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Certification of Nontermination Proofs

  • Christian Sternagel
  • René Thiemann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7406)

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.

Keywords

nontermination formalization interactive theorem proving term rewriting 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Sternagel
    • 1
  • René Thiemann
    • 2
  1. 1.Japan Advanced Institute of Science and TechnologyJapan
  2. 2.Institute of Computer ScienceUniversity of InnsbruckAustria

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