Optimal Normalization in Orthogonal Term Rewriting Systems

We design a normalizing strategy for orthogonal term rewriting systems (OTRSs), which is a generalization of the call-by-need strategy of Huet-L evy 4]. The redexes contracted in our strategy are essential in the sense that they have \descendants" under any reduction of a given term. There is an essential redex in any term not in normal form. We further show that contraction of the innermost essential redexes gives an optimal reduction to normal form, if it exists. We classify OTRSs depending on possible kinds of redex creation as non-creating, persistent, inside-creating, non-left-absorbing, etc. All these classes are decidable. TRSs in these classes are sequential, but they do not need to be strongly sequential. For non-creating and persistent OTRSs, we show that our optimal strategy is eecient as well.