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Totality in arena games

Abstract : We tackle the problem of preservation of totality by composition in arena games. We first explain how this problem reduces to a finiteness theorem on what we call pointer structures, similar to the parity pointer functions of Harmer, Hyland and Mélliès and the interaction sequences of Coquand. We discuss how this theorem relates to normalization of linear head reduction in simply-typed lambda-calculus, leading us to a semantic realizability proof à la Kleene of our theorem. We then present another proof of a more combinatorial nature. Finally, we discuss the exact class of strategies to which our theorems apply.
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https://hal.archives-ouvertes.fr/hal-00443535
Contributor : Pierre Clairambault <>
Submitted on : Wednesday, December 30, 2009 - 12:55:26 PM
Last modification on : Saturday, March 28, 2020 - 2:24:06 AM
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Pierre Clairambault, Russ Harmer. Totality in arena games. Annals of Pure and Applied Logic, Elsevier Masson, 2009, 161 (5), pp.673-689. ⟨10.1016/j.apal.2009.07.016⟩. ⟨hal-00443535⟩

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