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32
Probabilistic Game Semantics
 Computer Science Society
, 2000
"... A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a ..."
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Cited by 31 (1 self)
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A category of HO/Nstyle games and probabilistic strategies is developedwhere the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol.
Game Semantics and Subtyping
 In Proceedings of the fifteenth annual IEEE symposium on Logic in Computer Science
, 1999
"... While Game Semantics has been remarkably successful at modelling, often in a fully abstract manner, a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of ..."
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While Game Semantics has been remarkably successful at modelling, often in a fully abstract manner, a wide range of features of programming languages, there has to date been no attempt at applying it to subtyping. We show how the simple device of explicitly introducing error values in the syntax of the calculus leads to a notion of subtyping for game semantics. We construct an interpretation of a simple calculus with subtyping and show how the range of the interpretation of types is a complete lattice thus yielding an interpretation of bounded quantification.
DataAbstraction Refinement: A Game Semantic Approach
 In Proceedings of SAS, LNCS 3672
, 2005
"... Abstract. This paper presents a semantic framework for data abstraction and refinement for verifying safety properties of open programs. The presentation is focused on an Algollike programming language that incorporates data abstraction in its syntax. The fully abstract game semantics of the lang ..."
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Cited by 13 (7 self)
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Abstract. This paper presents a semantic framework for data abstraction and refinement for verifying safety properties of open programs. The presentation is focused on an Algollike programming language that incorporates data abstraction in its syntax. The fully abstract game semantics of the language is used for modelchecking safety properties, and an interactionsequencebased semantics is used for interpreting potentially spurious counterexamples and computing refined abstractions for the next iteration. 1
Full abstraction for nominal general references
 In LICS ’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science (Wroclaw, 2007), IEEE Computer
"... Vol. 5 (3:8) 2009, pp. 1–69 www.lmcsonline.org ..."
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Adjunction models for callbypushvalue with stacks
 Proceedings, 9th Conference on Category Theory and Computer Science, Ottawa, 2002, volume 69 of Electronic Notes in Theoretical Computer Science
, 2005
"... Callbypushvalue is a ”semantic machine code”, providing a set of simple primitives from which both the callbyvalue and callbyname paradigms are built. We present its operational semantics as a stack machine, suggesting a term judgement of stacks. We then see that CBPV, incorporating these st ..."
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Cited by 10 (6 self)
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Callbypushvalue is a ”semantic machine code”, providing a set of simple primitives from which both the callbyvalue and callbyname paradigms are built. We present its operational semantics as a stack machine, suggesting a term judgement of stacks. We then see that CBPV, incorporating these stack terms, has a simple categorical semantics based on an adjunction between values and stacks. There are no coherence requirements. We describe this semantics incrementally. First, we introduce locally indexed categories and the opGrothendieck construction, and use these to give the basic structure for interpreting the three judgements: values, stacks and computations. Then we look at the universal property required to interpret each type constructor. We define a model to be a strong adjunction with countable coproducts, countable products and exponentials. We see a wide range of instances of this structure: we give examples for divergence, storage, erratic choice, continuations, possible worlds and games (with or without a bracketing condition), in each case resolving the strong monad from the literature into a strong adjunction. And we give ways of constructing models from other models. Finally, we see that callbyvalue and callbyname are interpreted within the Kleisli and coKleisli parts, respectively, of a callbypushvalue adjunction.
The Anatomy of Innocence
 In Proceedings, Tenth Annual Conference of the European Association for Computer Science Logic
, 2001
"... We reveal a symmetric structure in the ho/n games model of innocent strategies, introducing rigid strategies, a concept dual to bracketed strategies. We prove a direct definability theorem of general innocent strategies with respect to a simply typed language of extended Bohm trees, which gives an o ..."
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Cited by 8 (2 self)
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We reveal a symmetric structure in the ho/n games model of innocent strategies, introducing rigid strategies, a concept dual to bracketed strategies. We prove a direct definability theorem of general innocent strategies with respect to a simply typed language of extended Bohm trees, which gives an operational meaning to rigidity in callbyname. A corresponding factorization of innocent strategies into rigid ones with some form of conditional as an oracle is constructed. 1
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.
Resource modalities in tensor logic
"... The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more ..."
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The description of resources in game semantics has never achieved the simplicity and precision of linear logic, because of the misleading conception that linear logic is more primitive than game semantics. Here, we defend the opposite view, and thus advocate that game semantics is conceptually more primitive than linear logic. This revised point of view leads us to introduce tensor logic, a primitive variant of linear logic where negation is not involutive. After formulating its categorical semantics, we interpret tensor logic in a model based on Conway games equipped with a notion of payoff, in order to reflect the various resource policies of the logic: linear, affine, relevant or exponential.
Constructing differential categories and deconstructing categories of games
 In Luca Aceto, Monika Henzinger, and Jiri Sgall, editors, ICALP (2), volume 6756 of Lecture Notes in Computer Science
, 2011
"... Abstract. We present an abstract construction for building differential categories useful to model resource sensitive calculi, and we apply it to categories of games. In one instance, we recover a category previously used to give a fully abstract model of a nondeterministic imperative language. The ..."
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Abstract. We present an abstract construction for building differential categories useful to model resource sensitive calculi, and we apply it to categories of games. In one instance, we recover a category previously used to give a fully abstract model of a nondeterministic imperative language. The construction exposes the differential structure already present in this model. A second instance corresponds to a new Cartesian differential category of games. We give a model of a Resource PCF in this category and show that it enjoys the finite definability property. Comparison with a relational semantics reveals that the latter also possesses this property and is fully abstract. 1