Least and greatest fixpoints in game semantics

Details Least and greatest fixpoints in game semantics Least and greatest fixpoints in game semantics

2010-01-05

arxiv.org/abs/1001.0641v1

Foundations of Software Science and Computational Structures, York : United Kingdom (2009)

Computer Science

Logic in Computer Science

Scientific paper

10.1007/978-3-642-00596-1_3

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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