In this paper, systems which interact permanently with their environment are considered. Such systems are encountered, for instance, in real-time control or signal processing systems, C3-systems, man-machine interfaces, to mention just a few. 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 assumption 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 synchronous programming language: SIGNAL. A SIGNAL program specifies dynamical relations between (internal and external) signal flows. The SIGNAL compiler checks deadlock and determinism of the program, and produces an intermediate level code equivalent to a nested family of concurrent automata. The compilation algorithm is supported by: (1) a behavioural semantics of SIGNAL programs in terms of conditional rewriting rules, (2) the coding of this semantics into the skew product of a dynamical system over the field of integers modulo 3 and directed graphs, (3) an algebraic algorithm to transform the above coding into an equivalent executable one, which provides by the way an execution semantics of the language. We briefly discuss the implementation aspects, and explain the capabilities and limitations of the current version of the SIGNAL compiler.
