Context-sensitive rewriting strategies

Author

Salvador Lucas

Abstract

Context-sensitive rewriting is a simple rewriting restriction which is formalized by imposing fixed restrictions on replacements. Such a restriction is given on a purely syntactic basis: it is given on the arguments of symbols of the signature and inductively extended to arbitrary positions of terms built from those symbols. The termination behavior is not only preserved but usually improved and several methods have been developed to formally prove it. In this paper, we investigate the definition, properties, and use of context-sensitive rewriting strategies, i.e., particular, fixed sequences of context-sensitive rewriting steps. We study how to define them in order to obtain efficient computations and to ensure that context-sensitive computations terminate whenever possible. We give conditions enabling the use of these strategies for root-normalization, normalization, and infinitary normalization. We show that this theory is suitable for formalizing the definition and analysis of real computational strategies which are used in programming languages such as OBJ or Elan.

Keywords

infinitary normalization, normalization, replacement restrictions, root-normalization, sequentiality, strategies, term rewriting.