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Normalizing narrowing for weakly terminating and confluent systems

  • Computational Logic
  • Conference paper
  • First Online:
Principles and Practice of Constraint Programming — CP '95 (CP 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

In this paper we show that narrowing strategies based on normalizing narrowing are complete for weakly terminating and confluent systems. Usually, in completeness results rewriting systems are assumed to be noetherian (and confluent) and this property is essential for the proof. We develop a new method to prove completeness where weak termination (and confluence) suffices. Basic narrowing is known to be incomplete for these systems. We prove that normalizing basic narrowing and its refinements are complete. Using our proof method we also obtain new results for narrowing modulo a (term finite) equational theory. Narrowing modulo equational theories allows us to use efficient built-in E-unification algorithms.

This work was supported by the Deutsche Forschungsgemeinschaft as part of the SPB 314 (project S2).

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Authors and Affiliations

  1. ILKD, University of Karlsruhe, D-76128, Karlsruhe

    Andreas Werner

Authors
  1. Andreas Werner
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Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Werner, A. (1995). Normalizing narrowing for weakly terminating and confluent systems. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_25

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  • DOI: https://doi.org/10.1007/3-540-60299-2_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

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