EQUATIONAL TERM GRAPH REWRITING

  • Authors:

  • Zena M. Ariola;Jan Willem Klop

  • Affiliations:

  • Computer & Information Science Department, University of Oregon, Eugene, OR 97401, USA. E-mail: ariola@cs.uoregon.edu;Department of Software Technology, CWI, Department of Computer Science, Free University, Amsterdam, The Netherlands. E-mail: jwk@cwi.nl

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 1996

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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 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.