License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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DOI: 10.4230/LIPIcs.FSCD.2018.7
URN: urn:nbn:de:0030-drops-91777
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9177/
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Ayala-Rincón, Mauricio ; Fernández, Maribel ; Nantes-Sobrinho, Daniele

Fixed-Point Constraints for Nominal Equational Unification

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Abstract

We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint. We show that the standard freshness relation between atoms and terms can be derived from the more primitive notion of permutation fixed-point, and use this result to prove the correctness of the new alpha-equivalence axiomatisation. This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. Although it may seem less natural than the standard notion of nominal unifier based on freshness constraints, the notion of unifier based on fixed-point constraints behaves better when equational theories are considered: for example, nominal unification remains finitary in the presence of commutativity, whereas it becomes infinitary when unifiers are expressed using freshness contexts.

BibTeX - Entry

@InProceedings{ayalarincn_et_al:LIPIcs:2018:9177,
  author =	{Mauricio Ayala-Rinc{\'o}n and Maribel Fern{\'a}ndez and Daniele Nantes-Sobrinho},
  title =	{{Fixed-Point Constraints for Nominal Equational Unification}},
  booktitle =	{3rd International Conference on Formal Structures for  Computation and Deduction (FSCD 2018)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{H{\'e}l{\`e}ne Kirchner},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9177},
  URN =		{urn:nbn:de:0030-drops-91777},
  doi =		{10.4230/LIPIcs.FSCD.2018.7},
  annote =	{Keywords: nominal terms, fixed-point equations, nominal unification, equational theories}
}

Keywords: nominal terms, fixed-point equations, nominal unification, equational theories
Collection: 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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