Demandness in Rewriting and Narrowing

Abstract The traditional investigation of rewriting and narrowing strategies aims at establishing fundamental properties, such as soundness, completeness and/or optimality, of a strategy. In this work, we analyze and compare rewriting and narrowing strategies from the point of view of the information taken into account by a strategy to compute a step. The notion of demandness provides a suitable framework for presenting and comparing well-known strategies. We find the existence of an almost linear sequence of strategies that take into account more and more information. We show on examples that, as we progress on this sequence, a strategy becomes more focused and avoids some useless steps computed by strategies preceding it in this sequence. Our work, which is still in progress, clarifies the behavior of similar or related strategies and it promises to simplify the transfer of some results from one strategy to another. It also suggest that the notion of demandness is both atomic and fundamental to the study of strategies.

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