S-narrowing for constructor systems

Abstract

Narrowing is a procedure that was conceived in the context of equational E-unification, and that has also been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation starting from an instance of an expression that has been obtained by using a normalized substitution can be 'lifted' to a narrowing derivation. Since then, several variants and extensions of narrowing have been developed in order to improve that result under certain assumptions or for particular classes of term rewriting systems. In this work we propose a new narrowing notion for constructor systems that is based on the novel notion of s-unifier, that essentially allows a variable to be bound to several expressions at the same time. A Maude-based implementation for this narrowing relation, using an adaptation of natural narrowing as on-demand evaluation strategy, is presented, and its use for symbolic reachability analysis applied to the verification of cryptographic protocols is also outlined. © 2012 Springer-Verlag.