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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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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
Hector: An equivalence checker for a higherorder fragment of ML
 In CAV
, 2012
"... Abstract. We present HECTOR, an observational equivalence checker for a higherorder fragment of ML. The input language is RML, the canonical restriction of standard ML to groundtype references. HECTOR accepts programs from a decidable fragment of RML identified by us at ICALP’11, which comprises ..."
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Cited by 2 (1 self)
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Abstract. We present HECTOR, an observational equivalence checker for a higherorder fragment of ML. The input language is RML, the canonical restriction of standard ML to groundtype references. HECTOR accepts programs from a decidable fragment of RML identified by us at ICALP’11, which comprises programs of shorttype (order at most 2 and arity at most 1) that may contain free variables whose arguments are also of shorttype. This is an expressive fragment that contains complex higherorder types, and includes many examples from the literature which have proven challenging to verify using other methods. To our knowledge, HECTOR is the first fullyautomated equivalence checker for higherorder, callbyvalue programs. Both sound and complete, the tool relies on the fully abstract game semantics of RML to construct, onthefly, visibly pushdown automata which precisely capture program behaviour. These automata are then checked for language equivalence, and if they are inequivalent a counterexample (in the form of a separating context) is constructed. 1
Predicate Abstraction and CEGAR . . .
, 2011
"... Higherorder model checking (more precisely, the model checking of higherorder recursion schemes) has been extensively studied recently, which can automatically decide properties of programs written in the simplytyped λcalculus with recursion and finite data domains. This paper formalizes predica ..."
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Higherorder model checking (more precisely, the model checking of higherorder recursion schemes) has been extensively studied recently, which can automatically decide properties of programs written in the simplytyped λcalculus with recursion and finite data domains. This paper formalizes predicate abstraction and counterexampleguided abstraction refinement (CEGAR) for higherorder model checking, enabling automatic verification of programs that use infinite data domains such as integers. A prototype verifier for higherorder functional programs based on the formalization has been implemented and tested for several programs.
Program Verication using Symbolic Game Semantics
"... We introduce a new symbolic representation of algorithmic game semantics, and show how it can be applied for efficient verification of open (incomplete) programs. The focus is on an Algollike programming language which contains the core ingredients of imperative and functional languages, especially ..."
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We introduce a new symbolic representation of algorithmic game semantics, and show how it can be applied for efficient verification of open (incomplete) programs. The focus is on an Algollike programming language which contains the core ingredients of imperative and functional languages, especially on its secondorder recursionfree fragment with infinite data types. We revisit the regularlanguage representation of game semantics of this language fragment. By using symbolic values instead of concrete ones, we generalize the standard notions of regularlanguage and automata representations of game semantics to that of corresponding symbolic representations. In this way programs with infinite data types, such as integers, can be expressed as finitestate symbolicautomata although the standard automata representation is infinitestate, i.e. the standard regularlanguage representation has infinite summations. Moreover, in this way significant reductions of the state space of game semantics models are obtained. This enables efficient verification of programs by our prototype tool based on symbolic game models, which is illustrated with several examples.
Hiroshi Unno
"... Higherorder model checking (more precisely, the model checking of higherorder recursion schemes) has been extensively studied recently, which can automatically decide properties of programs written in the simplytyped λcalculus with recursion and finite data domains. This paper formalizes pred ..."
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Higherorder model checking (more precisely, the model checking of higherorder recursion schemes) has been extensively studied recently, which can automatically decide properties of programs written in the simplytyped λcalculus with recursion and finite data domains. This paper formalizes predicate abstraction and counterexampleguided abstraction refinement (CEGAR) for higherorder model checking, enabling automatic verification of programs that use infinite data domains such as integers. A prototype verifier for higherorder functional programs based on the formalization has been implemented and tested for several programs.
This work is licensed under the Creative Commons Attribution License. Symbolic Representation of Algorithmic Game Semantics
"... In this paper we revisit the regularlanguage representation of game semantics of secondorder recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of regularlanguage and automata representations to that of cor ..."
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In this paper we revisit the regularlanguage representation of game semantics of secondorder recursion free Idealized Algol with infinite data types. By using symbolic values instead of concrete ones we generalize the standard notion of regularlanguage and automata representations to that of corresponding symbolic representations. In this way terms with infinite data types, such as integers, can be expressed as finite symbolicautomata although the standard automata interpretation is infinite. Moreover, significant reductions of the state space of game semantics models are obtained. This enables efficient verification of terms, which is illustrated with several examples. 1
Game Semantics Based Equivalence Checking of HigherOrder Programs
, 2012
"... This thesis examines the use of game semantics for the automatic equivalence checking of higherorder programs. Game semantics has proved to be a powerful method for constructing fully abstract models of logics and programming languages. Furthermore, the concrete nature of the semantics lends itse ..."
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This thesis examines the use of game semantics for the automatic equivalence checking of higherorder programs. Game semantics has proved to be a powerful method for constructing fully abstract models of logics and programming languages. Furthermore, the concrete nature of the semantics lends itself to algorithmic analysis. The gamesemantic model can be used to identify fragments of languages which have a decidable observational equivalence problem. We investigate decidability results for different languages as well as the efficiency of these algorithms in practice. First we consider the callbyvalue higherorder language with state, RML. This can be viewed as a canonical restriction of Standard ML to groundtype references. The Ostrict fragment of RML is the largest set of type sequents for which, in the gamesemantic denotation, justification pointers from Omoves are always uniquely reconstructible from the underlying move sequence. The Ostrict fragment is surprisingly expressive, including higherorder types and difficult examples from the literature. By representing strategies as Visibly Pushdown Automata (VPA) we show that