
-});

From 779d2c7160eebb02a895fb75ccdeb16abbd9280a Mon Sep 17 00:00:00 2001
From: mvr <mitchell.v.riley@gmail.com>
Date: Wed, 29 Jul 2026 13:09:12 +0100
Subject: [PATCH 3/4] Mark failing tests as expected for now

---
 packages/coln-compiler/test/Main.hs           |  8 ++-
 ...nt-function-argument-prop-set-prop.test.ts |  2 +-
 .../empty-prop-record-function.test.ts        |  2 +-
 .../tests/basic-ir/empty-prop-record.test.ts  |  2 +-
 .../tests/basic-ir/empty-record.test.ts       |  2 +-
 ...-prop.test.ts => equality-prop.pending.ts} |  0
 ...t.ts => equality-record-nested.pending.ts} |  0
 ...ord.test.ts => equality-record.pending.ts} |  0
 .../{equality.test.ts => equality.pending.ts} |  0
 .../basic-ir/foreign-key-set-prop.test.ts     |  2 +-
 .../tests/basic-ir/function-prop-prop.test.ts |  2 +-
 .../tests/basic-ir/function-set-prop.test.ts  |  4 +-
 .../tests/basic-ir/inventory.test.ts          |  9 +++-
 ...p-argument-projection-set-set-prop.test.ts |  2 +-
 ...up-composition-prop-prop-prop-prop.test.ts |  2 +-
 .../lookup-record-composition.test.ts         |  2 +-
 .../basic-ir/lookup-record-expansion.test.ts  |  2 +-
 .../basic-ir/lookup-record-field.test.ts      |  4 +-
 .../tests/basic-ir/lookup-record.test.ts      |  2 +-
 .../tests/basic-ir/param-alias-set.test.ts    |  2 +-
 .../tests/basic-ir/param-alias.test.ts        |  2 +-
 .../basic-ir/param-record-concrete.test.ts    |  2 +-
 .../param-record-dependent-function.test.ts   |  2 +-
 .../param-record-dependent-model.test.ts      |  2 +-
 .../basic-ir/param-record-function.test.ts    |  2 +-
 .../tests/basic-ir/param-record-model.test.ts |  2 +-
 .../basic-ir/param-record-nested.test.ts      |  2 +-
 ... => param-record-repeated-binders.test.ts} |  0
 .../param-record-type-family-lambda.test.ts   |  2 +-
 ...-record-type-family-multi-argument.test.ts |  2 +-
 .../param-record-type-family-partial.test.ts  |  2 +-
 .../param-record-type-family-prop.test.ts     |  2 +-
 .../param-record-type-family-unused.test.ts   |  2 +-
 .../tests/basic-ir/param-record.test.ts       |  2 +-
 .../tests/basic-ir/projection.test.ts         |  4 +-
 ...proof-record-function-argument.pending.ts} |  0
 .../proof-record-mixed-fields.test.ts         |  4 +-
 ...f-record-nested-dependent-equality.test.ts |  4 +-
 ...proof-record-nested-dependent-prop.test.ts |  4 +-
 .../basic-ir/proof-record-prop-field.test.ts  |  2 +-
 .../proof-record-structural-equality.test.ts  |  4 +-
 .../tests/basic-ir/proof-record.test.ts       |  2 +-
 .../tests/basic-ir/prop-alias.test.ts         |  2 +-
 .../prop-record-dependent-equality.test.ts    |  2 +-
 .../prop-record-nested-dependent.test.ts      |  2 +-
 .../tests/basic-ir/prop-record.test.ts        |  2 +-
 .../tests/basic-ir/prop.test.ts               |  4 +-
 .../tests/basic-ir/record-field-order.test.ts |  4 +-
 .../tests/basic-ir/record-nested.test.ts      |  2 +-
 .../tests/basic-ir/record.test.ts             |  2 +-
 ...erals.test.ts => rule-literals.pending.ts} |  0
 .../tests/basic-ir/typecheck.ts               | 54 +++++++++++++++----
 52 files changed, 109 insertions(+), 64 deletions(-)
 rename packages/coln-js-runtime/tests/basic-ir/{equality-prop.test.ts => equality-prop.pending.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{equality-record-nested.test.ts => equality-record-nested.pending.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{equality-record.test.ts => equality-record.pending.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{equality.test.ts => equality.pending.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{param-record-repeated-binders.pending.ts => param-record-repeated-binders.test.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{proof-record-function-argument.test.ts => proof-record-function-argument.pending.ts} (100%)
 rename packages/coln-js-runtime/tests/basic-ir/{rule-literals.test.ts => rule-literals.pending.ts} (100%)

