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Least and greatest fixpoints in game semantics

Abstract : We show how solutions to many recursive arena equations can be computed in a natural way by allowing loops in arenas. We then equip arenas with winning functions and total winning strategies. We present two natural winning conditions compatible with the loop construction which respectively provide initial algebras and terminal coalgebras for a large class of continuous functors. Finally, we introduce an intuitionistic sequent calculus, extended with syntactic constructions for least and greatest fixed points, and prove it has a sound and (in a certain weak sense) complete interpretation in our game model.
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https://hal.archives-ouvertes.fr/hal-00443537
Contributor : Pierre Clairambault <>
Submitted on : Wednesday, December 30, 2009 - 1:22:20 PM
Last modification on : Saturday, March 28, 2020 - 2:23:39 AM
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Pierre Clairambault. Least and greatest fixpoints in game semantics. Foundations of Software Science and Computational Structures, Mar 2009, York, United Kingdom. pp.16-31, ⟨10.1007/978-3-642-00596-1_3⟩. ⟨hal-00443537⟩

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