Stepanov

Pedagogical blog posts exploring generic programming and algorithmic mathematics in C++20.

Named for Alex Stepanov, whose work on the STL and Elements of Programming showed that algorithms arise from algebraic structure, not ad-hoc coding.

The Core Thesis

Algorithms arise from algebraic structure. The Russian peasant algorithm isn't about integers—it's about monoids. The same power() function computes integer exponentiation, Fibonacci numbers (via matrices), 3D rotation composition (via quaternions), and shortest paths (via tropical semirings).

See structure first, algorithm second.

Posts

Each post in post/ is self-contained with:

• index.md — The article (Hugo-compatible with YAML frontmatter)
• *.hpp — Minimal implementation (~100-400 lines)
• Tests

Post	Topic
2019-03-peasant-stepanov/	Russian peasant algorithm, exponentiation, 15 monoid examples
2019-06-modular-stepanov/	Integers mod N as rings and fields
2019-09-miller-rabin-stepanov/	Probabilistic primality testing
2020-02-rational-stepanov/	Exact fraction arithmetic, GCD
2020-07-polynomials-stepanov/	Polynomial arithmetic, Euclidean domains
2021-03-elementa-stepanov/	Pedagogical linear algebra, Matrix concept
2021-09-dual-stepanov/	Forward-mode autodiff via dual numbers
2022-04-finite-diff-stepanov/	Numerical differentiation
2023-01-autodiff-stepanov/	Reverse-mode autodiff (backpropagation)
2023-08-integration-stepanov/	Numerical quadrature
2024-02-type-erasure-stepanov/	Sean Parent's value-semantic polymorphism
2025-01-differentiation-stepanov/	Differentiation techniques compared
2026-01-18-synthesis-stepanov/	Synthesis: seeing structure first
2026-01-19-duality-stepanov/	Duality: forward/reverse, push/pull, encode/decode

Building

make build   # Configure and build
make test    # Run tests
make clean   # Remove build artifacts

Or manually:

cd post
cmake -B build
cmake --build build
ctest --test-dir build --output-on-failure

Directory Structure

stepanov/
├── post/                        # Blog posts (Hugo/mkdocs compatible)
│   ├── 2019-03-peasant-stepanov/
│   │   ├── index.md            # Article with YAML frontmatter
│   │   ├── peasant.hpp         # Implementation
│   │   └── examples/           # Monoid examples
│   ├── 2019-06-modular-stepanov/
│   │   └── ...
│   ├── CMakeLists.txt
│   └── build/                  # Generated (gitignored)
├── docs/                        # mkdocs site source
│   ├── index.md                # Landing page
│   └── about.md
├── mkdocs.yml                   # mkdocs configuration
├── CLAUDE.md                    # AI assistant instructions
├── Makefile
└── README.md

Reading Order

Number theory track:

1. peasant → modular → miller-rabin

Calculus track:

1. dual → finite-diff → integration → autodiff

Linear algebra track:

1. elementa → autodiff

Algebraic structures track:

1. rational → polynomials

Start anywhere. Each post is self-contained. The synthesis post ties everything together.

Philosophy

• Minimal: ~100-400 lines per implementation
• Pedagogical: Code teaches principles, not production patterns
• Algebraic: Structure determines algorithms
• Self-contained: Each post stands alone

Blog

These posts are published at metafunctor.com in the Stepanov series.

Further Reading

• Stepanov & McJones, Elements of Programming (2009)
• Stepanov & Rose, From Mathematics to Generic Programming (2014)
• Stepanov's collected papers

Author

Alex Towell — metafunctor.com — queelius@gmail.com

License

MIT