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Equational Term Graph Rewriting Zena M. Ariola Jan Willem Klop

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
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


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


Collections: Computer Technologies and Information Sciences