Detecting Redundant Narrowing Derivations by the LSE-SL Reducibility Test

Rewriting and narrowing provide a nice theoretical framework for the integration of logic and functional programming. For practical applications however, narrowing is still much too inefficient. In this paper we show how reducibility tests can be used to detect redundant narrowing derivations. We introduce a new narrowing strategy, LSE-SL left-to-right basic normal narrowing, prove its completeness for arbitrary canonical term rewriting systems, and demonstrate how it increases the efficiency of the narrowing process