# Haskell and mathematics

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Haskell is growing in popularity among mathematicians. As one blogger put it:

"after my involving myself in the subject, one thing that stands out is the relatively low distance between thought expressed in my ordinary day-to-day mathematical discourse, and thought expressed in Haskell code."

and

"How can Haskell not be the programming language that all mathematicians should learn?"

To paraphrase Hilbert ("Physics is too complicated for Physicists"), the relative obscurity of Haskell (a language with a strict notion of functions, higher-order-functions, and types) amongst mathematicians may be that:

"Haskell is too mathematical for many mathematicians."

This page collects resources for using Haskell to do mathematics.

## 1 Textbooks

Kees Doets and Jan van Eijck
The Haskell Road to Logic, Maths and Programming
King's College Publications, London, 2004. ISBN 0-9543006-9-6 (14.00 pounds, \$25.00).
Book description:
The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming. Throughout the text, abstract concepts are linked to concrete representations in Haskell. Everything one has to know about programming in Haskell to understand the examples in the book is explained as we go along, but we do not cover every aspect of the language. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. We do not assume that our readers have previous experience with either programming or construction of formal proofs. We do assume previous acquaintance with mathematical notation, at the level of secondary school mathematics. Wherever necessary, we will recall relevant facts. Everything one needs to know about mathematical reasoning or programming is explained as we go along. We do assume that our readers are able to retrieve software from the Internet and install it, and that they know how to use an editor for constructing program texts.

John O'Donnell, Cordelia Hall and Rex Page: Discrete Mathematics Using a Computer, 2nd edition Springer, 2006, 441 pages. ISBN 1-84628-241-1.

Book description:
This book introduces the main topics of discrete mathematics with a strong emphasis on applications to computer science. It uses computer programs to implement and illustrate the mathematical ideas, helping the reader to gain a concrete understanding of the abstract mathematics. The programs are also useful for practical calculations, and they can serve as a foundation for larger software packages. Designed for first and second year undergraduate students, the book is also ideally suited to self-study. No prior knowledge of functional programming is required; the book and the online documentation provide everything you will need.

Jürgen Bokowski
Computational Oriented Matroids,

Cambridge University Press, November 2005, 450 pages. ISBN 0521849306

Book description:
Oriented matroids play the role of matrices in discrete geometry, when metrical properties, such as angles or distances, are neither required nor available. Thus they are of great use in such areas as graph theory, combinatorial optimization and convex geometry. The combination of concrete applications and computation, the profusion of illustrations, and the large number of examples and exercises will make this an ideal introductory text on the subject. It will also be valuable for self-study for mathematicians and computer scientists working in discrete and computational geometry.

## 2 Libraries

A growing collection of Haskell math libraries.

## 3 Theorem proving

There has been a long tradition of mechanised reasoning in and about Haskell.

## 4 Mathematics from a Haskell perspective

Articles on computational and category theoretic branches of mathematics, and their role as a foundation for programming and Haskell itself.