Category Theory in Computing
Table of Contents
1. Introduction
Category theory provides a unifying mathematical framework for understanding computation, types, and program structure through objects, morphisms, and their compositions.
6. Implementation in Scheme
6.1. Category as Record
(define-record-type <category> (make-category objects morphisms compose identity) category? (objects category-objects) (morphisms category-morphisms) (compose category-compose) (identity category-identity)) (define (functor-map F f) "Apply functor F to morphism f" ((functor-fmap F) f))
6.2. Verification Pattern
7. Applications
- Type systems (Hindley-Milner as adjunction)
- Functional reactive programming
- Database query optimization
- Concurrent and distributed systems
- Effect systems and algebraic effects
8. Resources
- Categories for the Working Mathematician (Mac Lane)
- Category Theory for Programmers (Milewski)
- Seven Sketches in Compositionality (Fong & Spivak)