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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
Simone Martini
Affiliation:
Università di Pisa, Dipartimento do Informatica, Corso Italia, 40 I-56125 Pisa, Italy
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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
Information
Mathematical Structures in Computer Science , Volume 2 , Issue 3 , September 1992 , pp. 327 - 357
Copyright
Copyright © Cambridge University Press 1992

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