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== Maths ==
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Articles using Haskell for mathematics, and the mathematics of Haskell.
   
=== Haskell for mathematics ===
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For further references see the:
   
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* [[Haskell_and_mathematics|Haskell math community]].
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* [[Blog_articles/Monads|Mathematics of monads]]
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== Haskell for mathematics ==
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=== General ===
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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://www.polyomino.f2s.com/ Haskell for Maths]: commutative algebra, combinatorics, number theory, and group theory libraries ([http://haskellformaths.blogspot.com/ blog], [http://hackage.haskell.org/package/HaskellForMaths hackage])
 
* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell]
 
* [http://sigfpe.blogspot.com/2006/09/learn-maths-with-haskell.html Learn Maths with Haskell]
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* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
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* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?]
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=== Calculus and Differential Geometry ===
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* [http://sigfpe.blogspot.com/2006/09/practical-synthetic-differential.html Practical Synthetic Differential Geometry]
 
* [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]
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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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=== Algebraic Topology and Geometry ===
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* [http://sigfpe.blogspot.com/2006/08/algebraic-topology-in-haskell.html Algebraic Topology in 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]
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* [http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html More Low Cost Geometric Algebra]
 
* [http://sigfpe.blogspot.com/2006/08/geometric-algebra-for-free_30.html Geometric Algebra for Free!]
 
* [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]
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* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
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=== Geometry ===
* [http://blog.mikael.johanssons.org/archive/2006/11/a-algebras-and-group-cohomology/ <math>A_\infty</math>-algebras and group cohomology]
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* [http://www.alpheccar.org/content/57.html Haskell, PDF and Penrose Tilings]
* [http://blog.mikael.johanssons.org/archive/2006/10/prototyping-thought/ Prototyping thought]
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* [http://www.kennknowles.com/blog/2007/11/20/visualizing-2d-convex-hull-using-gtk-and-opengl-in-haskell/ Visualizing 2D convex hull using Gtk and OpenGL in Haskell]
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* [http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/ Calculating the reflect-rotate-translate normal form for an isometry of the plane in Haskell, and verifying it with QuickCheck.]
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* [http://www.kennknowles.com/blog/2008/04/16/drawing-fractals-in-haskell-with-a-cursor-graphics-dsel-and-a-cute-list-representation/ Drawing fractals in Haskell with a cursor graphics DSEL and a cute list representation]
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=== Group theory ===
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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]
 
* [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://blog.mikael.johanssons.org/archive/2006/07/carry-bits-and-group-cohomology/ Carry bits and group cohomology]
* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
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* [http://sigfpe.blogspot.com/2007/06/monads-from-algebra-and-the-gray-code.html Monads from Algebra and the the Gray Code from Groups]
* [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.kennknowles.com/blog/2007/12/20/infinite-lazy-knuth-bendix-completion-for-monoids-in-haskell/ Infinite lazy Knuth-Bendix completion for monoids in Haskell]
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=== Set theory ===
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* Ordinals in Haskell
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** [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable ordinals]
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** [http://japple.blogspot.com/2007/06/ordinals-part-2.html Uncountable ordinals and better representations for countable ordinals]
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** [http://blog.jbapple.com/2007/07/ord-countable-ordinals-and-idea-of.html Ord, Countable Ordinals, and an Idea of sigfpe]
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* [http://japple.blogspot.com/2007/06/constructability-uncountability-and.html Constructability, Uncountability, and &omega;-Haskell]
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* [http://community.livejournal.com/evan_tech/220036.html Defining a power set in one line]
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** [http://blog.mikedaum.com/2007/06/28/haskell-power/ Commentary on this powerset implementation]
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=== Ring theory ===
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* [http://sambangu.blogspot.com/2006/12/polynomials-as-numbers Polynomials] ([http://sambangu.blogspot.com/2006/12/questions-on-haskell-style-and update])
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=== Number theory ===
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* Number theory and Haskell:
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** [http://cdsmith.wordpress.com/2007/06/02/learning-number-theory-and-haskell-the-division-algorithm/ The Division Algorithm]
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** [http://cdsmith.wordpress.com/2007/06/03/learning-number-theory-and-haskell-more-quickcheck-and-divisors/ QuickCheck and Divisors]
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** [http://cdsmith.wordpress.com/2007/06/06/learning-number-theory-and-haskell-greatest-common-divisor/ Greatest Common Divisor]
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** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
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** [http://cdsmith.wordpress.com/2007/07/05/learning-haskell-and-number-theory-the-end-of-gcd/ The End of GCD]
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* [http://www.akalin.cx/2007/07/06/a-foray-into-number-theory-with-haskell/ A foray into number theory with Haskell]
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=== Cryptography and coding theory ===
 
* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell]
 
* [http://vandreev.wordpress.com/2007/06/18/feistel-ciphers-and-des-in-haskell/ Feistel Ciphers and DES in Haskell]
 
* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in Haskell]
 
* [http://vandreev.wordpress.com/2007/01/07/arithmetic-coding/ Arithmetic coding in 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]
 
* [http://www.serpentine.com/blog/2007/01/11/two-dimensional-spatial-hashing-with-space-filling-curves/ Two-dimensional spatial hashing with space-filling curves]
* [http://japple.blogspot.com/2007/02/countable-ordinals-in-haskell.html Countable Ordinals in Haskell]
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* [http://www.quetzal.com/sambangu/2006/12/polynomials-as-numbers Polynomials as numbers]
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=== Logic ===
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* [http://sigfpe.blogspot.com/2006/06/laws-of-form-opinion.html Laws of Form: An Opinion]
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=== Numerics ===
 
