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Partial Order Infinitary Term Rewriting and Böhm Trees

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Abstract

We investigate an alternative model of infinitary term rewriting. Instead of a metric, a partial order on terms is employed to formalise (strong) convergence. We compare this partial order convergence of orthogonal term rewriting systems to the usual metric convergence of the corresponding B{"o}hm extensions. The B{"o}hm extension of a term rewriting system contains additional rules to equate so-called root-active terms. The core result we present is that reachability w.r.t. partial order convergence coincides with reachability w.r.t. metric convergence in the B{"o}hm extension. This result is used to show that, unlike in the metric model, orthogonal systems are infinitarily confluent and infinitarily normalising in the partial order model. Moreover, we obtain, as in the metric model, a compression lemma. A corollary of this lemma is that reachability w.r.t. partial order convergence is a conservative extension of reachability w.r.t. metric convergence.

BibTeX - Entry

@InProceedings{bahr:LIPIcs:2010:2645,
  author =	{Patrick Bahr},
  title =	{{Partial Order Infinitary Term Rewriting and B{\"o}hm Trees}},
  booktitle =	{Proceedings of the 21st International Conference on Rewriting Techniques and Applications},
  pages =	{67--84},
  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/2010/2645},
  URN =		{urn:nbn:de:0030-drops-26455},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.RTA.2010.67},
  annote =	{Keywords: Infinitary term rewriting, B{\"o}hm trees, partial order, confluence, normalisation}
}

Keywords: Infinitary term rewriting, Böhm trees, partial order, confluence, normalisation
Seminar: Proceedings of the 21st International Conference on Rewriting Techniques and Applications
Issue date: 2010
Date of publication: 2010


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