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 so...

We introduce term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uniication. Our main result is that this mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and connuent. This includes, in particular, all convergent term rewriting syste...

Rewriting is a formalism widely used in computer science and mathematical logic. When using rewriting as a programming or modeling paradigm, the rewrite rules describe the transformations one wants to operate and rewriting strategies are used to control their application. The operational semantics of these strategies are generally accepted and approaches for analyzing the termination of specifi...

We review the concept of term graph narrowing as an approach for solving equations by transformations on term graphs. Term graph narrowing combines term graph rewriting with rst-order term uni cation. This mechanism is complete for all term rewriting systems over which term graph rewriting is normalizing and conuent. This includes, in particular, all convergent term rewriting systems. Completen...

This article proposes a compositional semantics for term rewriting systems, i.e. a semantics preserving structuring operations such as the disjoint union. The semantics is based on the categorical construct of a monad, adapting the treatment of universal algebra in category theory to term rewriting systems. As an example, the preservation of connuence under the disjoint union of two term rewrit...

Term rewriting systems are widely used throughout computer science as they provide an abstract model of computation while retaining a comparatively simple syntax and semantics. In order to reason within large term rewriting systems, structuring operations are used to build large term rewriting systems from smaller ones. Of particular interest is whether key properties are modular, that is, if t...

Term rewriting systems are a formalism in widespread use, often implemented by means of term graph rewriting. In this work we present preliminary results towards an elegant embedding of term graph rewriting in Constraint Handling Rules with rule priorities (CHR). As term graph rewriting is well-known to be incomplete with respect to term rewriting, we aim for sound jungle evaluation in CHR. Hav...

A judicious use of labelled terms makes it possible to bring together the simplicity of term rewriting and the sharing power of graph rewriting: this has been known for twenty years in the particular case of orthogonal first-order systems. The present paper introduces a concise and easily usable axiomatic presentation of sharing-via-labelling techniques that applies to higher-order term rewriti...

A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort. This is the posit...

Modular properties of term rewriting systems, i.e. properties which are preserved under disjoint unions, have attracted an increasing attention within the last few years. Whereas connuence is modular this does not hold true in general for termination. By means of a careful analysis of potential counterexamples we prove the following abstract result. Whenever the disjoint union R 1 R 2 of two ((...