License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2017.19
URN: urn:nbn:de:0030-drops-77252
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7725/
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Hirokawa, Nao ; Middeldorp, Aart ; Sternagel, Christian ; Winkler, Sarah

Infinite Runs in Abstract Completion

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Abstract

Completion is one of the first and most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In an earlier paper we presented a new and formalized correctness proof of abstract completion for finite runs. In this paper we extend our analysis and our formalization to infinite runs, resulting in a new proof that fair infinite runs produce complete presentations of the initial equations. We further consider ordered completion - an important extension of completion that aims to produce ground-complete presentations of the initial equations. Moreover, we revisit and extend results of Métivier concerning canonicity of rewrite systems. All proofs presented in the paper have been formalized in Isabelle/HOL.

BibTeX - Entry

@InProceedings{hirokawa_et_al:LIPIcs:2017:7725,
  author =	{Nao Hirokawa and Aart Middeldorp and Christian Sternagel and Sarah Winkler},
  title =	{{Infinite Runs in Abstract Completion}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Dale Miller},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7725},
  URN =		{urn:nbn:de:0030-drops-77252},
  doi =		{10.4230/LIPIcs.FSCD.2017.19},
  annote =	{Keywords: term rewriting, abstract completion, ordered completion, canonicity, Isabelle/HOL}
}

Keywords: term rewriting, abstract completion, ordered completion, canonicity, Isabelle/HOL
Collection: 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)
Issue Date: 2017
Date of publication: 30.08.2017

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