Difference between revisions of "Haskell and mathematics"

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.

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.

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

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

Mathematical hierarchy

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

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 ==Tutorials and blogs on Haskell for mathematicians==
+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/why-isnt-listt-monad.html Why isn't ListT list a monad?]
-* [http://sigfpe.blogspot.com/2006/11/yoneda-lemma.html Reverse Engineering Machines with the Yoneda Lemma]
-* [http://sigfpe.blogspot.com/2006/11/variable-substitution-gives.html Variable substitution gives a...]
-* [http://sigfpe.blogspot.com/2006/11/from-l-theorem-to-spreadsheet.html From Löb's Theorem to Spreadsheet Evaluation]
-* [http://sigfpe.blogspot.com/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.]
-* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry]
-* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra]
-* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell]
-* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in Haskell]
-* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types]
-* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!]
-* [http://sigfpe.blogspot.com/2006/01/eleven-reasons-to-use-haskell-as.html Eleven Reasons to use Haskell as a Mathematician]
-* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
-* [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ A-algebras and group cohomology]
-* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
-* [http://blog.mikael.johanssons.org/archive/2006/10/computational-group-theory-in-haskell-1-in-a-series/ Computational Group Theory in Haskell]
-* [http://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology]
-* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?]
-* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus]
-* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
-* [http://vandreev.wordpress.com/2006/12/04/non-standard-analysis-and-automatic-differentiation/ Non-standard analysis, automatic differentiation, Haskell]
-* [http://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory
-* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves]
 ==Mathematical hierarchy==