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Topological representation of the λ-calculus

Published online by Cambridge University Press:  01 February 2000

Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213 USA. Email:


The λ-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 λ-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 λ-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke λ-models.

Research Article
2000 Cambridge University Press

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