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Asynchronous Games 2  The true concurrency of innocence
, 2004
"... In game semantics, the higherorder value passing mechanisms of the #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 sequ ..."
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Cited by 29 (6 self)
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In game semantics, the higherorder value passing mechanisms of the #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 #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 #calculus, in which the game semantics of a #term is formulated directly as a trace semantics, performing the syntactic exploration or parsing of that #term.
Games on graphs and sequentially realizable functionals
 In Logic in Computer Science 02
, 2002
"... We present a new category of games on graphs and derive from it a model for Intuitionistic Linear Logic. Our category has the computational flavour of concrete data structures but embeds fully and faithfully in an abstract games model. It differs markedly from the usual Intuitionistic Linear Logic s ..."
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Cited by 17 (2 self)
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We present a new category of games on graphs and derive from it a model for Intuitionistic Linear Logic. Our category has the computational flavour of concrete data structures but embeds fully and faithfully in an abstract games model. It differs markedly from the usual Intuitionistic Linear Logic setting for sequential algorithms. However, we show that with a natural exponential we obtain a model for PCF essentially equivalent to the sequential algorithms model. We briefly consider a more extensional setting and the prospects for a better understanding of the Longley Conjecture. 1
Sequential algorithms and strongly stable functions
 in the Linear Summer School, Azores
, 2003
"... ..."
Comparing Hierarchies of Types in Models of Linear Logic
, 2003
"... We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distri ..."
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Cited by 6 (3 self)
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We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F : C D : G and transformations Id C ) GF and Id D ) FG, and (2) their exponentials ! are related by distributive laws % : ! : ! M G ) G ! N commuting to the promotion rule. The key ingredient of the proof is a notion of backandforth translation between the hierarchies of types induced by M and N. We apply this result to compare (1) the qualitative and the quantitative hierarchies induced by the coherence (or hypercoherence) space model, (2) several paradigms of games semantics: errorfree vs. erroraware, alternated vs. nonalternated, backtracking vs. repetitive, uniform vs. nonuniform.
Parallel and Serial Hypercoherences
 Theoretical Computer Science, NorthHolland
, 1995
"... It is known that the strongly stable functions which arise in the semantics of PCF can be realized by sequential algorithms, which can be considered as deterministic strategies in games associated to PCF types. Studying the connection between strongly stable functions and sequential algorithms, two ..."
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Cited by 4 (0 self)
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It is known that the strongly stable functions which arise in the semantics of PCF can be realized by sequential algorithms, which can be considered as deterministic strategies in games associated to PCF types. Studying the connection between strongly stable functions and sequential algorithms, two dual classes of hypercoherences naturally arise: the parallel and serial hypercoherences. The objects belonging to the intersection of these two classes are in bijective correspondence with the socalled "serialparallel" graphs, that can essentially be considered as games. We show how to associate to any hypercoherence a parallel hypercoherence together with a projection onto the given hypercoherence and present some properties of this construction. Intuitively, it makes explicit the computational time of a hypercoherence.
Playful, streamlike computation
, 2003
"... We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation – that is, computation of successive bits of information upon request. The core of the approach surveyed here dates back to the work of Berry and the author on sequential algorithms ..."
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We offer a short tour into the interactive interpretation of sequential programs. We emphasize streamlike computation – that is, computation of successive bits of information upon request. The core of the approach surveyed here dates back to the work of Berry and the author on sequential algorithms on concrete data structures in the late seventies, culminating in the design of the programming language CDS, in which the semantics of programs of any type can be explored interactively. Around one decade later, two major insights of Cartwright and Felleisen on one hand, and of Lamarche on the other hand gave new, decisive impulses to the study of sequentiality. Cartwright and Felleisen observed that sequential algorithms give a direct semantics to control operators like callcc and proposed to include explicit errors both in the syntax and in the semantics of the language PCF. Lamarche (unpublished) connected sequential algorithms to linear logic and games. The successful program of games semantics has spanned over the nineties until now, starting with syntaxindependent characterizations of the term model of PCF by Abramsky, Jagadeesan, and Malacaria on one hand, and by Hyland and Ong on the other hand.
Only a basic acquaintance with λcalculus, domains and linear logic is assumed in sections 1 through 3.