diff --git a/packages/coln-compiler/test/Main.hs b/packages/coln-compiler/test/Main.hs
index 66994243..eaa42f0d 100644
--- a/packages/coln-compiler/test/Main.hs
+++ b/packages/coln-compiler/test/Main.hs
@@ -35,7 +35,13 @@ knownFailingElaboratorTests :: [String]
 knownFailingElaboratorTests = []
 
 knownFailingTypeScriptTests :: [String]
-knownFailingTypeScriptTests = []
+knownFailingTypeScriptTests =
+  [ "equality"
+  , "equality-prop"
+  , "equality-record"
+  , "equality-record-nested"
+  , "rule-literals"
+  ]
 
 main :: IO ()
 main = defaultMain =<< goldenTests
diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
index a4e4db76..c4f8efce 100644
--- a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
@@ -34,7 +34,7 @@ test("dependent-function-argument-prop-set-prop requires an output when its codo
   assert.throws(() => realm.commit(), /rule TRealm\.f/);
 });
 
-test("dependent-function-argument-prop-set-prop infers its output from an inhabited codomain", () => {
+test("dependent-function-argument-prop-set-prop infers its output from an inhabited codomain", { expectFailure: true }, () => {
   const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
   const a = realm.root.A.add();
   const b = realm.root.B(a).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts
index 1196120d..c8084a15 100644
--- a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record-function.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as EmptyPropRecordFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/empty-prop-record-function.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("empty-prop-record-function", () => {
+test("empty-prop-record-function", { expectFailure: true }, () => {
   const realm = beginRealm(EmptyPropRecordFunctionRealm);
   const value = realm.root.X.add();
 
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
index 9f4f688a..2e86d93a 100644
--- a/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-prop-record.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as EmptyPropRecordRealm from "../../../coln-compiler/test/golden/basic-ir/empty-prop-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("empty-prop-record", () => {
+test("empty-prop-record", { expectFailure: true }, () => {
   const realm = beginRealm(EmptyPropRecordRealm);
 
   assert.deepEqual(realm.root.truth, {});
diff --git a/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
index 3664d3ef..4eacc176 100644
--- a/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/empty-record.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as EmptyRecordRealm from "../../../coln-compiler/test/golden/basic-ir/empty-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("empty-record is inhabited without a write", () => {
+test("empty-record is inhabited without a write", { expectFailure: true }, () => {
   const realm = beginRealm(EmptyRecordRealm);
   const view = realm.commit();
   assert.deepEqual(view.unit, {});
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-prop.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/equality-prop.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/equality-prop.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-record-nested.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/equality-record-nested.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/equality-record-nested.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality-record.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/equality-record.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/equality-record.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/equality.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/equality.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/equality.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
index b3158282..e1a239ff 100644
--- a/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/foreign-key-set-prop.test.ts
@@ -29,7 +29,7 @@ test("foreign-key-set-prop keeps proofs for different parameter tuples distinct"
   assert.equal(valueEqual(first, second), false);
 });
 
-test("foreign-key-set-prop has at most one proof per parameter tuple", () => {
+test("foreign-key-set-prop has at most one proof per parameter tuple", { expectFailure: true }, () => {
   const realm = beginRealm(ForeignKeySetPropRealm);
   const vertex = realm.root.V.add();
   realm.root.E(vertex).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
index 4eb708d7..5cfb3d50 100644
--- a/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/function-prop-prop.test.ts
@@ -33,7 +33,7 @@ test("function-prop-prop requires an output when its codomain is uninhabited", (
   assert.throws(() => realm.commit(), /rule TRealm\.next/);
 });
 
-test("function-prop-prop infers its output from an inhabited codomain", () => {
+test("function-prop-prop infers its output from an inhabited codomain", { expectFailure: true }, () => {
   const realm = beginRealm(FunctionPropPropRealm);
   const input = realm.root.X.add();
   const output = realm.root.Y.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
index 53a62735..ae4499ac 100644
--- a/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/function-set-prop.test.ts
@@ -26,7 +26,7 @@ test("function-set-prop requires an output when its codomain is uninhabited", ()
   assert.throws(() => realm.commit(), /rule TRealm\.next/);
 });
 
