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25
Algorithmic Game Semantics
 In Schichtenberg and Steinbruggen [16
, 2001
"... Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependen ..."
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Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with nonfunctional features such as control operators and locallyscoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computerassisted verification and program analysis. Some promising steps have already been taken in this
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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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.
A Fully Abstract Game Semantics for Finite Nondeterminism
 In Proceedings of the Fourteenth Annual Symposium on Logic in Computer Science, LICS ’99. IEEE Computer
, 1999
"... A game semantics of finite nondeterminism is proposed. In this model, a strategy may make a choice between different moves in a given situation; moreover, strategies carry extra information about their possible divergent behaviour. A Cartesian closed category is built and a model of a simple, higher ..."
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A game semantics of finite nondeterminism is proposed. In this model, a strategy may make a choice between different moves in a given situation; moreover, strategies carry extra information about their possible divergent behaviour. A Cartesian closed category is built and a model of a simple, higherorder nondeterministic imperative language is given. This model is shown to be fully abstract, with respect to an equivalence based on both safety and liveness properties, by means of a factorization theorem which states that every nondeterministic strategy is the composite of a deterministic strategy with a nondeterministic oracle. 1 Introductory remarks Nondeterminism, the notion that the behaviour of a computer system need not be completely determined by the behaviour of its environment, is a valuable abstraction in the analysis of programs. An unreliable hardware component, governed by laws of physics too complex to take into account, can be understood as a nondeterministic entity; mul...
Games and full abstraction for nondeterministic languages
, 1999
"... Abstract Nondeterminism is a pervasive phenomenon in computation. Often it arises as an emergent property of a complex system, typically as the result of contention for access to shared resources. In such circumstances, we cannot always know, in advance, exactly what will happen. In other circumstan ..."
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Abstract Nondeterminism is a pervasive phenomenon in computation. Often it arises as an emergent property of a complex system, typically as the result of contention for access to shared resources. In such circumstances, we cannot always know, in advance, exactly what will happen. In other circumstances, nondeterminism is explicitly introduced as a means of abstracting away from implementation details such as precise command scheduling and control flow. However, the kind of behaviours exhibited by nondeterministic computations can be extremely subtle in comparison to those of their deterministic counterparts and reasoning about such programs is notoriously tricky as a result. It is therefore important to develop semantic tools to improve our understanding of, and aid our reasoning about, such nondeterministic programs. In this thesis, we extend the framework of game semantics to encompass nondeterministic computation. Game semantics is a relatively recent development in denotational semantics; its main novelty is that it views a computation not as a static entity, but rather as a dynamic process of interaction. This perspective makes the theory wellsuited to modelling many aspects of computational processes: the original use of game semantics in modelling the simple functional language PCF has subsequently been extended to handle more complex control structures such as references and continuations.
On full abstraction for PCF: I. Models, observables and the full abstraction problem II. Dialogue games and innocent strategies III. A fully abstract and universal game model
 Information and Computation
, 2000
"... version) A categorical model for PCF is a map J : ( of cfix categories. ..."
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version) A categorical model for PCF is a map J : ( of cfix categories.
RegularLanguage Semantics for a CallbyValue Programming Language
"... We explain how game semantics can be used to reason about term equivalence in a finitary imperative first order language with arrays. For this language, the gamesemantic interpretation of types and terms is fully characterized by their sets of complete plays. Because these sets are regular over th ..."
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We explain how game semantics can be used to reason about term equivalence in a finitary imperative first order language with arrays. For this language, the gamesemantic interpretation of types and terms is fully characterized by their sets of complete plays. Because these sets are regular over the alphabet of moves, they are representable by (extended) regular expressions. The formal apparatus of game semantics is greatly simplified but the good theoretical properties of the model are preserved. The principal advantage of this approach is that it is mathematically elementary, while fully formalized. Since language equivalence for regular languages is decidable, this method of proving term equivalence is suitable for automation.
Syntactic Control of Concurrency
, 2004
"... We consider a finitary procedural programming language (finite datatypes, no recursion) extended with parallel composition and binary semaphores. Having first shown that mayequivalence of secondorder open terms is undecidable we set out to find a framework in which decidability can be regained wi ..."
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We consider a finitary procedural programming language (finite datatypes, no recursion) extended with parallel composition and binary semaphores. Having first shown that mayequivalence of secondorder open terms is undecidable we set out to find a framework in which decidability can be regained with minimum loss of expressivity. To that end we define an annotated type system that controls the number of concurrent threads created by terms and give a fully abstract game semantics for the notion of equivalence induced by typable terms and contexts. Finally, we show that the semantics of all typable terms, at any order and in the presence of iteration, has a regularlanguage representation and thus the restricted observational equivalence is decidable.
A RegularLanguage Model for HoareStyle Correctness Statements
 In Proceedings of the Verification and Computational Logic 2001 Workshop
, 2001
"... Recent developments in game semantics have led to fully abstract models for a variety of theoretically important programming languages. While the fullblown game models tend to be complex and unwieldy for practical purposes, language subsets without higherorder and recursive functions allow greatly ..."
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Recent developments in game semantics have led to fully abstract models for a variety of theoretically important programming languages. While the fullblown game models tend to be complex and unwieldy for practical purposes, language subsets without higherorder and recursive functions allow greatly simplified models. Two previous papers of the author show how imperative languages with first order functions, local variables and arrays can be modeled using regular languages only. This paper examines the possibility of using these theoretical developments as a basis for modelchecking Hoarestyle partial correctness statements for such languages. The modelchecking problem is shown to be decidable.
Games in the Semantics of Programming Languages
 Dept. of Philosophy, University of Amsterdam
, 1997
"... ion for PCF Motivated by the full completeness results, it became of compelling interest to reexamine perhaps the bestknown "open problem" in the semantics of programming languages, namely the "Full Abstraction problem for PCF", using the new tools provided by game semantics. 2 PCF is a highero ..."
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ion for PCF Motivated by the full completeness results, it became of compelling interest to reexamine perhaps the bestknown "open problem" in the semantics of programming languages, namely the "Full Abstraction problem for PCF", using the new tools provided by game semantics. 2 PCF is a higherorder functional programming language; modulo issues of the parameterpassing strategies, it forms a fragment of any programming language with higherorder procedures (which includes any reasonably expressive objectoriented language). The aspect of the Full Abstraction problem I personally found most interesting was: to construct a syntaxindependent model in which every element is the denotation of some program (note the analogy with full completeness, whose definition had in turn been motivated in part by this aspect of full abstraction). This is not how the problem was originally formulated, but by "general abstract nonsense", given such a model one can always quotient it to get a fully ab...
Abstract Models of Storage
, 2000
"... This note is a historical survey of Christopher Strachey's influence on the development of semantic models of assignment and storage management in procedural languages. ..."
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This note is a historical survey of Christopher Strachey's influence on the development of semantic models of assignment and storage management in procedural languages.