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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| Published in: | Theoretical computer science Vol. 258; no. 1; pp. 1 - 98 |
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| Format: | Journal Article |
| Language: | English |
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Amsterdam
Elsevier B.V
2001
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. copyright 2001 Elsevier Science B.V. All rights reserved. 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. |
| Author | van Breugel, Franck |
| Author_xml | – sequence: 1 givenname: Franck surname: van Breugel fullname: van Breugel, Franck email: franck@cs.yorku.ca organization: York University, Department of Computer Science, 4700 Keele Street, Toronto, Canada M3J 1P3 |
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| Keywords | 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 |
| Language | English |
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| SubjectTerms | 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 |
| Title | An introduction to metric semantics: operational and denotational models for programming and specification languages |
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