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Collapsed tree rewriting: Completeness, confluence, and modularity

  • Modularity and Termination
  • Conference paper
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Conditional Term Rewriting Systems (CTRS 1992)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 656))

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Abstract

Collapsed trees are (hyper)graphs which represent functional expressions such that common subexpressions can be shared. Rewrite steps with collapsed trees include applications of term rewrite rules as well as “folding steps” which identify common subexpressions. Different aspects of this model of computation are considered: (1) It is shown that collapsed tree rewriting is complete with respect to equational validity in the same sense as term rewriting is. (2) Collapsed tree rewriting and term rewriting are compared with respect to confluence. (3) Termination and convergence of collapsed tree rewriting turn out to be modular properties, in contrast to the situation for term rewriting.

Research supported by Deutsche Forschungsgemeinschaft and by ESPRIT Basic Research Working Group 3299, COMPUGRAPH.

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Author notes

  1. Detlef Plump

    Present address: Fachbereich Mathematik und Informatik, Universität Bremen, Postfach 33 04 40, 2800, Bremen 33, Germany

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    1. Detlef Plump
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    Correspondence to Detlef Plump .

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    Michaël Rusinowitch Jean-Luc Rémy

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    © 1993 Springer-Verlag Berlin Heidelberg

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    Plump, D. (1993). Collapsed tree rewriting: Completeness, confluence, and modularity. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_7

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    • DOI: https://doi.org/10.1007/3-540-56393-8_7

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    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-56393-8

    • Online ISBN: 978-3-540-47549-1

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