Abstraction of Clocks in Synchronous Data-flow Systems
Résumé
Synchronous data-flow languages such as Lustre manage infinite sequences or streams as basic values. Each stream is associated to a clock which defines the instants where the current value of the stream is present. This clock is a type information and a dedicated type system — the so-called clock-calculus — statically rejects programs which cannot be executed synchronously. In existing synchronous languages, it amounts at asking whether two streams have the same clocks and thus relies on clock equality only. Recent works have shown the interest of introducing some relaxed notion of synchrony, where two streams can be composed as soon as they can be synchronized through the introduction of a finite buffer (as done in the SDF model of Edward Lee). This technically consists in replacing typing by subtyping. The present paper introduces a simple way to achieve this relaxed model through the use of clock envelopes. These clock envelopes are sets of concrete clocks which are not necessarily periodic. This allows to model various features in real-time embedded software such as bounded jitter as found in video-systems, execution time of real-time processes and scheduling resources or the communication through buffers. We present the algebra of clock envelopes and its main theoretical properties.