# 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 | + | 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
of Epigram corresponds to
in Illative Combinatory Logic. I think e.g. the followings should correspond to each other:

## 2 Dependently typed languages

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*).

## 3 Dependent types in Haskell programming

- John Hughes: Dependent Types in Haskell (some ideas).
- SimulatingDependentTypes of HaWiki