# Category theory

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EndreyMark (Talk | contribs) (Including Books and tutorials#Categorical programming into here.) |
EndreyMark (Talk | contribs) (→Foundations: Copying reference of Toposes, Triples and Theories from Books and tutorials#Foundations here) |
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+ | Michael Barr and Charles Wells: [http://www.cwru.edu/artsci/math/wells/pub/ttt.html Toposes, Triples and Theories]. The online free available book is both an introductory and a detailed description of category theory. By the way, it is also a category theoretical descripton of the concept of ''monad'' (the book uses another name instead of monad: ''triple''). |
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== Categorical programming == |
== Categorical programming == |
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− | Catamorphisms and related concepts, categorical approach to functional programming, categorical programming. Many materials cited here refer to category theory, so as an introduction to this discipline see the ''Foundations'' section at the end of this page. |
+ | Catamorphisms and related concepts, categorical approach to functional programming, categorical programming. Many materials cited here refer to category theory, so as an introduction to this discipline see the [[#Foundations]] section. |

* Erik Meijer, Maarten Fokkinga, Ross Paterson: [http://citeseer.ist.psu.edu/meijer91functional.html Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire]. See also related documents (in the CiteSeer page). Understanding the article does not require a category theory knowledge -- a self-contained material on the concept of catamorphism, anamoprhism and other related concepts. |
* Erik Meijer, Maarten Fokkinga, Ross Paterson: [http://citeseer.ist.psu.edu/meijer91functional.html Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire]. See also related documents (in the CiteSeer page). Understanding the article does not require a category theory knowledge -- a self-contained material on the concept of catamorphism, anamoprhism and other related concepts. |
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* Varmo Vene and Tarmo Uustalu: [http://citeseer.ist.psu.edu/vene98functional.html Functional Programming with Apomorphisms / Corecursion] |
* Varmo Vene and Tarmo Uustalu: [http://citeseer.ist.psu.edu/vene98functional.html Functional Programming with Apomorphisms / Corecursion] |

## Revision as of 10:11, 7 June 2006

## 1 Foundations

Michael Barr and Charles Wells: Toposes, Triples and Theories. The online free available book is both an introductory and a detailed description of category theory. By the way, it is also a category theoretical descripton of the concept of *monad* (the book uses another name instead of monad: *triple*).

## 2 Categorical programming

Catamorphisms and related concepts, categorical approach to functional programming, categorical programming. Many materials cited here refer to category theory, so as an introduction to this discipline see the #Foundations section.

- Erik Meijer, Maarten Fokkinga, Ross Paterson: Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire. See also related documents (in the CiteSeer page). Understanding the article does not require a category theory knowledge -- a self-contained material on the concept of catamorphism, anamoprhism and other related concepts.
- Varmo Vene and Tarmo Uustalu: Functional Programming with Apomorphisms / Corecursion
- Varmo Vene: Categorical Programming with Inductive and Coinductive Types. The book accompanies the deep categorical theory topic with Haskell examples.
- Tatsuya Hagino: A Categorical Programming Language
- Charity, a categorical programming language implementation.
- Deeply uncurried products, as categorists might like them article mentions a conjecture: relatedness to Combinatory logic