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Formal Correctness of a Quadratic Unification Algorithm

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Abstract

We present a case study using ACL2 to verify a nontrivial algorithm that uses efficient data structures. The algorithm receives as input two first-order terms, and it returns a most general unifier of these terms if they are unifiable, failure otherwise. The verified implementation stores terms as directed acyclic graphs by means of a pointer structure. Its time complexity is \(O(n^2)\) and its space complexity \(O(n)\), and it can be executed in ACL2 at a speed comparable to a similar C implementation. We report the main issues encountered to achieve this formally verified implementation.

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Authors and Affiliations

  1. Computational Logic Group Department of Computer Science and Artificial Intelligence, University of Seville E.T.S.I. Informática, Avda. Reina Mercedes, s/n. 41012, Sevilla, Spain

    José-Luis Ruiz-Reina, Francisco-Jesús Martín-Mateos, José-Antonio Alonso & María-José Hidalgo

Authors
  1. José-Luis Ruiz-Reina
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  2. Francisco-Jesús Martín-Mateos
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  3. José-Antonio Alonso
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  4. María-José Hidalgo
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Corresponding author

Correspondence to José-Luis Ruiz-Reina.

Additional information

This work has been supported by project TIN2004-03884 (Ministerio de Educación y Ciencia, Spain) and FEDER funds.

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Ruiz-Reina, JL., Martín-Mateos, FJ., Alonso, JA. et al. Formal Correctness of a Quadratic Unification Algorithm. J Autom Reasoning 37, 67–92 (2006). https://doi.org/10.1007/s10817-006-9030-5

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  • DOI: https://doi.org/10.1007/s10817-006-9030-5

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