Difference between revisions of "Dependent type"
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== Type Theory == |
== Type Theory == |
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| + | Simon Thompson: [http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/ Type Theory and Functional Programming]. Section 6.3 deals with dependent types, but because of the strong emphasis on [http://en.wikipedia.org/wiki/Curry_Howard_isomorphism Curry-Howard isomorphism] and the connections between logic and programming, |
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| + | the book seemed cathartic for me even from its beginning. |
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| + | [http://lists.seas.upenn.edu/mailman/listinfo/types-list Types Forum] |
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== Illative Combinatory Logic == |
== Illative Combinatory Logic == |
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== Other techniques == |
== Other techniques == |
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| − | [http://www-sop.inria.fr/oasis/DTP00/ |
+ | [http://www-sop.inria.fr/oasis/DTP00/ APPSEM Workshop on Subtyping & Dependent Types in Programming] |
= Dependent types in Haskell programming = |
= Dependent types in Haskell programming = |
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Revision as of 17:19, 1 March 2006
The concept of dependent types
General
Dependent Types in Programming abstract in APPSEM'2000
Type Theory
Simon Thompson: Type Theory and Functional Programming. Section 6.3 deals with dependent types, but because of the strong emphasis on Curry-Howard isomorphism and the connections between logic and programming, the book seemed cathartic for me even from its beginning.
Illative Combinatory Logic
To see how Illative CombinatoryLogic deals with dependent types, see combinator G described in Systems of Illative Combinatory Logic complete for first-order propositional and predicate calculus by Henk Barendregt, Martin Bunder, Wil Dekkers. It seems to me that the dependent type construct of Epigram corresponds to in Illative Combinatory Logic. I think e.g. the followings should correspond to each other:
Dependently typed languages
Epigram
Epigram is a full dependently typed programming language see especially
- Epigram Tutorial by Conor McBride
- and Why dependent types matter by Thorsten Altenkirch, Conor McBride and James McKinna).
Dependent types (of this language) also provide a not-forgetful concept of views (already mentioned in the Haskell Future; the connection between these concepts is described in p. 32 of Epigram Tutorial (section 4.6 Patterns Forget; Matching Is Remembering).
Other techniques
APPSEM Workshop on Subtyping & Dependent Types in Programming
Dependent types in Haskell programming
- John Hughes: Dependent Types in Haskell (some ideas).
- SimulatingDependentTypes of HaWiki