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Reports (Research Report) Year : 1995

Collections, Sets and Types


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


  • HAL Id : inria-00073982 , version 1


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