### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 24-39 |

Number of pages | 16 |

Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Volume | 5438 LNCS |

DOIs | |

State | Published - Apr 6 2009 |

Event | 18th International Symposium on Logic-Based Program Synthesis and Transformation, LOPSTR 2008 - Valencia, Spain Duration: Jul 17 2008 → Jul 18 2008 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*,

*5438 LNCS*, 24-39. https://doi.org/10.1007/978-3-642-00515-2_3

**A modular equational generalization algorithm.** / Alpuente, María; Escobar, Santiago; Meseguer, José; Ojeda, Pedro.

Research output: Contribution to journal › Conference article

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*, vol. 5438 LNCS, pp. 24-39. https://doi.org/10.1007/978-3-642-00515-2_3

}

TY - JOUR

T1 - A modular equational generalization algorithm

AU - Alpuente, María

AU - Escobar, Santiago

AU - Meseguer, José

AU - Ojeda, Pedro

PY - 2009/4/6

Y1 - 2009/4/6

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.

UR - http://www.scopus.com/inward/record.url?scp=63449094344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63449094344&partnerID=8YFLogxK

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

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

M3 - Conference article

AN - SCOPUS:63449094344

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)

SN - 0302-9743

ER -