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18
Sequential algorithms and strongly stable functions
 in the Linear Summer School, Azores
, 2003
"... ..."
A graph abstract machine describing event structure composition
 In Proc. GT  VC, Graph Transformation for Verification and Concurrency, ENTCS
, 2006
"... Event structures, Game Semantics strategies and Linear Logic proofnets arise in different domains (concurrency, semantics, prooftheory) but can all be described by means of directed acyclic graphs (dag’s). They are all equipped with a specific notion of composition, interaction or normalization. W ..."
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Event structures, Game Semantics strategies and Linear Logic proofnets arise in different domains (concurrency, semantics, prooftheory) but can all be described by means of directed acyclic graphs (dag’s). They are all equipped with a specific notion of composition, interaction or normalization. We report ongoing work, aiming to investigate the common dynamics which seems to underly these different structures. In this paper we focus on confusion free event structures on one side, and linear strategies [Gir01,FM05] on the other side. We introduce an abstract machine which is based on (and generalizes) strategies interaction; it processes labelled dag’s, and provides a common presentation of the composition at work in these different settings. 1
From Asynchronous Games to Concurrent Games
, 2008
"... Game semantics was introduced in order to capture the dynamic behaviour of proofs and programs. In these semantics, the interaction between a program and its environment is modeled by a series of moves exchanged between two players in a game. Every program thus induces a strategy describing how it r ..."
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Game semantics was introduced in order to capture the dynamic behaviour of proofs and programs. In these semantics, the interaction between a program and its environment is modeled by a series of moves exchanged between two players in a game. Every program thus induces a strategy describing how it reacts when it is provided information by its environment. Traditionally, strategies considered in game semantics are alternating: the two protagonists play a move one after the other. This property is very natural when modeling sequential programming languages, but is not desirable for programs with concurrent features, since interactions cannot be synchronized globally anymore. Extending fundamental notions of game semantics to a nonalternating setting is far from being straightforward and requires to deeply rethink the definition of strategies. Recently, a series of interactive models, such as concurrent games where strategies are closure operators, were introduced in order to give denotational semantics of programming languages or logics with concurrent features. However, these models were poorly connected with traditional game semantics. We show here that asynchronous games, which combine true concurrency and game semantics, can be used to provide a precise link between these two kind of interactive semantics, thus laying foundations for game semantics of concurrent systems. 1
Interactive Observability in Ludics
 in Proc. of ICALP 2004, Lecture Notes in Computer Science
, 2003
"... MSCS, 2001) as an approach to logic founded on the notion of interaction. ..."
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MSCS, 2001) as an approach to logic founded on the notion of interaction.
A Calculus of Coroutines
"... We describe a simple but expressive calculus of sequential processes, represented as coroutines. We show that this calculus can be used to express a variety of programming language features including procedure calls, labelled jumps, integer references and stacks. We describe the operational properti ..."
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We describe a simple but expressive calculus of sequential processes, represented as coroutines. We show that this calculus can be used to express a variety of programming language features including procedure calls, labelled jumps, integer references and stacks. We describe the operational properties of the calculus using reduction rules and equational axioms. We describe a notion of categorical model for our calculus, and give a simple example of such a model based on a category of games and strategies. We prove full abstraction results showing that equivalence in the categorical model corresponds to observational equivalence in the calculus, and also to equivalence of evaluation trees, which are infinitary normal forms for the calculus. We show that our categorical model can be used to interpret the untyped λcalculus and use this fact to extract a sound translation of the latter into our calculus of coroutines.
Abstract CTCS 2004 Preliminary Version Asynchronous games 3 An innocent model of linear logic
"... Since its early days, deterministic sequential game semantics has been limited to linear or polarized fragments of linear logic. Every attempt to extend the semantics to full propositional linear logic has bumped against the socalled Blass problem, which indicates (misleadingly) that a category of ..."
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Since its early days, deterministic sequential game semantics has been limited to linear or polarized fragments of linear logic. Every attempt to extend the semantics to full propositional linear logic has bumped against the socalled Blass problem, which indicates (misleadingly) that a category of sequential games cannot be selfdual and cartesian at the same time. We circumvent this problem by considering (1) that sequential games are inherently positional; (2) that they admit internal positions as well as external positions. We construct in this way a sequential game model of propositional linear logic, which incorporates two variants of the innocent arena game model: the wellbracketed and the non wellbracketed ones.
Asynchronous Games 4 A Fully Complete Model of Propositional Linear Logic
"... We construct a denotational model of propositional linear logic based on asynchronous games and winning uniform innocent strategies. Every formula A is interpreted as an asynchronous game [A] and every proof π of A is interpreted as a winning uniform innocent strategy [π] of the game [A]. We show th ..."
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We construct a denotational model of propositional linear logic based on asynchronous games and winning uniform innocent strategies. Every formula A is interpreted as an asynchronous game [A] and every proof π of A is interpreted as a winning uniform innocent strategy [π] of the game [A]. We show that the resulting model is fully complete: every winning uniform innocent strategy σ of the asynchronous game [A] is the denotation [π] of a proof π of the formula A. 1
On dialogue games and coherent strategies ˚
"... We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended w ..."
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We explain how to see the set of positions of a dialogue game as a coherence space in the sense of Girard or as a bistructure in the sense of Curien, Plotkin and Winskel. The coherence structure on the set of positions results from a Kripke translation of tensorial logic into linear logic extended with a necessity modality. The translation is done in such a way that every innocent strategy defines a clique or a configuration in the resulting space of positions. This leads us to study the notion of configuration designed by Curien, Plotkin and Winskel for general bistructures in the particular case of a bistructure associated to a dialogue game. We show that every such configuration may be seen as an interactive strategy equipped with a backward as well as a forward dynamics based on the interplay between the stable order and the extensional order. In that way, the category of bistructures is shown to include a full subcategory of games and coherent strategies of an interesting nature.