# Haskell and mathematics

### From HaskellWiki

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:"How can Haskell not be the programming language that all mathematicians should learn?" |
:"How can Haskell not be the programming language that all mathematicians should learn?" |
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− | To paraphrase Hilbert ([http://www.autoren-heute.de/wissenschaft/trans_html/Physiker/index.html "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: |
+ | This page collects resources for using Haskell to do mathematics: |

− | :"Haskell is too mathematical for many mathematicians." |
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− | This page collects resources for using Haskell to do mathematics. |
+ | * [[Books and tutorials/Mathematics|Mathematics textbooks using Haskell]] |

+ | * The [http://hackage.haskell.org/packages/archive/pkg-list.html#cat:Math category of math libraries] on the Hackage library database. |
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+ | * A growing [[Libraries_and_tools/Mathematics|collection of Haskell math libraries]]. |
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+ | * There has been a long tradition of mechanised reasoning in and about Haskell. |
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+ | ** [[Research_papers/Testing_and_correctness#Verifying_Haskell_programs|Research papers]] |
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+ | ** [[Libraries_and_tools/Theorem_provers|Theorem provers]] |
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+ | * [[Mathematics|Articles]] on computational and category theoretic branches of mathematics, and their role as a foundation for programming and Haskell itself. |
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+ | * [http://haskell.org/haskellwiki/Blog_articles/Mathematics Articles about Haskell and mathematics] |
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+ | * [[Mathematical prelude discussion]]: Initiatives to develop a mathematically sound algebraic class hierarchy for Haskell. |
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+ | * [[Z4]] - a Ro/Haskell page with a small (not complete) implementation of Z4, as part of the Project "Boosting your Maths. Faculty with Haskell" . See paragraph # 3, on page [[Z4]] |
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− | ==Textbooks== |
+ | Math papers using Haskell: |

− | ;[[Image:Haskell_Road.jpg|Cover]] Kees Doets and Jan van Eijck: [http://www.cwi.nl/~jve/HR <em>The Haskell Road to Logic, Maths and Programming</em>] |
+ | * [http://www.cs.cmu.edu/~kw/pubs/conway.pdf Proving Conway's Lost Cosmological Theorem with Haskell] |

− | :King's College Publications, London, 2004. ISBN 0-9543006-9-6 (14.00 pounds, $25.00). <blockquote> <b>Book description:</b><br> 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. </blockquote> |
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− | <dt>[[Image:Discrete_Mathematics_Using_A_Computer.jpg|Cover]] John O'Donnell, Cordelia Hall and Rex Page: [http://www.dcs.gla.ac.uk/~jtod/discrete-mathematics/ <em>Discrete Mathematics Using a Computer</em>], 2nd edition |
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− | Springer, 2006, 441 pages. ISBN 1-84628-241-1. |
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− | <blockquote> |
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− | <b>Book description:</b><br> |
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− | This book introduces the main topics of discrete mathematics with a strong emphasis on |
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− | applications to computer science. It uses computer programs to implement and illustrate |
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− | the mathematical ideas, helping the reader to gain a concrete understanding of the |
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− | abstract mathematics. The programs are also useful for practical calculations, and they |
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− | can serve as a foundation for larger software packages. |
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− | Designed for first and second year undergraduate students, the book is also ideally suited |
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− | to self-study. No prior knowledge of functional programming is required; the book and |
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− | the online documentation provide everything you will need. |
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− | </blockquote> |
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− | ;[[Image:Computational_Oriented_Matroids.jpg|Cover]] Jrgen Bokowski: [http://www.bookzilla.de/shop/action/productDetails;jsessionid=fdc-3im7hb88d3c.www12?aUrl=90006951&artiId=4435822<em>Computational Oriented Matroids</em>], |
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− | Cambridge University Press, November 2005, 450 pages. ISBN 0521849306 |
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− | <blockquote><b>Book description:</b><br>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.</blockquote> |
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− | ==Libraries== |
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− | A growing [[Libraries_and_tools/Mathematics|collection of Haskell math libraries]]. |
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− | ==Theorem proving== |
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− | There has been a long tradition of mechanised reasoning in and about Haskell. |
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− | * [[Research_papers/Testing_and_correctness#Verifying_Haskell_programs|Research papers]] |
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− | * [[Libraries_and_tools/Theorem_provers|Theorem provers]] |
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− | ==Mathematics from a Haskell perspective == |
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− | [[Mathematics|Articles]] on computational and category theoretic branches of |
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− | mathematics, and their role as a foundation for programming and Haskell |
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− | itself. |
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− | ==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?] |
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− | * [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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[[Category:Community]] |
[[Category:Community]] |
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[[Category:Mathematics|*]] |
[[Category:Mathematics|*]] |

## Latest revision as of 23:18, 31 January 2009

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:

- Mathematics textbooks using Haskell
- The category of math libraries on the Hackage library database.
- A growing collection of Haskell math libraries.
- There has been a long tradition of mechanised reasoning in and about Haskell.
- Articles on computational and category theoretic branches of mathematics, and their role as a foundation for programming and Haskell itself.
- Articles about Haskell and mathematics
- Mathematical prelude discussion: Initiatives to develop a mathematically sound algebraic class hierarchy for Haskell.
- Z4 - a Ro/Haskell page with a small (not complete) implementation of Z4, as part of the Project "Boosting your Maths. Faculty with Haskell" . See paragraph # 3, on page Z4

Math papers using Haskell: