License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSCD.2022.7
URN: urn:nbn:de:0030-drops-162885
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16288/
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Schmidt-Schauß, Manfred ; Nantes-Sobrinho, Daniele

Nominal Anti-Unification with Atom-Variables

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LIPIcs-FSCD-2022-7.pdf (0.9 MB)

Abstract

Anti-unification is the task of generalizing a set of expressions in the most specific way. It was extended to the nominal framework by Baumgarter, Kutsia, Levy and Villaret, who defined an algorithm solving the nominal anti-unification problem, which runs in polynomial time. Unfortunately, when an infinite set of atoms are allowed in generalizations, a minimal complete set of solutions in nominal anti-unification does not exist, in general. In this paper, we present a more general approach to nominal anti-unification that uses atom-variables instead of explicit atoms, and two variants of freshness constraints: NL_A-constraints (with atom-variables), and Eqr-constraints based on Equivalence relations on atom-variables. The idea of atom-variables is that different atom-variables may be instantiated with identical or different atoms. Albeit simple, this freedom in the formulation increases its application potential: we provide an algorithm that is finitary for the NL_A-freshness constraints, and for Eqr-freshness constraints it computes a unique least general generalization. There is a price to pay in the general case: checking freshness constraints and other related logical questions will require exponential time. The setting of Baumgartner et al. is improved by the atom-only case, which runs in polynomial time and computes a unique least general generalization.

BibTeX - Entry

@InProceedings{schmidtschau_et_al:LIPIcs.FSCD.2022.7,
  author =	{Schmidt-Schau{\ss}, Manfred and Nantes-Sobrinho, Daniele},
  title =	{{Nominal Anti-Unification with Atom-Variables}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{7:1--7:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16288},
  URN =		{urn:nbn:de:0030-drops-162885},
  doi =		{10.4230/LIPIcs.FSCD.2022.7},
  annote =	{Keywords: Generalization, anti-unification, nominal algorithms, higher-order deduction}
}

Keywords: Generalization, anti-unification, nominal algorithms, higher-order deduction
Collection: 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)
Issue Date: 2022
Date of publication: 28.06.2022

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