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Nominal Anti-Unification

Authors Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret

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Alexander Baumgartner
Temur Kutsia
Jordi Levy
Mateu Villaret

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Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. Nominal Anti-Unification. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 57-73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
https://doi.org/10.4230/LIPIcs.RTA.2015.57

Abstract

We study nominal anti-unification, which is concerned with computing least general generalizations for given terms-in-context. In general, the problem does not have a least general solution, but if the set of atoms permitted in generalizations is finite, then there exists a least general generalization which is unique modulo variable renaming and alpha-equivalence. We present an algorithm that computes it. The algorithm relies on a subalgorithm that constructively decides equivariance between two terms-in-context. We prove soundness and completeness properties of both algorithms and analyze their complexity. Nominal anti-unification can be applied to problems where generalization of first-order terms is needed (inductive learning, clone detection, etc.), but bindings are involved.
Keywords
  • Nominal Anti-Unification
  • Term-in-context
  • Equivariance

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