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| HAL : hal-00310542, version 1 |
| DOI : 10.1007/978-3-540-77050-3 |
| Fiche détaillée |  Récupérer au format |
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| FSTTCS 2007: Foundations of Software Technology and Theoretical Computer Science, New Delhi : Inde (2007) |
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| A theory for game theories |
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| Michel Hirschowitz 1, 2André Hirschowitz 3 |
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| (2007) |
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| 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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| 1 : | Laboratoire d'Intégration des Systèmes et des Technologies (CEA LIST) |
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CEA : DRT/LIST |
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| 2 : | Laboratoire d'informatique de l'école polytechnique (LIX) |
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CNRS : UMR7161 – Polytechnique - X |
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| 3 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université de Nice Sophia Antipolis (UNS) |
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| 4 : | Laboratoire de Mathématiques (LAMA) |
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CNRS : UMR5127 – Université de Savoie |
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| Domaine | : | Informatique/Logique en informatique |
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| Game semantics – categories – double categories. |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00310542, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00310542 | |
| oai:hal.archives-ouvertes.fr:hal-00310542 | |
| Contributeur : Tom Hirschowitz | |
| Soumis le : Lundi 11 Août 2008, 08:42:29 | |
| Dernière modification le : Lundi 11 Août 2008, 11:20:03 | |