* The Division Bell
 
* The Division Bell
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One]
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me.html Part One]
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** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)]
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/division-bell-tolls-for-me-part-four.html Part Four (Conclusion)]
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath]
 
** [http://praisecurseandrecurse.blogspot.com/2006/12/divisive-aftermath.html The Divisive Aftermath]
* [http://www.alpheccar.org/en/posts/show/57 Haskell, PDF and penrose tilings]
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* Overloading Haskell numbers
 
* Overloading Haskell numbers
 
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions]
 
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html Part 1: symbolic expressions]
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** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision]
 
** [http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-3.html Part 3: Fixed Precision]
 
** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery]
 
** [http://augustss.blogspot.com/2007/05/i-was-asked-if-my-fixed-number-module.html Dynamic epsilons in Haskell with a bit of type hackery]
* Number theory
 
** [http://cdsmith.wordpress.com/2007/06/24/learning-haskell-and-number-theory-gcd-and-higher-order-functions/ GCD and Higher Order Functions]
 
* [http://www.alpheccar.org/en/posts/show/74 Category theory 1]
 
* [http://www.alpheccar.org/en/posts/show/76 Category theory 2]
 
 
=== Theorem proving ===
 
   
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== Theorem proving ==
 
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]
 
* [http://vandreev.wordpress.com/2006/12/24/quick-and-dirty-theorem-prover/ Quick and Dirty Theorem Prover]
   
=== Quantum computing ===
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== Quantum computing ==
   
 
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
 
* [http://sigfpe.blogspot.com/2007/02/essence-of-quantum-computing.html The Essence of Quantum Computing]
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* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
 
* [http://sigfpe.blogspot.com/2007/03/independence-entanglement-and.html Independence, entanglement and decoherence with the quantum monad]
 
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
 
* [http://sigfpe.blogspot.com/2007/03/shor-quantum-error-correcting-code-and.html The Shor Quantum Error Correcting Code (and a Monad for Heat)]
* [http://www.alpheccar.org/en/posts/show/68 The Frame Of Reference Monad]
 
   
=== Mathematics of Haskell ===
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== Mathematics of Haskell ==
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=== Category theoretic ===
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* Category Theory and the Category of Haskell programs:
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** [http://www.alpheccar.org/content/74.html Part 1]
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** [http://www.alpheccar.org/content/76.html Part 2]
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** [http://www.alpheccar.org/content/77.html Part 3]
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* [http://en.wikibooks.org/wiki/Haskell/Category_theory Category theory and Haskell]
   
 
* [http://sigfpe.blogspot.com/2006/11/why-isnt-listt-monad.html Why isn't ListT list a monad?]
 
* [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/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/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/2006/10/games-strategies-and-self-composition.html Games, Strategies and the Self-Composition of the List Monad.]
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=== Lambda and combinator calculi ===
 
* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus]
 
* [http://scienceblogs.com/goodmath/2006/09/programs_are_proofs_models_and_1.php Programs are Proofs: Models and Types in Lambda Calculus]
* [http://scienceblogs.com/goodmath/2006/11/why_haskell.php Why Haskell?]
 
 
* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator]
 
* [http://www.onebadseed.com/blog/?p=51 Don't need the Y combinator]
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=== Other formal logics ===
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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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=== Miscellaneous ===
 
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq]
 
* [http://www.rubrication.net/2007/04/21/how-a-real-module-system-should-work/ ML, Haskell and Coq]
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* [http://sigfpe.blogspot.com/2006/09/infinitesimal-types.html Infinitesimal Types]
 
* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell]
 
* [http://www.alpheccar.org/en/posts/show/70 Djinn, Coq, Monad and a bit of Haskell]
* [http://www.alpheccar.org/en/posts/show/74 Category Theory and the category of Haskell programs]
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* [http://disparatemathematician.blogspot.com/2007/07/peanos-axioms-iv-advanced-functions-and.html Peano's Axioms IV: Advanced Functions and Integers]
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* [http://sigfpe.blogspot.com/2005/07/formal-power-series-and-haskell.html Formal Power Series and Haskell]
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[[Category:Tutorials]]
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[[Category:Mathematics|*]]

Latest revision as of 15:22, 26 January 2012

Articles using Haskell for mathematics, and the mathematics of Haskell.

For further references see the:

Contents

[edit] 1 Haskell for mathematics

[edit] 1.1 General

[edit] 1.2 Calculus and Differential Geometry

[edit] 1.3 Algebraic Topology and Geometry

[edit] 1.4 Geometry

[edit] 1.5 Group theory

[edit] 1.6 Set theory

[edit] 1.7 Ring theory

[edit] 1.8 Number theory

[edit] 1.9 Cryptography and coding theory

[edit] 1.10 Logic

[edit] 1.11 Numerics

[edit] 2 Theorem proving

[edit] 3 Quantum computing

[edit] 4 Mathematics of Haskell

[edit] 4.1 Category theoretic

[edit] 4.2 Lambda and combinator calculi

[edit] 4.3 Other formal logics

[edit] 4.4 Miscellaneous