Abstract

In this work, we consider term rewriting from a functional point of view. A rewrite rule is a function that can be applied to a term using an explicit application function. From this starting point, we show how to build more elaborated functions, describing rst rewrite derivations, then sets of derivations. These functions, that we call strategies, can themselves be dened by rewrite rules and the construction can be iterated leading to higher-order strategies. Furthermore, the application function is itself dened using rewriting in the same spirit. We present this calculus and study its properties. Its implementation in the ELAN language is used to motivate and exemplify the whole approach. The expressiveness of ELAN is illustrated by examples of polymorphic functions and strategies. Keywords: Rewriting Calculus, Rewriting Logic, Strategy, Rewrite Based Language, Term Rewriting, Strategy, Matching. 1. Introduction Rule-based reasoning is present in many domains of compu...

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