Difference between revisions of "Dependent type"
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[http://www-sop.inria.fr/oasis/Caminha00/abstract.html Dependent Types in Programming] abstract in APPSEM'2000 |
[http://www-sop.inria.fr/oasis/Caminha00/abstract.html Dependent Types in Programming] abstract in APPSEM'2000 |
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− | To see how Illative |
+ | To see how Illative [[CombinatoryLogic]] deals with dependent types, see combinator '''G''' described in [http://citeseer.ist.psu.edu/246934.html 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 |
It seems to me that the dependent type construct |
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<math>\forall x : S \Rightarrow T</math> |
<math>\forall x : S \Rightarrow T</math> |
Revision as of 15:27, 1 March 2006
The concept of dependent types
Dependent Types in Programming abstract in APPSEM'2000
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 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).
Dependent types in Haskell programming
- John Hughes: Dependent Types in Haskell (some ideas).
- SimulatingDependentTypes of HaWiki