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Verification of the Completeness of Unification Algorithms à la Robinson

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Book cover Logic, Language, Information and Computation (WoLLIC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6188))

Abstract

This work presents a general methodology for verification of the completeness of first-order unification algorithms à la Robinson developed in the higher-order proof assistant PVS. The methodology is based on a previously developed formalization of the theorem of existence of most general unifiers for unifiable terms over first-order signatures. Termination and soundness proofs of any unification algorithm are proved by reusing the formalization of this theorem and completeness should be proved according to the specific way in that non unifiable inputs are treated by the algorithm.

Work supported by the District Federal Research Foundation - FAP-DF 8-004/2007.

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Authors and Affiliations

  1. Departamentos de Matemática, Universidade de Brasília, Brasília, Brazil

    Andréia B. Avelar & Mauricio Ayala-Rincón

  2. Ciência da Computação, Universidade de Brasília, Brasília, Brazil

    Flávio L. C. de Moura & Mauricio Ayala-Rincón

  3. Departamento de Matemática, Universidade Federal de Goiás, Catalão, Brazil

    André Luiz Galdino

Authors
  1. Andréia B. Avelar
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  2. Flávio L. C. de Moura
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  3. André Luiz Galdino
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  4. Mauricio Ayala-Rincón
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Editor information

Editors and Affiliations

  1. Computer Laboratory, University of Cambridge, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  2. Centro de Informática, Universidade Federal de Pernambuco, Avenida Prof Luis Freire s/n, Cidade Universitária, 50740-540, Recife, PE, Brazil

    Ruy de Queiroz

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Avelar, A.B., de Moura, F.L.C., Galdino, A.L., Ayala-Rincón, M. (2010). Verification of the Completeness of Unification Algorithms à la Robinson. In: Dawar, A., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2010. Lecture Notes in Computer Science(), vol 6188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13824-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-13824-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13823-2

  • Online ISBN: 978-3-642-13824-9

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