On strong fairness in UNITY

In [6] Tsay and Bagrodia present a correct and complete proof rule for proving within UNITY statements of the form “(true 7→ p) ⇒ (true 7→ q). Their result is obtained by specializing a proof rule due to Manna and Pnueli [5] and translating premises and conclusions into the UNITY framework. However, specializing the rule from [5] is not sufficient, details of the proof have to be invoked and modified. Here we give a straightforward and selfcontained proof of a rule that is more general in several respects. Firstly, our transition systems may have an infinite number of transitions, and secondly, p and q may be any temporal properties, as long as p is “observable” and q is “bounded”. In particular, temporal properties such as 23Enabledi ⇒ 23Takeni, in which Takeni is not naturally a state property, can be dealt with. Our main tool is a predicate transformer “w(p,q)” that specializes to the well known “wlt(q)” for p = true.