# Haskell and mathematics

### From HaskellWiki

BrettGiles (Talk | contribs) (→Mathematical Hierarchy: Case) |
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==Tutorials and blogs on Haskell for mathematicians== |
==Tutorials and blogs on Haskell for mathematicians== |
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− | * [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?] |
+ | There's an active commuity of (professional and amateur) mathematicians [http://haskell.org/haskellwiki/Blog_articles/Mathematics blogging about Haskell and mathetmatics]. |

− | * [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma] |
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− | * [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...] |
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− | * [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation] |
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− | * [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.] |
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− | * [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry] |
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− | * [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra] |
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− | * [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell] |
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− | * [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell] |
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− | * [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types] |
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− | * [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!] |
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− | * [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician] |
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− | * [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion] |
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− | * [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ A-algebras and group cohomology] |
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− | * [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought] |
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− | * [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell] |
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− | * [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology] |
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− | * [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?] |
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− | * [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus] |
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− | * [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers] |
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− | * [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell] |
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− | * [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory |
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− | * [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves] |
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==Mathematical hierarchy== |
==Mathematical hierarchy== |

## Revision as of 07:32, 29 June 2007

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.

## Contents |

## 1 Textbooks

See Books and tutorials/Mathematics

## 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.

## 5 Tutorials and blogs on Haskell for mathematicians

There's an active commuity of (professional and amateur) mathematicians blogging about Haskell and mathetmatics.

## 6 Mathematical hierarchy

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