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Topological Representation of the Lambda-Calculus

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posted on 05.03.1999, 00:00 authored by Steven AwodeySteven Awodey
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.

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05/03/1999

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