Hosts: Peter O’Hearn

TITLE: A games model of bunched implications

(joint work with David Pym, HP Labs, Bristol)

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 this work is that the model is fully complete: every finite, total strategy in the model is the denotation of a term of the alpha-lambda calculus, the term language for the fragment of BI under consideration.

If there’s time, the extension of the model to incorporate state, including local variables, will be discussed.