EQUATIONAL TERM GRAPH REWRITING
Zena M. Ariola, Jan Willem Klop · Fundamenta Informaticae · 1996
We present an equational framework for term graph rewriting with cycles. The usual notion of homomorphism is phrased in terms of the notion of bisimulation, which is well-known in process algebra and concurrency theory. Specifically, a homomorphism is a functional bisimulation. We prove that the bisimilarity class of a term graph, partially ordered by functional bisimulation, is a complete lattice. It is shown how Equational Logic induces a notion of copying and substitution on term graphs, or systems of recursion equations, and also suggests the introduction of hidden or nameless nodes in a term graph. Hidden nodes can be used only once. The general framework of term graphs with copying is compared with the more restricted copying facilities embodied in the μ-rule. Next, orthogonal term graph rewrite systems, also in the presence of copying and hidden nodes, are shown to be confluent.