Modular Aspects of Rewrite-based Speciications

We investigate modular properties of term rewriting systems, the basic operational formalism for equational speciications. First we study suucient conditions for the preservation of the termination property under disjoint (and more general) combinations of term rewriting systems. By means of a reened analysis of existing approaches we show how to prove several new asymmetric preservation results. For this purpose we introduce two interesting new properties of term rewriting systems related to collapsing reductions: uniquely collapsing and collapsing connuent. We discuss these properties w.r.t. well-known connuence, consistency and normal form properties, and show that they are modular for left-linear systems, but not in general.