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International Symposium on Logic-Based Program Synthesis and Transformation

LOPSTR 2017: Logic-Based Program Synthesis and Transformation pp 235–251Cite as

Nominal C-Unification

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10855))

Abstract

Nominal unification is an extension of first-order unification that takes into account the \(\alpha \)-equivalence relation generated by binding operators, following the nominal approach. We propose a sound and complete procedure for nominal unification with commutative operators, or nominal C-unification for short, which has been formalised in Coq. The procedure transforms nominal C-unification problems into simpler (finite families) of fixed point constraints, whose solutions can be generated by algebraic techniques on combinatorics of permutations.

Work supported by the Brazilian agencies FAPDF (DE 193.001.369/2016), CAPES (Proc. 88881.132034/2016-01, 2nd author) and CNPq (PQ 307009/2013, 1st author).

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Notes

  1. 1.

    Infix notation is adopted for commutative symbols: \(s * t\) abbreviates \(*\langle s,t\rangle \).

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Author information

Authors and Affiliations

  1. Depts. de Matemática e Ciência da Computação, Universidade de Brasília, Brasília, Brazil

    Mauricio Ayala-Rincón, Washington de Carvalho-Segundo & Daniele Nantes-Sobrinho

  2. Department of Informatics, King’s College London, London, UK

    Maribel Fernández

Authors
  1. Mauricio Ayala-Rincón
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  2. Washington de Carvalho-Segundo
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  3. Maribel Fernández
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  4. Daniele Nantes-Sobrinho
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Corresponding authors

Correspondence to Mauricio Ayala-Rincón , Washington de Carvalho-Segundo , Maribel Fernández or Daniele Nantes-Sobrinho .

Editor information

Editors and Affiliations

  1. University of Chieti-Pescara, Pescara, Italy

    Fabio Fioravanti

  2. Roskilde University, Roskilde, Denmark

    John P. Gallagher

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Ayala-Rincón, M., de Carvalho-Segundo, W., Fernández, M., Nantes-Sobrinho, D. (2018). Nominal C-Unification. In: Fioravanti, F., Gallagher, J. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2017. Lecture Notes in Computer Science(), vol 10855. Springer, Cham. https://doi.org/10.1007/978-3-319-94460-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-94460-9_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94459-3

  • Online ISBN: 978-3-319-94460-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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