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A game semantics of local names and good variables
 of Lecture Notes in Computer Science
, 2004
"... Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a mode ..."
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Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a model of the nucalculus in this category, and extend it with named references (without bad variables) using names as pointers to a store. After refining the semantics via a notion of garbage collection, we prove that the compact elements are definable as terms, and hence obtain a full abstraction result. 1 Introduction Local names are a pervasive and subtle feature of programming languages and other calculi. Not only are they used for manipulating important constructs such as locally bound references and exceptions, namepassing is itself a very expressive computational paradigm, as demonstrated by the sscalculus, for example. Local names can also represent items of secret information which are dynamically generated, passed between agents and used to access further information or activity. They therefore have a key r^ole in specifying properties of secure systems [1, 24].
Thirdorder Idealized Algol with iteration is decidable
 TCS
, 2008
"... Abstract. The problems of contextual equivalence and approximation are studied for the thirdorder fragment of Idealized Algol with iteration (IA ∗ 3). They are approached via a combination of game semantics and language theory. It is shown that for each IA ∗ 3term one can construct a pushdown auto ..."
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Abstract. The problems of contextual equivalence and approximation are studied for the thirdorder fragment of Idealized Algol with iteration (IA ∗ 3). They are approached via a combination of game semantics and language theory. It is shown that for each IA ∗ 3term one can construct a pushdown automaton recognizing a representation of the strategy induced by the term. The automata have some additional properties ensuring that the associated equivalence and inclusion problems are solvable in Ptime. This gives an Exptime decision procedure for contextual equivalence and approximation for βnormal terms. Exptimehardness is also shown in this case, even in the absence of iteration. 1
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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Cited by 15 (8 self)
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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.
Applications of Game Semantics: From Program Analysis to Hardware Synthesis
"... After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. C ..."
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Cited by 2 (2 self)
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After informally reviewing the main concepts from game semantics and placing the development of the field in a historical context we examine its main applications. We focus in particular on finite state model checking, higher order model checking and more recent developments in hardware design. 1. Chronology, methodology, ideology Game Semantics is a denotational semantics in the conventional sense: for any term, it assigns a certain mathematical object as its meaning, which is constructed compositionally from the meanings of its subterms in a way that is independent of the operational semantics of the object language. What makes Game Semantics particular, peculiar maybe, is that the mathematical objects it operates with
Compositional predicate abstraction from game semantics
 In TACAS
, 2009
"... Abstract. We introduce a technique for using conventional predicate abstraction methods to reduce the statespace of models produced using game semantics. We focus on an expressive procedural language that has both local store and local control, a language which enjoys a simple gamesemantic model y ..."
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Abstract. We introduce a technique for using conventional predicate abstraction methods to reduce the statespace of models produced using game semantics. We focus on an expressive procedural language that has both local store and local control, a language which enjoys a simple gamesemantic model yet is expressive enough to allow nontrivial examples. Our compositional approach allows the verification of incomplete programs (e.g. libraries) and offers the opportunity for new heuristics for improved efficiency. Gamesemantic predicate abstraction can be embedded in an abstractionrefinement cycle in a standard way, resulting in an improved version of our experimental modelchecking tool Mage, and we illustrate it with several toy examples. 1
Clipping: A SemanticsDirected Syntactic Approximation
"... In this paper we introduce “clipping, ” a new method of syntactic approximation which is motivated by and works in conjunction with a sound and decidable denotational model for a given programming language. Like slicing, clipping reduces the size of the source code in preparation for automatic verif ..."
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In this paper we introduce “clipping, ” a new method of syntactic approximation which is motivated by and works in conjunction with a sound and decidable denotational model for a given programming language. Like slicing, clipping reduces the size of the source code in preparation for automatic verification; but unlike slicing it is an imprecise but computationally inexpensive algorithm which does not require a wholeprogram analysis. The technique of clipping can be framed into an iterated refinement cycle to arbitrarily improve its precision. We first present this rather simple idea intuitively with some examples, then work out the technical details in the case of an Algollike programming language and a decidable approximation of its gamesemantic model inspired by Hankin and Malacaria’s “lax functor ” approach. We conclude by presenting an experimental model checking tool based on these ideas and some toy programs. 1.
