Least and greatest fixpoints in game semantics

Pierre Clairambault (1)

1 PPS - Preuves, Programmes et Systèmes

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.

Mots clés: game semantics; initial algebras; terminal coalgebras

Domaines: Langage de programmation [cs.PL]; Informatique et théorie des jeux [cs.GT]; Logique en informatique [cs.LO]

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⟩