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Publication Detail
A games model of bunched implications
  • Publication Type:
  • Authors:
    McCusker G, Pym D
  • Publication date:
  • Pagination:
    573, 588
  • Published proceedings:
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
  • Volume:
    4646 LNCS
  • ISBN-13:
  • Status:
  • Print ISSN:
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. © Springer-Verlag Berlin Heidelberg 2007.
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