The Functional Strategy and Transitive Term Rewriting Systems

The functional strategy has been widely used implicitly (Haskell, Miranda, Lazy ML) and explicitly (Clean) as an efficient, intuitively easy to understand reduction strategy for term (or graph) rewriting systems. However, little is known of its formal properties since the strategy deals with priority rewriting which significantly complicates the semantics. Nevertheless, this paper shows that some formal results about the functional strategy can be produced by studying the functional strategy entirely within the standard framework of orthogonal term rewriting systems. A concept is introduced that is one of the key aspects of the efficiency of the functional strategy: transitive indexes. The corresponding class of transitive term rewriting systems is characterized. An efficient normalizing strategy is given for these rewriting systems. It is shown that the functional strategy is normalizing for the class of left-incompatible term rewriting systems.