Collections, Sets and Types - Inria - Institut national de recherche en sciences et technologies du numérique
Rapport (Rapport De Recherche) Année : 1995

Collections, Sets and Types

Résumé

We give a first order formulation of Church's type theory in which types are mere sets. This formulation is obtained by replacing $\lambda$-calculus by a language of combinators (skolemized comprehension scheme), introducing a distinction between propositions and their contents, relativizing quantifiers and at last replacing typing predicates by membership to some sets. The theory obtained this way has both a type theoretical flavor and a set theoretical one. Like set theory, it is a first order theory, and it uses only one notion of collection. Like type theory, it gives an explicit notation for objects, a primitive notion of function and propositions are objects.

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Domaines

Autre [cs.OH]
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Dates et versions

inria-00073982 , version 1 (24-05-2006)

Identifiants

  • HAL Id : inria-00073982 , version 1

Citer

Gilles Dowek. Collections, Sets and Types. [Research Report] RR-2708, INRIA. 1995. ⟨inria-00073982⟩
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