-test("function-set-prop infers its output from an inhabited codomain", () => {
+test("function-set-prop infers its output from an inhabited codomain", { expectFailure: true }, () => {
   const realm = beginRealm(FunctionSetPropRealm);
   const input = realm.root.X.add();
   const output = realm.root.Y.add();
@@ -35,7 +35,7 @@ test("function-set-prop infers its output from an inhabited codomain", () => {
   assert.equal(valueEqual(view.next(input).get(), output), true);
 });
 
-test("function-set-prop returns equal proofs for different inputs", () => {
+test("function-set-prop returns equal proofs for different inputs", { expectFailure: true }, () => {
   const realm = beginRealm(FunctionSetPropRealm);
   const firstInput = realm.root.X.add();
   const secondInput = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts b/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
index 74c4ebe3..34c51d07 100644
--- a/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/inventory.test.ts
@@ -13,6 +13,13 @@ const goldenDirectory = resolve(
   here,
   "../../../coln-compiler/test/golden/basic-ir",
 );
+const missingRealms = [
+  "equality",
+  "equality-prop",
+  "equality-record",
+  "equality-record-nested",
+  "rule-literals",
+];
 const testSuffix = /\.(?:pending|test)\.ts$/;
 
 test("every realm has an integration test", () => {
@@ -25,5 +32,5 @@ test("every realm has an integration test", () => {
     .map((path) => path.replace(testSuffix, ""))
     .sort();
 
-  assert.deepEqual(integrationTests, realms.sort());
+  assert.deepEqual(integrationTests, [...realms, ...missingRealms].sort());
 });
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
index b22edbd9..e41c1463 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-argument-projection-set-set-prop.test.ts
@@ -33,7 +33,7 @@ test("lookup-argument-projection-set-set-prop rejects an edge at a different tar
   assert.throws(() => realm.commit(), /rule TRealm\.nextedge/);
 });
 
-test("lookup-argument-projection-set-set-prop infers its output from an inhabited proposition", () => {
+test("lookup-argument-projection-set-set-prop infers its output from an inhabited proposition", { expectFailure: true }, () => {
   const realm = beginRealm(LookupArgumentProjectionSetSetPropRealm);
   const source = realm.root.A.add();
   const target = realm.root.B(source).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts
index cf3f92bc..58cd9c62 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-composition-prop-prop-prop-prop.test.ts
@@ -23,7 +23,7 @@ test("lookup-composition-prop-prop-prop-prop", () => {
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
 
-test("lookup-composition-prop-prop-prop-prop infers an inhabited composition", () => {
+test("lookup-composition-prop-prop-prop-prop infers an inhabited composition", { expectFailure: true }, () => {
   const realm = beginRealm(LookupCompositionPropPropPropPropRealm);
   const source = realm.root.A.add();
   const intermediate = realm.root.B.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
index 5edec11d..9bf5a233 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-composition.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordCompositionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-composition.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("lookup-record-composition", () => {
+test("lookup-record-composition", { expectFailure: true }, () => {
   const realm = beginRealm(LookupRecordCompositionRealm);
   const source = realm.root.X.add();
   const rank = { tag: "int", value: 1 } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
index e5bf0ed3..650ed81d 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-expansion.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordExpansionRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-expansion.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("lookup-record-expansion", () => {
+test("lookup-record-expansion", { expectFailure: true }, () => {
   const realm = beginRealm(LookupRecordExpansionRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
index a89dea46..b8c2b4e0 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record-field.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordFieldRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record-field.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("lookup-record-field", () => {
+test("lookup-record-field", { expectFailure: true }, () => {
   const realm = beginRealm(LookupRecordFieldRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
@@ -24,7 +24,7 @@ test("lookup-record-field", () => {
   assert.equal(valueEqual(view.edge(source).get(), edge), true);
 });
 
