In this paper we present a new operational and denotational semantics for rewrite systems as logic programs. The main feature of our rewrite programs is that they allow us to define predicates not only by implications as in Prolog, but also by equivalences. We give a few examples showing how rewrite programs may turn out to be more effective than Prolog programs in capturing the user’s intended...

Abstract rewrite systems define a reduction relation by a set of rules. An important aspect of such rewrite relations is their behavior in an arbitrary context associated with the underlying congruence relation. This behavior is described by “compatibility properties”: a rewrite system is compatible if applying the same context to two objects preserves the rewrite relation among them. We presen...

First-order applicative term rewrite systems provide a natural framework for modeling higher-order aspects. In this paper we present a transformation from untyped applicative term rewrite systems to functional term rewrite systems that preserves and reflects termination. Our transformation is less restrictive than other approaches. In particular, head variables in right-hand sides of rewrite ru...

In this paper we present a new path order for rewrite systems, the exponential path order EPO. Suppose a term rewrite system is compatible with EPO, then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPO equals the class of functions computable in exponential time on...

We consider rewriting as a tool for solving identity problems in varieties of idempotent semigroups. It is known that there exist finite canonical term rewrite systems and finite canonical word rewrite systems for only a very limited number of those varieties. We present a finite canonical conditional word rewrite system for a particular variety in which the classical approaches cannot be appli...

We present a strongly normalising and confluent term rewrite system which describes addition, subtraction, and multiplication of positive and negative integers represented in base 10. We prove a general theorem giving an easily checkable syntactic condition on term rewrite systems which implies strong normalisation. The rewrite system for decimal arithmetic satisfies the condition. The method i...

Recent advances in the foundations and the implementations of functional logic programming languages originate from far-reaching results on narrowing evaluation strategies. Narrowing is a computation similar to rewriting which yields substitutions in addition to normal forms. In functional logic programming, the classes of rewrite systems to which narrowing is applied are, for the most part, su...