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DOI: 10.4230/LIPIcs.FSCD.2022.8

A Certified Algorithm for AC-Unification

Authors: Mauricio Ayala-Rincón, Maribel Fernández, Gabriel Ferreira Silva, and Daniele Nantes Sobrinho

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract

Implementing unification modulo Associativity and Commutativity (AC) axioms is crucial in rewrite-based programming and theorem provers. We modify Stickel’s seminal AC-unification algorithm to avoid mutual recursion and formalise it in the PVS proof assistant. More precisely, we prove the adjusted algorithm’s termination, soundness, and completeness. To do this, we adapted Fages' termination proof, providing a unique elaborated measure that guarantees termination of the modified AC-unification algorithm. This development (to the best of our knowledge) provides the first fully formalised AC-unification algorithm.

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Mauricio Ayala-Rincón, Maribel Fernández, Gabriel Ferreira Silva, and Daniele Nantes Sobrinho. A Certified Algorithm for AC-Unification. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 8:1-8:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ayalarincon_et_al:LIPIcs.FSCD.2022.8,
  author =	{Ayala-Rinc\'{o}n, Mauricio and Fern\'{a}ndez, Maribel and Silva, Gabriel Ferreira and Sobrinho, Daniele Nantes},
  title =	{{A Certified Algorithm for AC-Unification}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{8:1--8:21},
  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/entities/document/10.4230/LIPIcs.FSCD.2022.8},
  URN =		{urn:nbn:de:0030-drops-162894},
  doi =		{10.4230/LIPIcs.FSCD.2022.8},
  annote =	{Keywords: AC-Unification, PVS, Certified Algorithms, Formal Methods, Interactive Theorem Proving}
}

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A Certified Algorithm for AC-Unification

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