Haskell and mathematics

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?"

This page collects resources for using Haskell to do mathematics.

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.

Libraries

A growing collection of Haskell math libraries.

Theorem proving

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

• Research papers
• Theorem provers

Tutorials and Blogs

• Eleven Reasons to use Haskell as a Mathematician
• Prototyping thought
• Computational Group Theory in Haskell
• Carry bits and group cohomology
• Infinitesimal Types
• Practical Synthetic Differential Geometry
• More Low Cost Geometric Algebra
• Learn Maths with Haskell
• Geometric Algebra for Free!