Partial hyperdoctrines: Categorical models for partial function logic and Hoare logic
P Knijnenburg, F Nordemann - Mathematical Structures in Computer …, 1994 - cambridge.org
P Knijnenburg, F Nordemann
Mathematical Structures in Computer Science, 1994•cambridge.orgIn 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 …
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 …
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.
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