Abstract

The following theorem of Huet and L'evy forms the basis of all results on optimal reduction strategies for orthogonal term rewriting systems: every term not in normal form contains a needed redex, and repeated contraction of needed redexes results in the normal form, if the term under consideration has one. We generalize this theorem to computations to root-stable form and we argue that the resulting notion of root-neededness is more fundamental than (other variants of) neededness when it comes to infinitary normalization. 1 Introduction In this paper we are concerned with reduction strategies for term rewriting systems. A reduction strategy is called normalizing if repeated contraction of the redexes selected by the strategy leads to normal form. O'Donnell [13] showed that the parallel-outermost strategy, which contracts all outermost redexes in parallel, is normalizing for orthogonal term rewriting systems. Parallel-outermost is not an optimal reduction strategy since many of the r...

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