https://github.com/jpvillaisaza/cain

Category theory applied to functional programming (undergraduate project)
https://github.com/jpvillaisaza/cain

agda category-theory functional-programming haskell

Last synced: 5 months ago
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Category theory applied to functional programming (undergraduate project)

• Host: GitHub
• URL: https://github.com/jpvillaisaza/cain
• Owner: jpvillaisaza
• Created: 2014-08-17T19:02:32.000Z (over 11 years ago)
• Default Branch: master
• Last Pushed: 2025-05-01T14:13:57.000Z (7 months ago)
• Last Synced: 2025-06-13T01:45:16.080Z (6 months ago)
• Topics: agda, category-theory, functional-programming, haskell
• Language: TeX
• Homepage: https://jpvillaisaza.github.io/cain/cain.pdf
• Size: 921 KB
• Stars: 33
• Watchers: 5
• Forks: 0
• Open Issues: 2
• Metadata Files:
  • Readme: README.md

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README

          
# Category theory applied to functional programming

## Abstract

We study some of the applications of category theory to functional

programming, particularly in the context of the Haskell functional

programming language, and the Agda dependently typed functional

programming language and proof assistant. More specifically, we

describe and explain the concepts of category theory needed for

conceptualizing and better understanding algebraic data types and

folds, functors, monads, and parametrically polymorphic functions.

With this purpose, we give a detailed account of categories, functors

and endofunctors, natural transformations, monads and Kleisli triples,

algebras and initial algebras over endofunctors, among others. In

addition, we explore all of these concepts from the standpoints of

categories and programming in Haskell, and, in some cases, Agda. In

other words, we examine functional programming through category

theory.