Asynchronous Games 2: The True Concurrency of Innocence

Abstract

AbstractIn game semantics, one expresses the higher-order value passing mechanisms of the λ-calculus as sequences of atomic actions exchanged by a Player and its Opponent in the course of time. This is reminiscent of trace semantics in concurrency theory, in which a process is identified to the sequences of requests it generates. We take as working hypothesis that game semantics is, indeed, the trace semantics of the λ-calculus. This brings us to a notion of asynchronous game, inspired by Mazurkiewicz traces, which generalizes the usual notion of arena game. We then extract the true concurrency semantics of λ-terms from their interleaving semantics formulated as innocent strategies. This reveals that innocent strategies are positional strategies regulated by forward and backward interactive confluence properties. We conclude by defining a non uniform variant of the λ-calculus, whose game semantics is formulated as a trace semantics.KeywordsIEEE Computer SocietyPositional StrategyGame SemanticConcurrency TheoryTrace SemanticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.