A denotational theory of synchronous reactive systems

In this paper, systems which interact permanently with their environments are considered. Such systems are encountered, for instance, in real-time control or signal processing systems, C³-systems, and man-machine interfaces, to mention just a few cases. The design and implementation of such systems require a concurrent programming language which can be used to verify and synthesize the synchronization mechanisms, and to perform transformations of the concurrent source code to match a particular target architecture. Synchronous languages are convenient tools for such a purpose: they rely on the assumptions that: (1) internal actions of synchronous systems are instantaneous, and (2) communication with the environment is performed via instantaneous flashes involving some external stimuli. In this paper, we present a mathematical model of synchronous languages and illustrate its use on the language. This model is denotational, and encompasses both relational and functional styles of specification. It allows us to answer fundamental questions related to synchronous languages, such as “what are the basic constructions which should be provided by such languages?”