Extending Context-Sensitivity in Term Rewriting

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 s hould 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 i mproved termination behaviour while still being powerful enough to compute meaningful results. Suffic ient criteria for both kinds of properties in certain classes of rewrite systems with forbidden patter ns are presented.

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