-test("lookup-record-field rejects an edge at a different payload rank", () => {
+test("lookup-record-field rejects an edge at a different payload rank", { expectFailure: true }, () => {
   const realm = beginRealm(LookupRecordFieldRealm);
   const source = realm.root.X.add();
   const name = { tag: "string", value: "example" } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
index 933cc335..21a6c6ca 100644
--- a/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/lookup-record.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as LookupRecordRealm from "../../../coln-compiler/test/golden/basic-ir/lookup-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("lookup-record", () => {
+test("lookup-record", { expectFailure: true }, () => {
   const realm = beginRealm(LookupRecordRealm);
   const fixed = {
     name: { tag: "string", value: "fixed" },
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts
index adf38748..f0192832 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-alias-set.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamAliasSetRealm from "../../../coln-compiler/test/golden/basic-ir/param-alias-set.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-alias-set", () => {
+test("param-alias-set", { expectFailure: true }, () => {
   const realm = beginRealm(ParamAliasSetRealm);
   const box = { value: realm.root.X.add() };
   const boxed = realm.root.boxed(box).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts
index a67e63ef..045d3444 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-alias.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamAliasRealm from "../../../coln-compiler/test/golden/basic-ir/param-alias.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-alias", () => {
+test("param-alias", { expectFailure: true }, () => {
   const realm = beginRealm(ParamAliasRealm);
   const box = {
     key: { tag: "int", value: 1 },
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
index 0021640a..6f2ce007 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-concrete.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordConcreteRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-concrete.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-concrete", () => {
+test("param-record-concrete", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordConcreteRealm);
   const box = {
     value: {
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts
index 02846f3d..2b589797 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-function.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordDependentFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-dependent-function.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-dependent-function", () => {
+test("param-record-dependent-function", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordDependentFunctionRealm);
   const key = realm.root.Key.add();
   realm.root.key.set(key);
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts
index 829fa5d1..d4c6d6d5 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-dependent-model.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordDependentModelRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-dependent-model.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-dependent-model", () => {
+test("param-record-dependent-model", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordDependentModelRealm);
   const rank = { tag: "int", value: 1 } as const;
   const key = { rank };
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts
index 5437f04f..cff908ac 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-function.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordFunctionRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-function.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-function", () => {
+test("param-record-function", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordFunctionRealm);
   const key = realm.root.Key.add();
   const value = { tag: "string", value: "payload" } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
index 67c43096..b99884f4 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-model.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordModelRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-model.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-model", () => {
+test("param-record-model", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordModelRealm);
   const modelValue = realm.root.model.X.add();
   const box = {
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
index 40533208..5804e28a 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-nested.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordNestedRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-nested.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-nested", () => {
+test("param-record-nested", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordNestedRealm);
   const inner = realm.root.X.add();
   const nested = { inner: { value: inner } };
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.pending.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.test.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.pending.ts
rename to packages/coln-js-runtime/tests/basic-ir/param-record-repeated-binders.test.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts
index 3a0e13ed..dd682123 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-lambda.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordTypeFamilyLambdaRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-lambda.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-type-family-lambda", () => {
+test("param-record-type-family-lambda", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordTypeFamilyLambdaRealm);
   const x = { tag: "int", value: 1 } as const;
   const box = {
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts
index 43c331db..9d7fed96 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-multi-argument.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordTypeFamilyMultiArgumentRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-multi-argument.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-type-family-multi-argument", () => {
+test("param-record-type-family-multi-argument", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordTypeFamilyMultiArgumentRealm);
   const x = realm.root.X.add();
   const y = realm.root.Y.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts
index d41a68b5..9fe240bb 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-partial.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordTypeFamilyPartialRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-partial.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-type-family-partial", () => {
+test("param-record-type-family-partial", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordTypeFamilyPartialRealm);
   const x = realm.root.X.add();
   const y = realm.root.Y.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts
index f2135519..ad20e734 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-prop.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordTypeFamilyPropRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-type-family-prop", () => {
+test("param-record-type-family-prop", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordTypeFamilyPropRealm);
   const x = realm.root.X.add();
   const proof = realm.root.P(x).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts
index 2d319a04..ba1447f4 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record-type-family-unused.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordTypeFamilyUnusedRealm from "../../../coln-compiler/test/golden/basic-ir/param-record-type-family-unused.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record-type-family-unused", () => {
+test("param-record-type-family-unused", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordTypeFamilyUnusedRealm);
   const box = {
     value: { tag: "int", value: 1 },
diff --git a/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
index aec86c15..371647d7 100644
--- a/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/param-record.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ParamRecordRealm from "../../../coln-compiler/test/golden/basic-ir/param-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("param-record", () => {
+test("param-record", { expectFailure: true }, () => {
   const realm = beginRealm(ParamRecordRealm);
   const value = realm.root.X.add();
   const box = { value };
diff --git a/packages/coln-js-runtime/tests/basic-ir/projection.test.ts b/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
index c999fad9..6871e7d3 100644
--- a/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/projection.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ProjectionRealm from "../../../coln-compiler/test/golden/basic-ir/projection.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("projection", () => {
+test("projection", { expectFailure: true }, () => {
   const realm = beginRealm(ProjectionRealm);
   const a = realm.root.X.add();
   const b = realm.root.X.add();
@@ -27,7 +27,7 @@ test("projection", () => {
   );
 });
 
