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arXiv · 2504.21097

Nominal anti-unification

Alexander Baumgartner·Temur Kutsia·Jordi Levy·Mateu Villaret
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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 were generalization of first-order terms is needed (inductive learning, clone detection, etc.), but bindings are involved.

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Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret. 2025-04-29. Nominal anti-unification. https://arxiv.org/abs/2504.21097

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