Comparative Metric Semantics of Programming Languages: Nondeterminism and Recursion (1998)

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.