Asynchronous games 2: The true concurrency of innocence

In game semantics, the higher-order value passing mechanisms of the λ -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 seq...

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Published in	Theoretical computer science Vol. 358; no. 2; pp. 200 - 228
Main Author	MELLIES, Paul-André
Format	Journal Article Conference Proceeding
Language	English
Published	Amsterdam Elsevier B.V 07.08.2006 Elsevier
Subjects	[formula omitted]-calculus Algorithmics. Computability. Computer arithmetics Applied sciences Computer Science Computer science; control theory; systems Exact sciences and technology Game semantics General logic Language theory and syntactical analysis Logic and foundations Logic in Computer Science Mathematical logic, foundations, set theory Mathematics Mazurkiewicz traces Sciences and techniques of general use Theoretical computing λ -calculus Game semantics Mazurkiewicz traces Asynchronous Computer theory Confluence Concurrency A-calculus Lambda calculus Mazurkiewicz trace innocence linear logic concurrency theory lambda-calculus game semantics asynchronous transition systems
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Abstract	In game semantics, the higher-order value passing mechanisms of the λ -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 λ -terms, expressed as innocent strategies, may be analysed 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 λ -calculus, in which the game semantics of a λ -term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that λ -term.
AbstractList	In game semantics, the higher-order value passing mechanisms of the λ -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 λ -terms, expressed as innocent strategies, may be analysed 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 λ -calculus, in which the game semantics of a λ -term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that λ -term. 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.
Author	Melliès, Paul-André
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Cites_doi	10.1109/LICS.1997.614931 10.1006/inco.2000.2917 10.1007/978-1-4471-0615-9_3 10.1017/S0960129503003980 10.1109/LICS.1999.782638 10.1007/3-540-58140-5_25 10.1007/BFb0017483 10.7146/dpb.v6i78.7691 10.1007/978-1-4757-3851-3_9 10.1109/LICS.2002.1029834 10.1006/inco.2000.2930 10.1016/j.entcs.2004.06.057 10.1007/BFb0032041 10.1017/S0960129500003133 10.1145/99583.99625 10.1109/LICS.2002.1029835 10.1016/S1571-0661(04)80965-4 10.1007/3-540-45610-4_4 10.1109/LICS.1996.561456 10.1016/0304-3975(77)90053-6 10.1007/978-3-540-24727-2_16
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References_xml	– reference: D. Kuske, Non deterministic automata with concurrency relations and domains, in: S. Tison (Ed.), Proc. Colloq. Trees in Algebra and Programming, CAAP’94, Lecture Notes in Computer Science, Vol. 787, Springer, Berlin, 1994. – reference: J.-J. Lévy, Réductions correctes et optimales dans le lambda-calcul, Thèse de Doctorat d’Etat, Université Paris VII, 1978. – reference: Terese, Term Rewriting Systems, Cambridge Tracts in Theoretical Computer Science, Vol. 55, Cambridge University Press, Cambridge, 2003. – reference: M. Bezem, J.W. Klop, Abstract reduction systems, in: Bezem et al. [Terese, Term Rewriting Systems, Cambridge Tracts in Theoretical Computer Science, Vol. 55, Cambridge University Press, Cambridge, 2003.], pp. 7–23. – reference: E.W.S.P. Panangaden, V. Shanbhogue, Stability and sequentiality in data flow networks, in: A. Nerode, Y.V. Matiyasevich (Eds.), Internat. Conf. 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Snippet	In game semantics, the higher-order value passing mechanisms of the λ -calculus are decomposed as sequences of atomic actions exchanged by a Player and its... 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...
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SubjectTerms	[formula omitted]-calculus Algorithmics. Computability. Computer arithmetics Applied sciences Computer Science Computer science; control theory; systems Exact sciences and technology Game semantics General logic Language theory and syntactical analysis Logic and foundations Logic in Computer Science Mathematical logic, foundations, set theory Mathematics Mazurkiewicz traces Sciences and techniques of general use Theoretical computing
Title	Asynchronous games 2: The true concurrency of innocence
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