Changing Nothing Is Sometimes Doing Something: Fairness in Extensonal Semantics

We investigate the use of Lamport's TLA as a convenient formalism for describing concurrent programs based on multiset rewriting. Such a stuttering invariant temporal logic is useful for guaranteeing extensionality of the semantics and for allowing composition. However, rewrites are more usually approached in an intensional way and we face some diiculties with our description. The problems concern the need to be able to express general fairness requirements especially when some of the rewrites might sometimes be trivial| and then are actually a form of stuttering. We nd that we have to formulate new fairness constructs and to use old ones in new ways. Thus, we are led to a more generally correct TLA approach to specifying fairness requirements. We show that using this approach for the semantics of rewrite languages makes it relatively easy to use TLA to be precise about and reason about fairness properties which rewrite languages exhibit.