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Certification of Nontermination Proofs

  • Conference paper
Interactive Theorem Proving (ITP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7406))

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Abstract

Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is to find a loop, a finite derivation of a special shape that implies nontermination. For standard termination, certifying loops is easy. However, it is not at all trivial to certify whether a given loop also implies innermost nontermination. To this end, a complex decision procedure has been developed in [1]. We formalized this decision procedure in Isabelle/HOL and were able to simplify some parts considerably. Furthermore, from our formalized proofs it is easy to obtain a low complexity bound. Along the way of presenting our formalization, we report on generally applicable ideas that allow to reduce the formalization effort and improve the efficiency of our certifier.

This research is supported by the Austrian Science Fund (FWF): J3202, P22767.

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Author information

Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Japan

    Christian Sternagel

  2. Institute of Computer Science, University of Innsbruck, Austria

    René Thiemann

Authors
  1. Christian Sternagel
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  2. René Thiemann
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Princeton University, 35 Olden Street, 08540, Princeton, NJ, USA

    Lennart Beringer

  2. School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward Ave., K1N 6N5, Ottawa, ON, Canada

    Amy Felty

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Sternagel, C., Thiemann, R. (2012). Certification of Nontermination Proofs. In: Beringer, L., Felty, A. (eds) Interactive Theorem Proving. ITP 2012. Lecture Notes in Computer Science, vol 7406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32347-8_18

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  • DOI: https://doi.org/10.1007/978-3-642-32347-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32346-1

  • Online ISBN: 978-3-642-32347-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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