Category Theory for Programming

TL;DR

These lecture notes introduce category theory concepts like initial algebras and monads, focusing on their applications to functional programming and effects management.

Contribution

The notes connect category theory fundamentals directly to functional programming, emphasizing initial algebras and monads for data types and effects.

Findings

Initial algebras characterize recursive data types.

Monads provide a framework for managing effects.

Includes problems and solutions for practical understanding.

Abstract

In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical characterization of datatypes and recursive functions on them. Secondly, we study monads, which give a mathematical framework for effects in functional languages. The notes include many problems and solutions.