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Certified Subterm Criterion and Certified Usable Rules

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Abstract

In this paper we present our formalization of two important termination techniques for term rewrite systems: the subterm criterion and the reduction pair processor in combination with usable rules. For both techniques we developed executable check functions in the theorem prover Isabelle/HOL which can certify the correct application of these techniques in some given termination proof. As there are several variants of usable rules we designed our check function in such a way that it accepts all known variants, even those which are not explicitly spelled out in previous papers. We integrated our formalization in the publicly available IsaFoR-library. This led to a significant increase in the power of CeTA, the corresponding certified termination proof checker that is extracted from IsaFoR.

BibTeX - Entry

@InProceedings{sternagel_et_al:LIPIcs:2010:2661,
  author =	{Christian Sternagel and Ren{\'e} Thiemann},
  title =	{{Certified Subterm Criterion and Certified Usable Rules}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{325--340},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-18-7},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{6},
  editor =	{Christopher Lynch},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2661},
  URN =		{urn:nbn:de:0030-drops-26611},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2010.325},
  annote =	{Keywords: Term Rewriting, Certification, Termination, Theorem Proving}
}

Keywords: Term Rewriting, Certification, Termination, Theorem Proving
Seminar: Proceedings of the 21st International Conference on Rewriting Techniques and Applications
Issue date: 2010
Date of publication: 2010


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