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A Modular Equational Generalization Algorithm

  • Conference paper
Logic-Based Program Synthesis and Transformation (LOPSTR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5438))

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.

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.

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Author information

Authors and Affiliations

  1. Universidad Politécnica de Valencia, Spain

    María Alpuente, Santiago Escobar & Pedro Ojeda

  2. University of Illinois at Urbana–Champaign, USA

    José Meseguer

Authors
  1. María Alpuente
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  2. Santiago Escobar
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  3. José Meseguer
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  4. Pedro Ojeda
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Christian-Albrechts-Universität Kiel, 24098, Kiel, Germany

    Michael Hanus

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Alpuente, M., Escobar, S., Meseguer, J., Ojeda, P. (2009). A Modular Equational Generalization Algorithm . In: Hanus, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2008. Lecture Notes in Computer Science, vol 5438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00515-2_3

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  • DOI: https://doi.org/10.1007/978-3-642-00515-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00514-5

  • Online ISBN: 978-3-642-00515-2

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