Generic-Programming

Bits Follow Types

Codecs are not ad-hoc bit formats. They are constructions on the algebraic structure of types.

When Lists Become Bits

Prefix-freeness is the property that lifts the free-monoid construction into bit space.

Free Algebras: Why Lists and Polynomials Are Universal

The free monoid on a set is the type of lists over that set. The universal property says fold is the unique homomorphism from lists to any monoid. This explains why lists, multisets, and polynomials appear everywhere.

Homomorphisms: The Maps Between Structures

A homomorphism preserves structure. fold is the universal homomorphism from the free monoid. This is the algebraic reason that fold, evaluation, and parallelism work.

Lattices: Fixed Points and Iteration

A lattice has two operations, meet and join, satisfying absorption laws. Tarski's theorem gives a generic fixed-point algorithm. Lattice structure determines the iteration, just as monoid structure determines power-by-squaring.

Semirings: One Algorithm, Six Graph Problems

A semiring has two monoidal operations linked by distributivity. Matrix multiplication over different semirings gives shortest paths, longest paths, widest paths, reachability, and path counting, all from the same code.

Streaming Statistics, One Monoid at a Time

Online accumulators are monoids. Default construction is the identity, combination via += is the binary operation, and parallel composition gives the product monoid, computing arbitrary statistics in a single pass.

A Map of My Open Source Ecosystem

A guided tour through my open-source ecosystem: encrypted search theory, statistical reliability, Unix-philosophy CLI tools, AI research, and speculative fiction. How the projects connect and where to start.

Duality: The Hidden Structure of Opposites

Many structures come in pairs: forward/reverse AD, push/pull iteration, encode/decode. Recognizing duality lets you transfer theorems and insights between domains.

Seeing Structure First

A reflection on eleven explorations in generic programming, and how algorithms arise from algebraic structure.

Alexander Stepanov: Efficient Programming with Components (A9 Lectures)

Notes

18-part lecture series on efficient programming. Covers the intellectual foundations behind STL.

Elements of Programming

Notes

Rigorous foundations of generic programming. Connects algebra and algorithms. Stepanov’s magnum opus.

From Mathematics to Generic Programming

Notes

History of mathematical ideas underlying generic programming. More accessible than EoP.

Sean Parent: C++ Seasoning (That's a Rotate)

Notes

Classic talk on recognizing algorithmic patterns. ‘No raw loops’ - shows how rotate solves many problems elegantly.

Choosing the Algebra

The Stepanov series showed that algorithms arise from algebraic structure. This post is about the flip side: sometimes you choose a different structure to make the algorithm trivial.

PFC: Zero-Copy Data Compression Through Prefix-Free Codecs and Generic Programming

PFC: Zero-Copy Data Compression Through Prefix-Free Codecs

A header-only C++20 library that achieves 3-10x compression with zero marshaling overhead using prefix-free codes and Stepanov-style generic programming.

Runtime Polymorphism Without Inheritance

Sean Parent's type erasure gives you value-semantic polymorphism without inheritance. Combined with Stepanov's algebraic thinking, you can type-erase entire algebraic structures.

Numerical Integration with Generic Concepts

Numerical integration meets generic programming. By requiring only ordered field operations, the quadrature routines work with dual numbers, giving you differentiation under the integral for free.

Teaching Linear Algebra with C++20 Concepts

elementa is a linear algebra library built to teach. Every design decision prioritizes clarity over cleverness. Code that reads like a textbook and compiles.

Polynomials as Euclidean Domains

The same GCD algorithm works for integers and polynomials because both are Euclidean domains. One structure, many types, same algorithms.

Exact Rational Arithmetic

Rational numbers give exact arithmetic where floating-point fails. The implementation connects GCD, the Stern-Brocot tree, and the algebraic structure of fields.

How Iterators Give You N+M Instead of NxM

Iterators reduce the NxM algorithm-container problem to N+M by interposing an abstraction layer, following Stepanov's generic programming approach.

Modular Arithmetic as Rings

Integers modulo N form a ring, an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.

One Algorithm, Infinite Powers

The Russian peasant algorithm computes products, powers, Fibonacci numbers, and more, once you see the underlying algebraic structure.

Packed Containers: Zero-Waste Bit-Level Storage in C++

What if containers wasted zero bits? A C++ library for packing arbitrary value types at the bit level using pluggable codecs.