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On narrowing, refutation proofs and constraints

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Rewriting Techniques and Applications (RTA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 914))

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Abstract

We develop a proof technique for dealing with narrowing and refutational theorem proving in a uniform way, clarifying the exact relationship between the existing results in both fields and allowing us to obtain several new results. Refinements of narrowing (basic, LSE, etc.) are instances of the technique, but are also defined here for arbitrary (possibly ordering and/or equality constrained or not yet convergent or saturated) Horn clauses, and shown compatible with simplification and other redundancy notions. By narrowing modulo equational theories like AC, compact representations of solutions, expressed by AC-equality constraints, can be obtained. Computing AC-unifiers is only needed at the end if one wants to “uncompress” such a constraint into its (doubly exponentially many) concrete substitutions.

This work was presented in a preliminary stage at the Unif'94 workshop in june 1994 in Val d'Ajol, France. I wish to thank Albert Rubio and Christopher Lynch for several useful discussions. The author is partially supported by the ESPRIT Basic Research working group 6028, CCL.

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Authors and Affiliations

  1. Technical University of Catalonia, Pau Gargallo 5, 08028, Barcelona, Spain

    Robert Nieuwenhuis

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  1. Robert Nieuwenhuis
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Jieh Hsiang

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© 1995 Springer-Verlag Berlin Heidelberg

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Nieuwenhuis, R. (1995). On narrowing, refutation proofs and constraints. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_47

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  • DOI: https://doi.org/10.1007/3-540-59200-8_47

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  • Print ISBN: 978-3-540-59200-6

  • Online ISBN: 978-3-540-49223-8

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