Reasoning about VHDL using operational and observational semantics

We define a Plotkin-style structural operational semantics for a subset of vhdl that includes delta time, zero-delay scheduling and waits, arbitrary wait statements, and (commutative) resolution functions. While most of these features have been dealt with in separation, their combination is intricate. We follow closely the “careful prose” definition of vhdl as given in [9]. We prove a (conditional) monogenicity result for the operational semantics showing that the parallelism present in vhdl is benign. A classification of program behaviours is also given. While the semantics is of interest, of greater importance is the interpretation of the mature process algebra theory to our particular setting. An adaptation of bisimulation may be constructed but the concept of an observer, a process which inspects or acts as a test harness, turns out to be more useful. It leads naturally to a notion of observational equality that is a congruence with respect to parallel composition. This important result enables substitution of behaviourally equivalent subprograms without affecting the overall program behaviour. The capability to pass (incapability to fail) a test gives rise to a the may (must) preorder on processes. These preorders are shown to coincide. A shorter version of this report appears as [8]. This work is supported by the euroform network sponsored by the Human Capital and Mobility programme of the European Community.