Implementing conditional term rewriting by graph rewriting

Abstract

For reasons of efficiency, term rewriting is usually implemented by graph rewriting. Barendregt et al. showed that graph rewriting is a sound and complete implementation of (almost) orthogonal term rewriting systems. Their result was strengthened by Kennaway et al. who showed that graph rewriting is adequate for simulating term rewriting. In this paper, we extend the aforementioned results to a class of conditional term rewriting systems which plays a key role in the integration of functional and logic programming. In these systems extra variables are allowed in conditions and right-hand sides of rules. Moreover, it is shown that orthogonal conditional rules give rise to a subcommutative conditional graph rewrite relation. This implies that the graph rewrite relation is level-confluent.