Nominal anti-unification modulo equational theories
This paper investigates nominal anti-unification, i.e., the problem of computing least general generalizations of terms in the presence of binding structures and freshness constraints. We extend this problem to account for equational theories, specifically associativity (A), commutativity (C), and t...
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| Vydané v: | Journal of logical and algebraic methods in programming Ročník 149; s. 101100 |
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| Abstract | This paper investigates nominal anti-unification, i.e., the problem of computing least general generalizations of terms in the presence of binding structures and freshness constraints. We extend this problem to account for equational theories, specifically associativity (A), commutativity (C), and their combination (AC), yielding the notion of anti-unification modulo a theory E. Solutions in this setting, called E-generalizations, must consider both, the syntactic structure of nominal terms, and the algebraic properties imposed by E. In the general case, the problem has no solution due to the unbounded supply of atoms. To obtain a finitary setting, we fix a finite set of atoms A and introduce a rule-based algorithm for computing E-generalizations where only atoms from A are allowed to appear. The algorithm includes dedicated rules for reasoning modulo E and systematically explores permutations of subterms, which may lead to exponential blow-up in the number of generalizations. Although the computed set is not minimal, we describe heuristics that lead to computing promising E-generalizations in reasonable time. We also give an implementation of our algorithm which can be used to explore different optimization strategies that improve efficiency in practice, up to archiving tractability. |
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| AbstractList | This paper investigates nominal anti-unification, i.e., the problem of computing least general generalizations of terms in the presence of binding structures and freshness constraints. We extend this problem to account for equational theories, specifically associativity (A), commutativity (C), and their combination (AC), yielding the notion of anti-unification modulo a theory E. Solutions in this setting, called E-generalizations, must consider both, the syntactic structure of nominal terms, and the algebraic properties imposed by E. In the general case, the problem has no solution due to the unbounded supply of atoms. To obtain a finitary setting, we fix a finite set of atoms A and introduce a rule-based algorithm for computing E-generalizations where only atoms from A are allowed to appear. The algorithm includes dedicated rules for reasoning modulo E and systematically explores permutations of subterms, which may lead to exponential blow-up in the number of generalizations. Although the computed set is not minimal, we describe heuristics that lead to computing promising E-generalizations in reasonable time. We also give an implementation of our algorithm which can be used to explore different optimization strategies that improve efficiency in practice, up to archiving tractability. |
| ArticleNumber | 101100 |
| Author | Nantes-Sobrinho, Daniele Baumgartner, Alexander |
| Author_xml | – sequence: 1 givenname: Alexander orcidid: 0000-0002-4757-5907 surname: Baumgartner fullname: Baumgartner, Alexander email: alexander.baumgartner.x@gmail.com organization: Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua, Chile – sequence: 2 givenname: Daniele orcidid: 0000-0002-1959-8730 surname: Nantes-Sobrinho fullname: Nantes-Sobrinho, Daniele email: dnantess@imperial.ac.uk organization: Department of Mathematics, University of Brasília, Brazil, and Department of Computing, Imperial College London, London, UK |
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| Cites_doi | 10.1016/S0019-9958(73)90301-X 10.1016/S0890-5401(03)00138-X 10.1007/BF03037227 10.1007/s10817-013-9285-6 10.1016/j.tcs.2020.10.020 10.1016/j.future.2017.07.024 10.1145/3571207 10.1016/j.ic.2014.01.006 10.1093/logcom/1.4.497 10.1007/BF00243794 10.1016/j.tcs.2019.02.020 10.1017/S0960129520000110 10.1017/S0960129521000050 10.1007/s10994-021-06089-1 10.1007/978-3-319-11558-0_40 10.1145/1614431.1614437 10.1016/j.ic.2017.01.005 10.1007/s10994-020-05934-z 10.1016/j.ic.2006.12.002 10.1145/3359060 10.1007/s10994-019-05862-7 10.1145/2159531.2159532 10.1007/s10817-016-9383-3 |
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| Keywords | Binding constructs Equational theories Anti-unification Nominal techniques |
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| Title | Nominal anti-unification modulo equational theories |
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