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Foundations of Software Science and Computational Structures, York : Royaume-Uni (2009)
Least and greatest fixpoints in game semantics
Pierre Clairambault 1
(2009-03-27)

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.
1:  Preuves, Programmes et Systèmes (PPS)
CNRS : UMR7126 – Université Paris VII - Paris Diderot
Computer Science/Programming Languages

Computer Science/Computer Science and Game Theory

Computer Science/Logic in Computer Science
game semantics – initial algebras – terminal coalgebras
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