Recursive Types in Games: Axiomatics and Process Representation

This paper presents two basic results on game-based semantics of FPC, a metalanguage with sums, products, exponentials and recursive types. First we give an axiomatic account of the category of games G introduced in [15], offering a fundamental structural analysis of the category as well as a transparent way to prove computational adequacy. As a consequence we obtain an intensional fullabstraction result through a standard definability argument. Next we extend the category G by introducing a category of games Gi with optimised strategies; we show that the denotational semantics in Gi gives a compilation of FPC terms into core Pict codes (the asynchronous polyadic -calculus without summation). The process representation follows a pioneering idea of Hyland and Ong [18]. However, we advance their representation by introducing semantically well-founded optimisation techniques; we also extend the setting to encompass the rich type structure of FPC. The resulting code gives basic insight on the relationship between the abstract, categorical, types and their possible implementations.