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Dependent type

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m (Specifying exactly which papers are meant as I referred to HaskelDB)
(Replacing the Smart constructors link with Type link. So the reference became more general, because Smart constructors can be reached from Type)
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== Simulating them ==
== Simulating them ==
* [ SimulatingDependentTypes] of HaWiki
* [ SimulatingDependentTypes] of HaWiki
* [[Smart constructors]]
* The ''See also'' section of [[Type]] page contains links to many related idioms.
* On the usefulness of such idioms in practice, see HaskellDB's pages
* On the usefulness of such idioms in practice, see HaskellDB's pages
** [ updated] page (see ''Papers'' subsection on [ Documentation])
** [ updated] page (see ''Papers'' subsection on [ Documentation])

Revision as of 12:56, 6 March 2006


1 The concept of dependent types

1.1 General


Dependent Types in Programming abstract in APPSEM'2000

1.2 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.

Types Forum

1.3 Illative Combinatory Logic

To see how Illative Combinatory logic 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

2.1 Epigram

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).

2.2 Other techniques

APPSEM Workshop on Subtyping & Dependent Types in Programming

3 Dependent types in Haskell programming

3.1 Proposals

John Hughes: Dependent Types in Haskell (some ideas).

3.2 Simulating them