Block structure vs scope extrusion: between innocence and omniscience
"... Abstract. We study the semantic meaning of block structure using game semantics and introduce the notion of blockinnocent strategies, which turns out to characterise callbyvalue computation with blockallocated storage through soundness, finitary definability and universality results. This puts u ..."
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Abstract. We study the semantic meaning of block structure using game semantics and introduce the notion of blockinnocent strategies, which turns out to characterise callbyvalue computation with blockallocated storage through soundness, finitary definability and universality results. This puts us in a good position to conduct a comparative study of purely functional computation, computation with block storage and dynamic memory allocation respectively. For example, we show that dynamic variable allocation can be replaced with blockallocated variables exactly when the term involved (open or closed) is of base type and that blockallocated storage can be replaced with purely functional computation when types of order two are involved. To illustrate the restrictive nature of block structure further, we prove a decidability result for a finitary fragment of callbyvalue Idealized Algol for which it is known that allowing for dynamic memory allocation leads to undecidability. 1
The Advent of Recursion . . .
"... The term ‘recursive’ has had different meanings during the past two centuries among various communities of scholars. Its historical epistemology has already been described by Soare (1996) with respect to the mathematicians, logicians, and recursivefunction theorists. The computer practitioners, on ..."
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The term ‘recursive’ has had different meanings during the past two centuries among various communities of scholars. Its historical epistemology has already been described by Soare (1996) with respect to the mathematicians, logicians, and recursivefunction theorists. The computer practitioners, on the other hand, are discussed in this paper by focusing on the definition and implementation of the ALGOL60 programming language. Recursion entered ALGOL60 in two novel ways: (i) syntactically with what we now call BNF notation, and (ii) dynamically by means of the recursive procedure. As is shown, both (i) and (ii) were introduced by linguisticallyinclined programmers who were not versed in logic and who, rather unconventionally, abstracted away from the downtoearth practicalities of their computing machines. By the end of the 1960s, some computer practitioners had become aware of the theoretical insignificance of the recursive procedure in terms of computability, though without relying on recursivefunction theory. The presented results help us to better understand the technological ancestry of modernday computer science, in the hope that contemporary researchers can more easily build upon its past.
Reachability games and game semantics: comparing nondeterministic programs ∗
"... We investigate the notions of may and mustapproximation in Erratic Idealized Algol (a nondeterministic extension of Idealized Algol), and give explicit characterizations of both inside its game model. Notably, mustapproximation is captured by a novel preorder on nondeterministic strategies, whose ..."
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We investigate the notions of may and mustapproximation in Erratic Idealized Algol (a nondeterministic extension of Idealized Algol), and give explicit characterizations of both inside its game model. Notably, mustapproximation is captured by a novel preorder on nondeterministic strategies, whose definition is formulated in terms of winning regions in a reachability game. The game is played on traces of one of the strategies and its objective is reaching a complete position without encountering any divergences. The concrete accounts of may and mustapproximation make it possible to derive tight complexity bounds for the corresponding decision problems in the finitary (finite datatypes) variant EIAf of Erratic Idealized Algol. In fact we give a complete classification of the complexity of may and mustapproximation for fragments of EIAf of bounded type order (for terms in βnormal form). The complexity of the decidable cases ranges from PSPACE to 2EXPTIME for mayapproximation and from EXPSPACE to 3EXPTIME for mustapproximation. Our decidability results rely on a representation theorem for nondeterministic strategies which, for a given term, yields a single (finite or visibly pushdown) automaton capturing both traces and divergences of the corresponding strategy with two distinct sets of final states. The decision procedures producing optimal bounds incorporate numerous automatatheoretic techniques: complementation, determinization, computation of winning regions in reachability games over finite and pushdown graphs as well as product constructions. We see our work as a starting point of research that relates game semantics with other gamebased theories. 1.