title: The Functional Strategy and Transitive Term Rewriting Systems
authors: Yoshihito Toyama, Sjaak Smetsers, Marko van Eekelen, Rinus Plasmeijer
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.