An introduction to metric semantics: operational and denotational models for programming and specification languages

Our focus is on the semantics of programming and specification languages. Over the years, different approaches to give semantics to these languages have been put forward. We restrict ourselves to the operational and the denotational approach, two main streams in the field of semantics. Two notions w...

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Vydané v:Theoretical computer science Ročník 258; číslo 1; s. 1 - 98
Hlavný autor: van Breugel, Franck
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 2001
Elsevier
Predmet:
Applied sciences
Computer science; control theory; systems
Denotational semantics
Exact sciences and technology
Labelled transition system
Language theory and syntactical analysis
Metric semantics
Metric space
Nondeterminism
Nontermination
Operational semantics
Programming language
Specification language
Theoretical computing
Specification language
Operational semantics
Programming language
Metric space
Denotational semantics
Metric semantics
Nondeterminism
Nontermination
Labelled transition system
Transition system
Semantics
Lambda calculus
Specification
Non termination
Non determinism
ISSN:0304-3975, 1879-2294
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Shrnutí:Our focus is on the semantics of programming and specification languages. Over the years, different approaches to give semantics to these languages have been put forward. We restrict ourselves to the operational and the denotational approach, two main streams in the field of semantics. Two notions which play an important role in this paper are ( non) determinism and ( non) termination. Nondeterminism arises naturally in concurrent languages and it is a key concept in specification languages. Nontermination is usually caused by recursive constructs which are crucial in programming. The operational models are based on labelled transition systems. The definition of these systems is guided by the structure of the language. Metric spaces are an essential ingredient of our denotational models. We exploit the metric structure to model recursive constructs and to define operators on infinite entities. Furthermore, we also employ the metric structure to relate operational and denotational models for a given language. On the basis of four toy languages, we develop some general theory for defining operational and denotational semantic models and for relating them. This theory is applicable to a wide variety of languages. We start with a very simple deterministic and terminating imperative programming language. By adding the recursive while statement, we obtain a deterministic and nonterminating language. Next, we augment the language with the parallel composition resulting in a bounded nondeterministic and nonterminating language. Finally, we add some timed constructs. We obtain an unbounded nondeterministic and nonterminating specification language.
Bibliografia:ObjectType-Article-2
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content type line 23
ISSN:0304-3975
1879-2294
DOI:10.1016/S0304-3975(00)00403-5