Stepanov: Generic Programming in C++

These posts explore the philosophy and practice of generic programming as taught by Alex Stepanov, architect of the C++ Standard Template Library.

The central insight: algorithms arise from algebraic structure. The same algorithm that works on integers works on matrices, polynomials, and modular integers---not by accident, but because they share algebraic properties.

Each post demonstrates one beautiful idea with minimal, pedagogical C++ code (~100-300 lines).

Core Topics

• Monoids and exponentiation: The Russian peasant algorithm reveals the universal structure of repeated operations
• Rings and fields: Modular arithmetic teaches which algorithms apply where
• Euclidean domains: The same GCD algorithm works for integers and polynomials
• Generic concepts: C++20 concepts express algebraic requirements as compile-time contracts

Reading Order

Foundations: Peasant → Modular → Miller-Rabin → Rational → Polynomials

Linear Algebra Track: Elementa → Type Erasure

Calculus Track: Dual → Finite Differences → Autodiff → Integration

Philosophy: Synthesis → Duality

Further Reading

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

---

By Alex Towell. These posts also appear on metafunctor.com.