# Difference between revisions of "Dependent type"

EndreyMark (talk | contribs) m (Dependent types moved to Dependent type) |
EndreyMark (talk | contribs) (Adding link to Agda and Cayene, as examples of dependently typed languages. Reference to Cayene will create a new First-class module page) |
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Dependent types (of this language) also provide a not-forgetful concept of '''views''' (already mentioned in the Haskell [[Future]]; |
Dependent types (of this language) also provide a not-forgetful concept of '''views''' (already mentioned in the Haskell [[Future]]; |
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the connection between these concepts is described in p. 32 of Epigram Tutorial (section ''4.6 Patterns Forget; Matching Is Remembering''). |
the connection between these concepts is described in p. 32 of Epigram Tutorial (section ''4.6 Patterns Forget; Matching Is Remembering''). |
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+ | == Agda == |
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+ | “[http://www.cs.chalmers.se/~catarina/agda/ Agda] is a system for incrementally developing proofs and programs. Agda is also a functional language with dependent types. This language is very similar to [http://www.cs.chalmers.se/~augustss/cayenne/index.html cayenne] and agda is intended to be a (almost) full implementation of it in the future.“ |
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+ | People who are interested also in theorem proving may sse the [[Libraries and tools/Theorem provers|theorem provers]] page. |
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+ | == Cayene == |
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+ | [http://www.cs.chalmers.se/~augustss/cayenne/index.html Cayene] is influenced also by constructive type theory (see its page). Dependent types make it possible not to have a separate module lenguage and a core language. This idea may concern Haskell too, see [[First-class module]] page. |
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== Other techniques == |
== Other techniques == |

## Revision as of 20:38, 25 March 2006

## Contents

# 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*).

## Agda

“Agda is a system for incrementally developing proofs and programs. Agda is also a functional language with dependent types. This language is very similar to cayenne and agda is intended to be a (almost) full implementation of it in the future.“

People who are interested also in theorem proving may sse the theorem provers page.

## Cayene

Cayene is influenced also by constructive type theory (see its page). Dependent types make it possible not to have a separate module lenguage and a core language. This idea may concern Haskell too, see First-class module page.

## 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)

- updated page (see