Category theory: Difference between revisions
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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== Foundations == | |||
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''). | |||
== Categorical programming == | == 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 | 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. | ||
* 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
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).
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