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?"

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.

Textbooks

See Books and tutorials/Mathematics

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

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.

Tutorials and blogs on Haskell for mathematicians

• Why isn't ListT list a monad?
• Reverse Engineering Machines with the Yoneda Lemma
• Variable substitution gives a...
• From Löb's Theorem to Spreadsheet Evaluation
• Games, Strategies and the Self-Composition of the List Monad.
• Practical Synthetic Differential Geometry
• More Low Cost Geometric Algebra
• Learn Maths with Haskell
• Algebraic Topology in Haskell
• Infinitesimal Types
• Geometric Algebra for Free!
• Eleven Reasons to use Haskell as a Mathematician
• Laws of Form: An Opinion
• A-algebras and group cohomology
• Prototyping thought
• Computational Group Theory in Haskell
• Carry bits and group cohomology
• Why Haskell?
• Programs are Proofs: Models and Types in Lambda Calculus
• Polynomials as numbers
• Non-standard analysis, automatic differentiation, Haskell
• Haskell for Maths: commutative algebra, combinatorics, number theory, and group theory
• Two-dimensional spatial hashing with space-filling curves

Mathematical hierarchy

An initiative to develop a mathematically sound algebraic class hierarchy for Haskell. See Haskell and mathematics/Hierarchy