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.RTA.2015.301
URN: urn:nbn:de:0030-drops-52042
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5204/
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Suzuki, Takaki ; Kikuchi, Kentaro ; Aoto, Takahito ; Toyama, Yoshihito

Confluence of Orthogonal Nominal Rewriting Systems Revisited

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Abstract

Nominal rewriting systems (Fernandez, Gabbay, Mackie, 2004;
Fernandez, Gabbay, 2007) have been introduced as a new framework
of higher-order rewriting systems based on the nominal approach
(Gabbay, Pitts, 2002; Pitts, 2003), which deals with variable
binding via permutations and freshness conditions on atoms.
Confluence of orthogonal nominal rewriting systems has been shown in
(Fernandez, Gabbay, 2007). However, their definition of
(non-trivial) critical pairs has a serious weakness so that the
orthogonality does not actually hold for most of standard nominal
rewriting systems in the presence of binders. To overcome this
weakness, we divide the notion of overlaps into the self-rooted and
proper ones, and introduce a notion of alpha-stability which
guarantees alpha-equivalence of peaks from the self-rooted
overlaps. Moreover, we give a sufficient criterion for uniformity and alpha-stability. The new definition of orthogonality and the
criterion offer a novel confluence condition effectively applicable to many standard nominal rewriting systems. We also report on an
implementation of a confluence prover for orthogonal nominal rewriting systems based on our framework.

BibTeX - Entry

@InProceedings{suzuki_et_al:LIPIcs:2015:5204,
  author =	{Takaki Suzuki and Kentaro Kikuchi and Takahito Aoto and Yoshihito Toyama},
  title =	{{Confluence of Orthogonal Nominal Rewriting Systems Revisited}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{301--317},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Maribel Fern{\'a}ndez},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5204},
  URN =		{urn:nbn:de:0030-drops-52042},
  doi =		{10.4230/LIPIcs.RTA.2015.301},
  annote =	{Keywords: Nominal rewriting, Confluence, Orthogonality, Higher-order rewriting, alpha-equivalence}
}

Keywords: Nominal rewriting, Confluence, Orthogonality, Higher-order rewriting, alpha-equivalence
Collection: 26th International Conference on Rewriting Techniques and Applications (RTA 2015)
Issue Date: 2015
Date of publication: 18.06.2015

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