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Higher-order proof by consistency

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Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1180))

Abstract

We investigate an integration of the first-order method of proof by consistency (PBC), also known as term rewriting induction, into theorem proving in higher-order specifications. PBC may be seen as well-founded induction over an ordering which contains the rewrite relation, and in this paper we extend this method to the higher-order rewrite relation due to Nipkow. This yields a proof procedure which has several advantages over conventional induction. First, it is less control demanding; second, it is more flexible in the sense that it does not instantiate variables precisely with every constructor, but instantiates according to the rewrite rules. We show how a number of technical problems can be solved in order for this integration to work, and point out some desirable refinements that involve challenging problems.

Partly supported by the Norwegian Research Council.

Supported by Esprit projects OMI-MACRAME and OMI-ARCHES.

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Author information

Authors and Affiliations

  1. Department of Informatics, University of Oslo, Blindem, PB 1080, 0316, Oslo, Norway

    Henrik Linnestad & Olav Lysne

  2. Institut für Informatik, Technische UniversitÄt München, 80290, München, Germany

    Christian Prehofer

Authors
  1. Henrik Linnestad
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  2. Christian Prehofer
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  3. Olav Lysne
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Editor information

V. Chandru V. Vinay

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© 1996 Springer-Verlag Berlin Heidelberg

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Linnestad, H., Prehofer, C., Lysne, O. (1996). Higher-order proof by consistency. In: Chandru, V., Vinay, V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1996. Lecture Notes in Computer Science, vol 1180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62034-6_56

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  • DOI: https://doi.org/10.1007/3-540-62034-6_56

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  • Online ISBN: 978-3-540-49631-1

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