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Nominal AC-Matching

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Intelligent Computer Mathematics (CICM 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14101))

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Abstract

The nominal syntax is an extension of the first-order syntax that smoothly represents languages with variable bindings. Nominal matching is first-order matching modulo alpha-equivalence. This work extends a certified first-order AC-unification algorithm to solve nominal AC-matching problems. To our knowledge, this is the first mechanically-verified nominal AC-matching algorithm. Its soundness and completeness were verified using the proof assistant PVS. The formalisation enriches the first-order AC-unification algorithm providing structures and mechanisms to deal with the combinatorial aspects of nominal atoms, permutations and abstractions. Furthermore, by adding a parameter for “protected variables” that cannot be instantiated during the execution, it enables nominal matching. Such a general treatment of protected variables also gives rise to a verified nominal AC-equality checker as a byproduct.

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Acknowledgments

Partially supported by the Austrian Science Fund (FWF) Project P 35530, Brazilian FAP-DF Project DE 00193.00001175/2021-11, Brazilian CNPq Project Universal 409003/2021-2, and Georgian Rustaveli National Science Foundation Project FR-21-16725. First author was partially funded by a CNPq productivity research grant 313290/2021-0.

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Authors and Affiliations

  1. University of Brasília, Brasília, Brazil

    Mauricio Ayala-Rincón, Gabriel Ferreira Silva & Daniele Nantes-Sobrinho

  2. King’s College London, London, UK

    Maribel Fernández

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. Imperial College London, London, UK

    Daniele Nantes-Sobrinho

Authors
  1. Mauricio Ayala-Rincón
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  2. Maribel Fernández
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  3. Gabriel Ferreira Silva
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  4. Temur Kutsia
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  5. Daniele Nantes-Sobrinho
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Corresponding author

Correspondence to Gabriel Ferreira Silva .

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Editors and Affiliations

  1. ENSIIE, Evry, France

    Catherine Dubois

  2. University of Birmingham, Birmingham, UK

    Manfred Kerber

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Ayala-Rincón, M., Fernández, M., Silva, G.F., Kutsia, T., Nantes-Sobrinho, D. (2023). Nominal AC-Matching. In: Dubois, C., Kerber, M. (eds) Intelligent Computer Mathematics. CICM 2023. Lecture Notes in Computer Science(), vol 14101. Springer, Cham. https://doi.org/10.1007/978-3-031-42753-4_4

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  • DOI: https://doi.org/10.1007/978-3-031-42753-4_4

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