An introduction to compositional methods for concurrency and their application to real-time

Formal methods to specify and verify concurrent programs with synchronous message passing are discussed. We stress the development towards compositional methods, i.e. methods in which the specification of a compound program can be inferred from specifications of its constituents without reference to the internal structure of those parts. Compositionality enables verification during the process of (top-down) design — the derivation of correct programs — instead of the more familiar a-posteriori verification based on already completed program codes. We sketch the transition from non-compositional towards compositional methods for concurrent programs, indicating the main principles behind compositionality. Having achieved a compositional framework based on classical Hoare triples, we discuss extensions to achieve a convenient formalism to specify and verify reactive systems that have an intensive interaction with their environment. Next this Hoare-style framework is adapted to specify and verify real-time properties, and a compositional proof method is formulated for real-time distributed computing. Compositional reasoning during top-down development of a real-time program is illustrated by an example concerning a watchdog timer