The applicability of term rewriting to program transformation is limited by the lack of control over rule application and by the context-free nature of rewrite rules. The first problem is addressed by languages supporting user-definable rewriting strategies. The second problem is addressed by the extension of rewriting strategies with scoped dynamic rewrite rules. Dynamic rules are defined at r...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

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...

Introducing priorities in rewriting increases the expressive power of rules and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe an inductive proof method for termination of priority rewriting, relying on an explicit ind...

In this paper the concurrent semantics of double-pushout (DPO) graph rewriting, which is classically deened in terms of shift-equivalence classes of graph derivations, is axiomatised via the construction of a free monoidal bi-category. In contrast to a previous attempt based on 2-categories, the use of bi-categories allows to deene rewriting on concrete graphs. Thus, the problem of composition ...

This paper is an extended abstract of an analysis of term rewriting where the terms in the rewrite rules as well as the term to be rewritten are compressed by a singleton tree grammar (STG). This form of compression is more general than node sharing or representing terms as dags since also partial trees (contexts) can be shared in the compression. In the first part efficient but complex algorit...

Syntactically complex sentences constitute an obstacle for some people with Autistic Spectrum Disorders. This paper evaluates a set of simplification rules specifically designed for tackling complex and compound sentences. In total, 127 different rules were developed for the rewriting of complex sentences and 56 for the rewriting of compound sentences. The evaluation assessed the accuracy of th...

We present a term rewriting system for interval arithmetic (addition, subtraction and multiplication), toward a mathematical model for interval computation. We start presenting a term rewriting system whose rules (directed equations) perform binary floating-point arithmetic, which is based on IEEE-754 Standard. Next, this primitive system is extended with rules for interval arithmetic. Finally,...

In 12] we introduced the tile model, a framework encompassing a wide class of computational systems, whose behaviour can be described by certain rewriting rules. We gathered our inspiration both from the world of term rewriting and of con-currency theory, and our formalism recollects many properties of these sources. For example, it provides a compositional way to describe both the states and t...