TY - JOUR

T1 - A modular equational generalization algorithm

AU - Alpuente, María

AU - Escobar, Santiago

AU - Meseguer, José

AU - Ojeda, Pedro

N1 - Funding Information:
This work has been partially supported by the EU (FEDER) and the Spanish MEC/MICINN under grant TIN 2007-68093-C02-02, Integrated Action HA 2006-0007, UPV PAID-06-07 project, and Generalitat Valenciana under grants GVPRE/2008/113 and BFPI/2007/076; also by NSF Grant CNS 07-16638.

PY - 2009

Y1 - 2009

N2 - This paper presents a modular equational generalization algorithm, where function symbols can have any combination of associativity, commutativity, and identity axioms (including the empty set). This is suitable for dealing with functions that obey algebraic laws, and are typically mechanized by means of equational atributes in rule-based languages such as ASF+SDF, Elan, OBJ, Cafe-OBJ, and Maude. The algorithm computes a complete set of least general generalizations modulo the given equational axioms, and is specified by a set of inference rules that we prove correct. This work provides a missing connection between least general generalization and computing modulo equational theories, and opens up new applications of generalization to rule-based languages, theorem provers and program manipulation tools such as partial evaluators, test case generators, and machine learning techniques, where function symbols obey algebraic axioms. A Web tool which implements the algorithm has been developed which is publicly available.

AB - This paper presents a modular equational generalization algorithm, where function symbols can have any combination of associativity, commutativity, and identity axioms (including the empty set). This is suitable for dealing with functions that obey algebraic laws, and are typically mechanized by means of equational atributes in rule-based languages such as ASF+SDF, Elan, OBJ, Cafe-OBJ, and Maude. The algorithm computes a complete set of least general generalizations modulo the given equational axioms, and is specified by a set of inference rules that we prove correct. This work provides a missing connection between least general generalization and computing modulo equational theories, and opens up new applications of generalization to rule-based languages, theorem provers and program manipulation tools such as partial evaluators, test case generators, and machine learning techniques, where function symbols obey algebraic axioms. A Web tool which implements the algorithm has been developed which is publicly available.

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U2 - 10.1007/978-3-642-00515-2_3

DO - 10.1007/978-3-642-00515-2_3

M3 - Conference article

AN - SCOPUS:63449094344

SN - 0302-9743

VL - 5438 LNCS

SP - 24

EP - 39

JO - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

JF - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

T2 - 18th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2008

Y2 - 17 July 2008 through 18 July 2008

ER -