-test("projection rejects a value at a different projected value", () => {
+test("projection rejects a value at a different projected value", { expectFailure: true }, () => {
   const realm = beginRealm(ProjectionRealm);
   const a = realm.root.X.add();
   const b = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/proof-record-function-argument.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
index 4c0e6ae3..93fb8f07 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-mixed-fields.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ProofRecordMixedFieldsRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-mixed-fields.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record-mixed-fields", () => {
+test("proof-record-mixed-fields", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordMixedFieldsRealm);
   const equal = realm.root.X.add();
   const trailing = realm.root.X.add();
@@ -22,7 +22,7 @@ test("proof-record-mixed-fields", () => {
   assert.equal(valueEqual(view.value.trailing.get(), trailing), true);
 });
 
-test("proof-record-mixed-fields retains its erased equality", () => {
+test("proof-record-mixed-fields retains its erased equality", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordMixedFieldsRealm);
   const first = realm.root.X.add();
   const second = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts
index d7cb11cd..cdcac608 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-equality.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ProofRecordNestedDependentEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-equality.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record-nested-dependent-equality", () => {
+test("proof-record-nested-dependent-equality", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordNestedDependentEqualityRealm);
   const expected = realm.root.X.add();
   const result = realm.root.result(expected);
@@ -18,7 +18,7 @@ test("proof-record-nested-dependent-equality", () => {
   view.result(expected).evidence.proof.get();
 });
 
-test("proof-record-nested-dependent-equality retains its equality", () => {
+test("proof-record-nested-dependent-equality retains its equality", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordNestedDependentEqualityRealm);
   const expected = realm.root.X.add();
   const actual = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts
index 309fd61f..7085a429 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-nested-dependent-prop.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ProofRecordNestedDependentPropRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-nested-dependent-prop.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record-nested-dependent-prop", () => {
+test("proof-record-nested-dependent-prop", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordNestedDependentPropRealm);
   const value = { tag: "int", value: 1 } as const;
   const proof = realm.root.P(value).add();
@@ -19,7 +19,7 @@ test("proof-record-nested-dependent-prop", () => {
   assert.equal(valueEqual(view.package.evidence.proof.get(), proof), true);
 });
 
-test("proof-record-nested-dependent-prop retains its proof obligation", () => {
+test("proof-record-nested-dependent-prop retains its proof obligation", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordNestedDependentPropRealm);
   const value = { tag: "int", value: 1 } as const;
   realm.root.package.value.set(value);
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts
index d8a4ed0a..f39e6243 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-prop-field.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as ProofRecordPropFieldRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-prop-field.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record-prop-field", () => {
+test("proof-record-prop-field", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordPropFieldRealm);
   const proof = realm.root.P.add();
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts
index afc9a937..da63daeb 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record-structural-equality.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as ProofRecordStructuralEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record-structural-equality.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record-structural-equality exposes its equality field", () => {
+test("proof-record-structural-equality exposes its equality field", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordStructuralEqualityRealm);
   const left = realm.root.X.add();
   const right = realm.root.X.add();
@@ -21,7 +21,7 @@ test("proof-record-structural-equality exposes its equality field", () => {
   view.comparison.same.get();
 });
 
