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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
   
To see how Illative Combinatory Logic 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.
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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
 
<math>\forall x : S \Rightarrow T</math>
 
<math>\forall x : S \Rightarrow T</math>

Revision as of 15:27, 1 March 2006

Contents


1 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 \forall x : S \Rightarrow T of Epigram corresponds to \mathbf G\;S\;(\lambda x . T) in Illative Combinatory Logic. I think e.g. the followings should correspond to each other:

  • \mathrm{realNullvector} :\;\;\;\forall n: \mathrm{Nat} \Rightarrow \mathrm{RealVector}\;n
  • \mathbf G\;\,\mathrm{Nat}\;\,\mathrm{RealVector}\;\,\mathrm{realNullvector}


2 Dependently typed languages

Epigram is a full dependently typed programming language see especially

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).

3 Dependent types in Haskell programming