Comparative Metric Semantics of Programming Languages

During the last three decades several different styles of semantics for program­ ming languages have been developed. This book compares two of them: the operational and the denotational approach. On the basis of several exam­ ples we show how to define operational and denotational semantic models for programming languages. Furthermore, we introduce a general technique for comparing various semantic models for a given language. We focus on different degrees of nondeterminism in programming lan­ guages. Nondeterminism arises naturally in concurrent languages. It is also an important concept in specification languages. In the examples discussed, the degree of non determinism ranges from a choice between two alternatives to a choice between a collection of alternatives indexed by a closed interval of the real numbers. The former arises in a language with nondeterministic choices. A real time language with dense choices gives rise to the latter. We also consider the nondeterministic random assignment and parallel composition, both couched in a simple language. Besides non determinism our four example languages contain some form of recursion, a key ingredient of programming languages.

Contenu

Nondeterminism and recursion.- Operational semantics.- Denotational semantics.- Metric spaces.- Comparative semantics.- Bibliographic notes.- I.- 1 Domain equations.- 1.1 Building domain equations.- 1.2 Solving domain equations.- 1.3 Bibliographic notes.- 2 Linear and branching domains.- 2.1 Two linear domains.- 2.2 Comparison of the linear domains.- 2.3 Three branching domains.- 2.4 Comparison of the branching domains.- 2.5 Relating linear and branching domains.- 2.6 Bibliographic notes.- II.- 3 Operational semantics.- 3.1 Labelled transition systems.- 3.2 Operational semantics.- 3.3 Linear semantics transformations.- 3.3.1 Compactness preserving.- 3.3.2 Closedness preserving.- 3.4 Branching semantics transformations.- 3.4.1 Compactness preserving.- 3.4.2 Closedness preserving.- 3.5 Relating semantics transformations.- 3.6 Bibliographic notes.- 4 Nondeterministic choice.- 4.1 Language definition.- 4.2 Operational semantics.- 4.3 Denotational semantics.- 4.4 Relating O and D.- 4.5 Bibliographic notes.- 5 Random assignment.- 5.1 Language definition.- 5.2 Operational semantics.- 5.3 Denotational semantics.- 5.4 Relating O and D.- 5.5 Bibliographic notes.- III.- 6 Generalized finiteness conditions.- 6.1 Metric labelled transition systems.- 6.2 Operational semantics.- 6.3 Linear semantics transformations.- 6.3.1 Compactness and nonexpansiveness preserving.- 6.3.2 Closedness and nonexpansiveness preserving.- 6.4 Branching semantics transformations.- 6.5 Relating semantics transformations.- 6.6 Bibliographic notes.- 7 Dense choice.- 7.1 Language definition.- 7.2 Operational semantics.- 7.3 Denotational semantics.- 7.4 Relating O and D.- 7.5 Bibliographic notes.- 8 Second order communication.- 8.1 Language definition.- 8.2 Operational semantics.- 8.3 Denotational semantics.- 8.4 Relating O and D.- 8.4.1 Intermediate semantics.- 8.4.2 Relating I and D.- 8.4.3 Relating O and I.- 8.5 Bibliographic notes.- A Metric spaces.- A.1 Metrics.- A.2 Completeness and contractiveness.- A.3 Hyperspaces.- A.4 Nonexpansive functions.- A.5 Bibliographic notes.- Author index.