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Communication Dans Un Congrès Année : 2007

A theory for game theories

Résumé

Game semantics is a valuable source of fully abstract models of programming languages or proof theories based on categories of so-called games and strategies. However, there are many variants of this technique, whose interrelationships largely remain to be elucidated. This raises the question: what is a category of games and strategies? Our central idea, taken from the first author's PhD thesis, is that positions and moves in a game should be morphisms in a base category: playing move m in position f consists in factoring f through m, the new position being the other factor. Accordingly, we provide a general construction which, from a selection of "legal moves" in an almost arbitrary category, produces a category of games and strategies, together with subcategories of deterministic and winning strategies. As our running example, we instantiate our construction to obtain the standard category of Hyland-Ong games subject to the switching condition. The extension of our framework to games without the switching condition is handled in the first author's PhD thesis.
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Dates et versions

hal-00310542 , version 1 (11-08-2008)

Identifiants

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Michel Hirschowitz, André Hirschowitz, Tom Hirschowitz. A theory for game theories. FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science, 2007, New Delhi, India. pp.192-203, ⟨10.1007/978-3-540-77050-3⟩. ⟨hal-00310542⟩
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