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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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