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DOI: 10.4230/LIPIcs.FSCD.2018.9

Term-Graph Anti-Unification

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

Published in: LIPIcs, Volume 108, 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)

Abstract

We study anti-unification for possibly cyclic, unranked term-graphs and develop an algorithm, which computes a minimal complete set of generalizations for them. For bisimilar graphs the algorithm computes the join in the lattice generated by a functional bisimulation. These results generalize anti-unification for ranked and unranked terms to the corresponding term-graphs, and solve also anti-unification problems for rational terms and dags. Our results open a way to widen anti-unification based code clone detection techniques from a tree representation to a graph representation of the code.

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Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. Term-Graph Anti-Unification. In 3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 108, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{baumgartner_et_al:LIPIcs.FSCD.2018.9,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Term-Graph Anti-Unification}},
  booktitle =	{3rd International Conference on Formal Structures for Computation and Deduction (FSCD 2018)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-077-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{108},
  editor =	{Kirchner, H\'{e}l\`{e}ne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2018.9},
  URN =		{urn:nbn:de:0030-drops-91797},
  doi =		{10.4230/LIPIcs.FSCD.2018.9},
  annote =	{Keywords: Cyclic term-graps, anti-unification, least general generalization}
}

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DOI: 10.4230/LIPIcs.RTA.2015.57

Nominal Anti-Unification

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

Published in: LIPIcs, Volume 36, 26th International Conference on Rewriting Techniques and Applications (RTA 2015)

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.

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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)

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@InProceedings{baumgartner_et_al:LIPIcs.RTA.2015.57,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{Nominal Anti-Unification}},
  booktitle =	{26th International Conference on Rewriting Techniques and Applications (RTA 2015)},
  pages =	{57--73},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-85-9},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{36},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2015.57},
  URN =		{urn:nbn:de:0030-drops-51895},
  doi =		{10.4230/LIPIcs.RTA.2015.57},
  annote =	{Keywords: Nominal Anti-Unification, Term-in-context, Equivariance}
}

Document

DOI: 10.4230/LIPIcs.RTA.2013.113

A Variant of Higher-Order Anti-Unification

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

Published in: LIPIcs, Volume 21, 24th International Conference on Rewriting Techniques and Applications (RTA 2013)

Abstract

We present a rule-based Huet's style anti-unification algorithm for simply-typed lambda-terms in eta-long beta-normal form, which computes a least general higher-order pattern generalization. For a pair of arbitrary terms of the same type, such a generalization always exists and is unique modulo alpha-equivalence and variable renaming. The algorithm computes it in cubic time within linear space. It has been implemented and the code is freely available.

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Alexander Baumgartner, Temur Kutsia, Jordi Levy, and Mateu Villaret. A Variant of Higher-Order Anti-Unification. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 113-127, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{baumgartner_et_al:LIPIcs.RTA.2013.113,
  author =	{Baumgartner, Alexander and Kutsia, Temur and Levy, Jordi and Villaret, Mateu},
  title =	{{A Variant of Higher-Order Anti-Unification}},
  booktitle =	{24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
  pages =	{113--127},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-53-8},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{21},
  editor =	{van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2013.113},
  URN =		{urn:nbn:de:0030-drops-40579},
  doi =		{10.4230/LIPIcs.RTA.2013.113},
  annote =	{Keywords: higher-order anti-unification, higher-order patterns}
}

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Documents authored by Baumgartner, Alexander

Term-Graph Anti-Unification

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Nominal Anti-Unification

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A Variant of Higher-Order Anti-Unification

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