Category-Theory

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.

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.

Category Theory for Programmers

Cipher Maps: A Unified Framework for Oblivious Function Approximation Through Algebraic Structures and Bernoulli Models

Algebraic Cipher Types: A Functorial Framework for Secure Computation

The Dot Ecosystem: From Simple Paths to Data Algebras

A composable ecosystem of tools for manipulating nested data structures. From a simple helper function to a full data algebra, guided by purity, pedagogy, and the principle of least power.