Abstract
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 [11], 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 [11].
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Hirschowitz, M., Hirschowitz, A., Hirschowitz, T. (2007). A Theory for Game Theories. In: Arvind, V., Prasad, S. (eds) FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2007. Lecture Notes in Computer Science, vol 4855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77050-3_16
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DOI: https://doi.org/10.1007/978-3-540-77050-3_16
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