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Categorical models for non-extensional λ-calculi and combinatory logic

Published online by Cambridge University Press:  04 March 2009

Simone Martini
Affiliation:
Università di Pisa, Dipartimento do Informatica, Corso Italia, 40 I-56125 Pisa, Italy

Abstract

The notions of weak Cartesian closed category and very weak CCC are introduced by dropping the extensionality (and the naturality) requirements in the adjunction defining the closed structure of a CCC. A number of specific examples of these categories are given. The weak notions are shown to be equivalent from both the semantic and syntactic standpoint to the typed non-extensional lambda-calculus and to the typed Combinatory Logic, extended with surjective pairs. Type-free models are characterized as reflexive objects in wCCCs. Finally, categorical models for the second-order non-extensional calculus are defined, by introducing a simple generalization of the notion of PL-category.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1992

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