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Automated Reasoning in Higher-Order Regular Algebra

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Relational and Algebraic Methods in Computer Science (RAMICS 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7560))

Abstract

We extend a large Isabelle/HOL repository for regular algebras towards higher-order variants based on directed sets and quantales, including reasoning based on general fixpoint properties and Galois connections. In this context we demonstrate that Isabelle’s recent integration of automated theorem proving technology effectively supports higher-order reasoning. We present four case studies that underpin this claim: the calculus of Galois connections and fixpoints, action algebras and Galois connections, solvability conditions for regular equations and fixpoint fusion, and the implementation of formal language quantales.

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Author information

Authors and Affiliations

  1. Department of Computer Science, The University of Sheffield, UK

    Alasdair Armstrong & Georg Struth

Authors
  1. Alasdair Armstrong
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  2. Georg Struth
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Editor information

Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  2. Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, CB3 0FD, Cambridge, UK

    Timothy G. Griffin

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Armstrong, A., Struth, G. (2012). Automated Reasoning in Higher-Order Regular Algebra. In: Kahl, W., Griffin, T.G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2012. Lecture Notes in Computer Science, vol 7560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33314-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-33314-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33313-2

  • Online ISBN: 978-3-642-33314-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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