Algebraic specification of concurrent systems

Abstract

This article presents an extension of the formalism of algebraic specifications to the specification of concurrent systems. The key concept is that of process specifications, which have two hierarchical layers: processes and data. Processes apply to data via an application operator, eventually yielding a set of data as a result. Syntax and semantics of process specifications are presented, with emphasis on methodological issues (how to write hierarchically consistent and complete specifications). A suitable notion of observational congruence is introduced and characterized. A notion of implementation is defined, and a general method for proving correction is considered, based on the notion of serializability proof. A primitive for putting specifications together, in parallel, is analyzed. Finally, richer primitives for building basic specifications are discussed. Our proposal is illustrated via several examples including the one of the systematic, stepwise development of a complex specification.