Asynchronous games 2: the true concurrency of innocence

Paul-André Melliès (1)

1 PPS - Preuves, Programmes et Systèmes

In game semantics, the higher-order value passing mechanisms of the lambda-calculus are decomposed as sequences of atomic actions exchanged by a Player and its Opponent. Seen from this angle, game semantics is reminiscent of trace semantics in concurrency theory, where a process is identified to the sequences of requests it generates in the course of time. Asynchronous game semantics is an attempt to bridge the gap between the two subjects, and to see mainstream game semantics as a refined and interactive form of trace semantics. Asynchronous games are positional games played on Mazurkiewicz traces, which reformulate (and generalize) the familiar notion of arena game. The interleaving semantics of lambda-terms, expressed as innocent strategies, may be analyzed in this framework, in the perspective of true concurrency. The analysis reveals that innocent strategies are positional strategies regulated by forward and backward confluence properties. This captures, we believe, the essence of innocence. We conclude the article by defining a non uniform variant of the lambda-calculus, in which the game semantics of a lambda-term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that lambda-term.

Mots clés: lambda-calculus; game semantics; concurrency theory; asynchronous transition systems; Mazurkiewicz traces; innocence; linear logic

Domaines: Logique en informatique [cs.LO]

Paul-André Melliès. Asynchronous games 2: the true concurrency of innocence. CONCUR 2004 -- Concurrency Theory, Sep 2004, Londres, United Kingdom. pp.448-465. ⟨hal-00154286⟩