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- Publisher
- Association for Computing Machinery
- Copyright
- Copyright © 2019 ACM
- ISSN
- 1529-3785
- eISSN
- 1557-945X
- DOI
- 10.1145/3359060
- Publisher site
- See Article on Publisher Site
Abstract
In this article, we address two problems related to idempotent anti-unification. First, we show that there exists an anti-unification problem with a single idempotent symbol that has an infinite minimal complete set of generalizations. It means that anti-unification with a single idempotent symbol has infinitary or nullary generalization type, similar to anti-unification with two idempotent symbols, shown earlier by Loïc Pottier. Next, we develop an algorithm that takes an arbitrary idempotent anti-unification problem and computes a representation of its solution set in the form of a regular tree grammar. The algorithm does not depend on the number of idempotent function symbols in the input terms. The language generated by the grammar is the minimal complete set of generalizations of the given anti-unification problem, which implies that idempotent anti-unification is infinitary.
Journal
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Nov 2, 2019
Keywords: Anti-unification