by **Sergio Antoy, Rachid Echahed, Michael Hanus**

*Proc. of the 21th Annual SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL'94), *ACM Press, pp. 268-279, 1994

© ACM Press

*Revised and extended version*

Narrowing is the operational principle of languages that integrate functional and logic programming. We propose a notion of a needed narrowing step that, for inductively sequential rewrite systems, extends the Huet and Levy notion of a needed reduction step. We define a strategy, based on this notion, that computes only needed narrowing steps. Our strategy is sound and complete for a large class of rewrite systems, is optimal w.r.t. the cost measure that counts the number of distinct steps of a derivation, computes only independent unifiers, and is efficiently implemented by pattern matching.

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