Automatic code generators often contain pattern matchers that are based on tree grammars. In this work we generalise this approach by developing pattern matchers that are based on more powerful term rewrite systems. A pattern matcher based on a term rewrite system computes all the sequences of rewrite rules that will reduce a given expression tree to a given goal. While the number of sequences ...

dimensional situations containing objects (Figure 1). Situations can be interpreted with respect to objects contained and spatial relationships holding between these objects. The differences between situations imply one or more actions capable of transforming one situation into another. Figure 1 depicts a rewrite rule containing cars, traffic lights, and roads. One possible interpretation for t...

We survey the basic concepts and properties of transfinite rewriting for orthogonal term rewrite systems, lambda calculus, higher-order rewrite systems, and abstract rewrite systems.

The general form of safe recursion (or ramified recurrence) can be expressed by an infinite graph rewrite system including unfolding graph rewrite rules introduced by Dal Lago, Martini and Zorzi, in which the size of every normal form by innermost rewriting is polynomially bounded. Every unfolding graph rewrite rule is precedence terminating in the sense of Middeldorp, Ohsaki and Zantema. Altho...