 
Summary: Equational Term Graph Rewriting
Zena M. Ariola Jan Willem Klop
Computer & Information Science Dept. Dept. of Software Technology, CWI
University of Oregon Dept. of Computer Science, Free University
Eugene, OR 97401 Amsterdam, The Netherlands
ariola@cs.uoregon.edu jwk@cwi.nl
Abstract
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 wellknown 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 ¯rule. Next, orthogonal term
graph rewrite systems, also in the presence of copying and hidden nodes, are
shown to be confluent.
1 Introduction
