 
Summary: Equational Term Graph Rewriting
Zena M. Ariola
Computer & Information Science Department
University of Oregon. Eugene, OR 97401, USA
email: ariola@cs.uoregon.edu
Jan Willem Klop
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
and
Department of Mathematics and Computer Science
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam
email: 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, and translations are given between term graphs and ¯expressions. Using these, a
