Towards a Signal Calculus for Event-Based Synchronous Languages

A theory of programming is intended to support the practice of programming by relating each program to the specification of what it is intended to achieve. Our intention is to develop a signal calculus for event-based synchronous languages used for specification and programming of embedded systems. In this paper, we mainly tackle conceptually instantaneous reactions, i.e., zero-time reactions. The delay-time reactions will be investigated in the follow-up work. To explore the semantic definition of instantaneous reactions (I-calculus), a set of algebraic laws is provided, which can be used to reduce all instantaneous reactions to a normal form algebraically. The normal form, surprisingly, exposes the internal implicit dependence explicitly. Consequently, that two differently written reactions happen to mean the same thing can be proved from the equations of an algebraic presentation.