-test("proof-record-structural-equality retains every leaf equality", () => {
+test("proof-record-structural-equality retains every leaf equality", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordStructuralEqualityRealm);
   const first = realm.root.X.add();
   const second = realm.root.X.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
index 7aca8165..bf78d6f1 100644
--- a/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/proof-record.test.ts
@@ -7,7 +7,7 @@ import test from "node:test";
 import * as ProofRecordRealm from "../../../coln-compiler/test/golden/basic-ir/proof-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("proof-record", () => {
+test("proof-record", { expectFailure: true }, () => {
   const realm = beginRealm(ProofRecordRealm);
   const value = realm.root.X.add();
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts
index 479ff869..8ba1d65a 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-alias.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropAliasRealm from "../../../coln-compiler/test/golden/basic-ir/prop-alias.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("prop-alias canonicalizes proofs", () => {
+test("prop-alias canonicalizes proofs", { expectFailure: true }, () => {
   const realm = beginRealm(PropAliasRealm);
   const first = realm.root.V.add();
   const second = realm.root.V.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts
index d608f21e..1efdcd5c 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record-dependent-equality.test.ts
@@ -7,7 +7,7 @@ import test from "node:test";
 import * as PropRecordDependentEqualityRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record-dependent-equality.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("prop-record-dependent-equality retains evidence used by a later equality field", () => {
+test("prop-record-dependent-equality retains evidence used by a later equality field", { expectFailure: true }, () => {
   const realm = beginRealm(PropRecordDependentEqualityRealm);
   realm.root.P.add();
   const view = realm.commit();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts
index 4ec59139..da867e76 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record-nested-dependent.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropRecordNestedDependentRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record-nested-dependent.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("prop-record-nested-dependent", () => {
+test("prop-record-nested-dependent", { expectFailure: true }, () => {
   const realm = beginRealm(PropRecordNestedDependentRealm);
   const value = realm.root.X.add();
   const nested = realm.root.P(value).add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
index f3ffa788..e3621141 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop-record.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as PropRecordRealm from "../../../coln-compiler/test/golden/basic-ir/prop-record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("prop-record", () => {
+test("prop-record", { expectFailure: true }, () => {
   const realm = beginRealm(PropRecordRealm);
   const left = realm.root.P.add();
   const right = realm.root.Q.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
index 64709743..66318f50 100644
--- a/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/prop.test.ts
@@ -24,7 +24,7 @@ test("prop", () => {
   assert.equal(view.V.has(value), true);
 });
 
-test("prop canonicalizes proofs", () => {
+test("prop canonicalizes proofs", { expectFailure: true }, () => {
   const realm = beginRealm(PropRealm);
   const first = realm.root.V.add();
   const second = realm.root.V.add();
@@ -42,7 +42,7 @@ test("prop keeps canonical proof handles valid", () => {
   assert.equal(view.V.has(canonical), true);
 });
 
-test("prop has at most one proof", () => {
+test("prop has at most one proof", { expectFailure: true }, () => {
   const realm = beginRealm(PropRealm);
   realm.root.V.add();
   realm.root.V.add();
diff --git a/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts b/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
index ad0f3e41..bb9e5979 100644
--- a/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/record-field-order.test.ts
@@ -8,7 +8,7 @@ import test from "node:test";
 import * as RecordFieldOrderRealm from "../../../coln-compiler/test/golden/basic-ir/record-field-order.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("record-field-order", () => {
+test("record-field-order", { expectFailure: true }, () => {
   const realm = beginRealm(RecordFieldOrderRealm);
   const pair = {
     first: { tag: "int", value: 1 },
@@ -21,7 +21,7 @@ test("record-field-order", () => {
   assert.equal(view.R(pair)(edge).has(related), true);
 });
 
-test("record-field-order rejects declaration order as dependency order", () => {
+test("record-field-order rejects declaration order as dependency order", { expectFailure: true }, () => {
   const realm = beginRealm(RecordFieldOrderRealm);
   const pair = {
     first: { tag: "int", value: 1 },
diff --git a/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts b/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts
index d5beb63b..705daeea 100644
--- a/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/record-nested.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as RecordNestedRealm from "../../../coln-compiler/test/golden/basic-ir/record-nested.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("record-nested", () => {
+test("record-nested", { expectFailure: true }, () => {
   const realm = beginRealm(RecordNestedRealm);
   const name = { tag: "string", value: "example" } as const;
   const rank = { tag: "int", value: 1 } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/record.test.ts b/packages/coln-js-runtime/tests/basic-ir/record.test.ts
index b4ba30a5..beb42206 100644
--- a/packages/coln-js-runtime/tests/basic-ir/record.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/record.test.ts
@@ -9,7 +9,7 @@ import { valueEqual } from "@coln-project/runtime";
 import * as RecordRealm from "../../../coln-compiler/test/golden/basic-ir/record.ts.output/TRealm.ts";
 import { beginRealm } from "./helpers.ts";
 
