abstract.tex

\chapter{Abstract}
\label{chap: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.

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\noindent
Keywords: Agda, category theory, functional programming, Haskell.

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