Difference between revisions of "Dependent type"
EndreyMark (talk | contribs) m (Specifying exactly which papers are meant as I referred to HaskelDB) |
EndreyMark (talk | contribs) (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 == |
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* [http://haskell.org/hawiki/SimulatingDependentTypes SimulatingDependentTypes] of HaWiki |
* [http://haskell.org/hawiki/SimulatingDependentTypes SimulatingDependentTypes] of HaWiki |
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| + | * The ''See also'' section of [[Type]] page contains links to many related idioms. |
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| − | * [[Smart constructors]] |
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* On the usefulness of such idioms in practice, see HaskellDB's pages |
* On the usefulness of such idioms in practice, see HaskellDB's pages |
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** [http://haskelldb.sourceforge.net/ updated] page (see ''Papers'' subsection on [http://haskelldb.sourceforge.net/#documentation Documentation]) |
** [http://haskelldb.sourceforge.net/ updated] page (see ''Papers'' subsection on [http://haskelldb.sourceforge.net/#documentation Documentation]) |
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Revision as of 12:56, 6 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 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 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
Proposals
John Hughes: Dependent Types in Haskell (some ideas).
Simulating them
- SimulatingDependentTypes of HaWiki
- 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
- updated page (see Papers subsection on Documentation)
- which presupposes reading also paper on the original page (see Documentation subpage, PostScript version)