An axiomatic treatment of a parallel programming language

Abstract

This paper describes a semantically-based axiomatic treatment of a parallel programming language with shared variable concurrency and conditional critical regions, essentially the language discussed by Owicki and Gries [20,21]. We use a structural operational semantics for this language, based on work of Hennessy and Plotkin [22,26], and we use the semantic structure to suggest a class of assertions for expressing properties of commands. We then define syntactic operations on assertions which correspond precisely to syntactic constructs of the programming language; in particular, we define sequential and parallel composition of assertions. This enables us to design a truly compositional proof system for program properties. Our proof system is sound and relatively complete. We examine the relationship between our proof system and the Owicki-Gries proof system. Our assertions are more expressive than Owicki's, and her proof outlines correspond roughly to a special subset of our assertion language. Owicki's parallel rule can be thought of as being based on a slightly different form of parallel composition of assertions; our form does not require interference-freedom, and our proof system is relatively complete without the need for auxiliary variables. Connections with other work, including the “Generalized Hoare Logic” of Lamport and Schneider [16,17], and with the Transition Logic of Gerth [11], are discussed briefly.KeywordsAuxiliary VariableProof SystemSequential CompositionParallel CompositionAtomic ActionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.