What's in a game? A theory of game models

TL;DR

This paper develops a unified abstract framework for game semantics, constructing categories of games and strategies, and extends it to innocent strategies, covering many existing models.

Contribution

It introduces a generic construction for game settings, creating a unified categorical framework for various game semantics models.

Findings

Constructed a category of games and strategies for any game setting.

Extended the framework to include innocent strategies as a subcategory.

Demonstrated that the framework encompasses many existing models, including sheaf-based ones.

Abstract

Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of strategies. We set out to unify these models into a basic abstract framework for game semantics, game settings. Our main contribution is the generic construction, for any game setting, of a category of games and strategies. Furthermore, we extend the framework to deal with innocence, and prove that innocent strategies form a subcategory. We finally show that our constructions cover many concrete cases, mainly among the early models and the very recent sheaf-based ones.