A games model of bunched implications

Authors:
Guy McCusker;David Pym
Affiliations:
Department of Computer Science, University of Bath, Bath, United Kingdom;Hewlett-Packard Laboratories, Bristol, United Kingdom
Venue:
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Year:
2007

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Abstract

A game semantics of the (→*,→)-fragment of the logic of bunched implications, BI, is presented. To date, categorical models of BI have been restricted to two kinds: functor category models; and the category Cat itself. The game model is not of this kind. Rather, it is based on Hyland-Ong-Nickau-style games and embodies a careful analysis of the notions of resource sharing and separation inherent in BI. The key to distinguishing between the additive and multiplicative connectives of BI is a semantic notion of separation. The main result of the paper is that the model is fully complete: every finite, total strategy in the model is the denotation of a term of the αλ-calculus, the term language for the fragment of BI under consideration.