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Dependent type

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(Adding a new section ,,Simulating them [dependent types in Haskell]''. Links to wikipages: how to achieve static type checks instead of runtime assertions. Link to Smart constructors wikipage)
(Referring to HaskelDB, as a practical case study on the usefulness of such idioms (i.e. those related to simulating dependent types))
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* [http://haskell.org/hawiki/SimulatingDependentTypes SimulatingDependentTypes] of HaWiki
 
* [http://haskell.org/hawiki/SimulatingDependentTypes SimulatingDependentTypes] of HaWiki
 
* [[Smart constructors]]
 
* [[Smart constructors]]
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* On the usefulness of such idioms in practice, see HaskellBD's [http://haskelldb.sourceforge.net/ updated] and [http://www.haskell.org/haskellDB/ original] pages
   
 
[[Category:Theoretical foundations]]
 
[[Category:Theoretical foundations]]

Revision as of 11:00, 6 March 2006

Contents


1 The concept of dependent types

1.1 General

Wikipedia

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