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Implementing term rewriting by graph reduction: Termination of combined systems

  • Chapter 4 Combined Systems, Combined Languages And Modularity
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Conditional and Typed Rewriting Systems (CTRS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 516))

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Abstract

It is well known that the disjoint union of terminating term rewriting systems does not yield a terminating system in general. We show that this undesirable phenomenon vanishes if one implements term rewriting by graph reduction: given two terminating term rewrite systems ℝ0 and ℝ1, the graph reduction system implementing ℝ0+ℝ1 is terminating. In fact, we prove the stronger result that the graph reduction system for the union ℝ0∪ℝ1 is terminating provided that the left-hand sides of ℝ i have no common function symbols with the right-hand sides of ℝ1−i (i=0, 1).

The implementation is complete in the sense that it computes a normal form for each term over the signature of ℝ0∪ℝ1.

Work supported by ESPRIT project #390, PROSPECTRA, and by ESPRIT Basic Research Working Group #3264, COMPASS.

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Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Bremen, Postfach 33 04 40, D-2800, Bremen 33

    Detlef Plump

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  1. Detlef Plump
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S. Kaplan M. Okada

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© 1991 Springer-Verlag Berlin Heidelberg

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Plump, D. (1991). Implementing term rewriting by graph reduction: Termination of combined systems. In: Kaplan, S., Okada, M. (eds) Conditional and Typed Rewriting Systems. CTRS 1990. Lecture Notes in Computer Science, vol 516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54317-1_100

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  • DOI: https://doi.org/10.1007/3-540-54317-1_100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54317-6

  • Online ISBN: 978-3-540-47558-3

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