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

Source: Ariola, Zena M. - Department of Computer and Information Science, University of Oregon

Collections: Computer Technologies and Information Sciences