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DOI: 10.4230/LIPIcs.FSCD.2017.19
URN: urn:nbn:de:0030-drops-77252
URL: https://drops.dagstuhl.de/opus/volltexte/2017/7725/
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 | |
| Seminar: | 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017) | |
| Issue date: | 2017 | |
| Date of publication: | 30.08.2017 |
