Extending Context-Sensitivity in Term Rewriting

TL;DR

This paper introduces a generalized form of context-sensitivity in term rewriting using forbidden patterns, aiming to improve termination behavior while maintaining computational power.

Contribution

It presents a novel approach to context-sensitivity in term rewriting based on forbidden patterns, analyzing its properties and feasibility.

Findings

Established relationships between forbidden patterns and traditional context-sensitivity

Provided criteria for termination and computational effectiveness

Demonstrated the approach's potential for improved rewriting behavior

Abstract

We propose a generalized version of context-sensitivity in term rewriting based on the notion of "forbidden patterns". The basic idea is that a rewrite step should be forbidden if the redex to be contracted has a certain shape and appears in a certain context. This shape and context is expressed through forbidden patterns. In particular we analyze the relationships among this novel approach and the commonly used notion of context-sensitivity in term rewriting, as well as the feasibility of rewriting with forbidden patterns from a computational point of view. The latter feasibility is characterized by demanding that restricting a rewrite relation yields an improved termination behaviour while still being powerful enough to compute meaningful results. Sufficient criteria for both kinds of properties in certain classes of rewrite systems with forbidden patterns are presented.