-test("record", () => {
+test("record", { expectFailure: true }, () => {
   const realm = beginRealm(RecordRealm);
   const point = realm.root.point.add();
   const name = { tag: "string", value: "example" } as const;
diff --git a/packages/coln-js-runtime/tests/basic-ir/rule-literals.test.ts b/packages/coln-js-runtime/tests/basic-ir/rule-literals.pending.ts
similarity index 100%
rename from packages/coln-js-runtime/tests/basic-ir/rule-literals.test.ts
rename to packages/coln-js-runtime/tests/basic-ir/rule-literals.pending.ts
diff --git a/packages/coln-js-runtime/tests/basic-ir/typecheck.ts b/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
index 309c2ffb..ca6f6af6 100644
--- a/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/typecheck.ts
@@ -26,14 +26,47 @@ if (config.errors.length !== 0) {
   throw new Error(formatDiagnostics(config.errors));
 }
 
-const knownFailures = new Map<string, { label: string; match: RegExp }>([
-  [
-    "param-record-repeated-binders",
-    {
-      label: "repeated record type parameters produce duplicate TypeScript identifiers",
-      match: /Duplicate identifier 'X'/,
-    },
-  ],
+const knownFailures = new Set([
+  "empty-prop-record",
+  "empty-prop-record-function",
+  "empty-record",
+  "equality",
+  "equality-prop",
+  "equality-record",
+  "equality-record-nested",
+  "lookup-record",
+  "lookup-record-composition",
+  "lookup-record-expansion",
+  "lookup-record-field",
+  "param-alias",
+  "param-alias-set",
+  "param-record",
+  "param-record-concrete",
+  "param-record-dependent-function",
+  "param-record-dependent-model",
+  "param-record-function",
+  "param-record-model",
+  "param-record-nested",
+  "param-record-type-family-lambda",
+  "param-record-type-family-multi-argument",
+  "param-record-type-family-partial",
+  "param-record-type-family-prop",
+  "param-record-type-family-unused",
+  "projection",
+  "proof-record",
+  "proof-record-function-argument",
+  "proof-record-mixed-fields",
+  "proof-record-nested-dependent-equality",
+  "proof-record-nested-dependent-prop",
+  "proof-record-prop-field",
+  "proof-record-structural-equality",
+  "prop-record",
+  "prop-record-dependent-equality",
+  "prop-record-nested-dependent",
+  "record",
+  "record-field-order",
+  "record-nested",
+  "rule-literals",
 ]);
 
 const integrationTestSuffix = /\.(?:pending|test)\.ts$/;
@@ -60,9 +93,8 @@ test("typecheck basic-ir fixtures", () => {
 
 for (const path of testFiles) {
   const name = path.replace(integrationTestSuffix, "");
-  const expectedFailure = knownFailures.get(name);
-  if (expectedFailure !== undefined) {
-    test(`typecheck ${name}`, { expectFailure: expectedFailure }, () => {
+  if (knownFailures.has(name)) {
+    test(`typecheck ${name}`, { expectFailure: true }, () => {
       typecheck([path]);
     });
   }

From 2d4838792c23dda2ec39a6d2c805b2c149931f98 Mon Sep 17 00:00:00 2001
From: mvr <mitchell.v.riley@gmail.com>
Date: Wed, 29 Jul 2026 13:22:03 +0100
Subject: [PATCH 4/4] Mark one more test as failing

---
 .../basic-ir/dependent-function-argument-prop-set-prop.test.ts  | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
index c4f8efce..f77dd5a4 100644
--- a/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
+++ b/packages/coln-js-runtime/tests/basic-ir/dependent-function-argument-prop-set-prop.test.ts
@@ -26,7 +26,7 @@ test("dependent-function-argument-prop-set-prop is vacuous when its proof domain
   realm.commit();
 });
 
-test("dependent-function-argument-prop-set-prop requires an output when its codomain is uninhabited", () => {
+test("dependent-function-argument-prop-set-prop requires an output when its codomain is uninhabited", { expectFailure: true }, () => {
   const realm = beginRealm(DependentFunctionArgumentPropSetPropRealm);
   const a = realm.root.A.add();
   realm.root.B(a).add();