Static analysis of pattern-free properties

Rewriting is a widely established formalism with major applications in computer science. It is indeed a staple of many formal verification applications as it is especially well suited to describe program semantics and transformations. In particular, constructor based term rewriting systems are generally used to illustrate the behaviour of functional programs. In the context of formal verification, it is often necessary to characterize the shape of the reducts of such rewrite systems and, in a typed context, the underlying type system provides syntactic guarantees on the form of these terms by exhibiting, among others, the constructor symbols that they can contain. On the other hand, when performing (program) transformations we often want to eliminate some symbols and, more generally, to ensure that some patterns are absent from the result of the transformation. We propose in this paper an approach to statically verify the absence of specified patterns from the reachable terms of constructor based term rewriting systems. The proposed approach consists in annotating the function symbols with a set of profiles outlining pre- and post-conditions that must be verified by the rewrite relation, and using a rewrite based method to statically verify that the rewrite system is indeed consistent with the respective annotations.