Understanding Game Semantics Through Coherence Spaces

Game Semantics has successfully provided fully abstract models for a variety of programming languages not possible using other denotational approaches. Although it is a flexible and accurate way to give semantics to a language, its underlying mathematics is awkward. For example, the proofs that strategies compose associatively and maintain properties imposed on them such as innocence are intricate and require a lot of attention. This work aims at beginning to provide a more elegant and uniform mathematical ground for Game Semantics. Our quest is to find mathematical entities that will retain the properties that make games an accurate way to give semantics to programs, yet that are simple and familiar to work with. Our main result is a full, faithful strong monoidal embedding of a category of games into a category of coherence spaces, where composition is simple composition of relations.