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A Modular Order-sorted Equational Generalization Algorithm
Authors
Albert
Alpuente
+53 more
Alpuente
Alpuente
Alpuente
Alpuente
Alpuente
Armengol
Armengol
Aït-Kaci
Aït-Kaci
Aït-Kaci
Baader
Baader
Belli
Bergstra
Borovanský
Boyer
Burghardt
Clavel
Clavel
Diaconescu
Eker
Frisch
Gallagher
Goguen
Goguen
Hullot
Javier Espert
José Meseguer
Jouannaud
Kaufmann
Kitzelmann
Kutsia
Lassez
Lu
Martelli
María Alpuente
Meseguer
Meseguer
Mogensen
Muggleton
Pfenning
Plaza
Plotkin
Plotkin
Popplestone
Pottier
Reynolds
Santiago Escobar
Schmidt-Schauss
Siekmann
Smolka
Smolka
Østvold
Publication date
1 April 2014
Publisher
'Elsevier BV'
Doi
Cite
Abstract
Generalization, also called anti-unification, is the dual of unification. Given terms t and t , a generalizer is a term t of which t and t are substitution instances. The dual of a most general unifier (mgu) is that of least general generalizer (lgg). In this work, we extend the known untyped generalization algorithm to, first, an order-sorted typed setting with sorts, subsorts, and subtype polymorphism; second, we extend it to work modulo equational theories, where function symbols can obey any combination of associativity, commutativity, and identity axioms (including the empty set of such axioms); and third, to the combination of both, which results in a modular, order-sorted equational generalization algorithm. Unlike the untyped case, there is in general no single lgg in our framework, due to order-sortedness or to the equational axioms. Instead, there is a finite, minimal and complete set of lggs, so that any other generalizer has at least one of them as an instance. Our generalization algorithms are expressed by means of inference systems for which we give proofs of correctness. This opens up new applications to partial evaluation, program synthesis, and theorem proving for typed equational reasoning systems and typed rulebased languages such as ASF+SDF, Elan, OBJ, Cafe-OBJ, and Maude. © 2014 Elsevier Inc. All rights reserved. 1.M. Alpuente, S. Escobar, and J. Espert have been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2010-21062-C02-02, and by Generalitat Valenciana PROMETEO2011/052. J. Meseguer has been supported by NSF Grants CNS 09-04749, and CCF 09-05584.Alpuente Frasnedo, M.; Escobar Román, S.; Espert Real, J.; Meseguer, J. (2014). A Modular Order-sorted Equational Generalization Algorithm. Information and Computation. 235:98-136. https://doi.org/10.1016/j.ic.2014.01.006S9813623
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oai:riunet.upv.es:10251/46953
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