Date of Original Version

3-5-1999

Type

Article

Published In

Mathematical Structures in Computer Science 10, 1 (Feb 2000): 81-96.

Rights Management

All Rights Reserved

Abstract or Description

The [lambda]-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from category theory, the usual calculus of [lambda]-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ‘minimal’ topological model in which every continuous function is [lambda]-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke [lambda]-models.

DOI

10.1017/S0960129599002972

Included in

Philosophy Commons

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