An Abstract View of Contexts in Reduction Systems

In this paper we propose an abstract model of rewriting based on a functional view of terms abstractly considered as contexts that can be applied to other contexts yelding new ones Some basic operations on contexts are de ned and their properties pointed out that allow us to reformulate the de nition of the main concepts involved in rewriting and to prove Knuth Bendix theorem The notion of occurrence essential in the traditional approach to term rewriting is treated implicitely via the properties ruling the behaviour of contexts The key operation allowing a proper treatment of the notion of occurrence is a composition of two contexts that under particular conditions yelds a context that can be parallely applied to terms