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Partial hyperdoctrines: categorical models for partial function logic and Hoare logic

Published online by Cambridge University Press:  04 March 2009

Peter Knijnenburg  and
Frank Nordemann
Peter Knijnenburg
Affiliation:
Department of Computer Science, Utrecht University, Padualaan 14, 3584 CH Utrecht, the Netherlands
Frank Nordemann
Affiliation:
Department of Computer Science, Utrecht University, Padualaan 14, 3584 CH Utrecht, the Netherlands
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Abstract

In this paper we provide a categorical interpretation of the first-order Hoare logic of a small programming language by giving a weakest precondition semantics for the language. To this end, we extend the well-known notion of a (first-order) hyperdoctrine to include partial maps. The most important new aspect of the resulting partial (first-order) hyperdoctrine is a different notion of morphism between the fibres. We also use this partial hyperdoctrine to give a model for Beeson's Partial Function Logic such that (a version of) his axiomatization is complete with respect to this model. This shows the usefulness of the notion, independent of its intended use as a model for Hoare logic.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 4 , Issue 2 , June 1994 , pp. 117 - 146
Copyright
Copyright © Cambridge University Press 1994

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