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Structured Formal Development with Quotient Types in Isabelle/HOL

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Intelligent Computer Mathematics (CICM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6167))

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Abstract

General purpose theorem provers provide sophisticated proof methods, but lack some of the advanced structuring mechanisms found in specification languages. This paper builds on previous work extending the theorem prover Isabelle with such mechanisms. A way to build the quotient type over a given base type and an equivalence relation on it, and a generalised notion of folding over quotiented types is given as a formalised high-level step called a design tactic. The core of this paper are four axiomatic theories capturing the design tactic. The applicability is demonstrated by derivations of implementations for finite multisets and finite sets from lists in Isabelle.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Universität Bremen,  

    Maksym Bortin

  2. Deutsches Forschungszentrum für Künstliche Intelligenz, Bremen,  

    Christoph Lüth

Authors
  1. Maksym Bortin
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  2. Christoph Lüth
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Editor information

Editors and Affiliations

  1. German Research Center for Artificial Intelligence Bremen, Germany

    Serge Autexier

  2. Karlsruhe Institute of Technology, Germany

    Jacques Calmet

  3. CEDRIC/CNAM, Paris, France

    David Delahaye

  4. American Mathematical Society, Ann Arbor, USA

    Patrick D. F. Ion

  5. INRIA Sophia-Antipolis, France

    Laurence Rideau

  6. École Nationale Supérieure d’Informatique pour l’industrie et l’Entreprise, Evry, France

    Renaud Rioboo

  7. School of Computer Science, Edgbaston, University of Birmingham, B15 2TT, Birmingham, UK

    Alan P. Sexton

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Bortin, M., Lüth, C. (2010). Structured Formal Development with Quotient Types in Isabelle/HOL. In: Autexier, S., et al. Intelligent Computer Mathematics. CICM 2010. Lecture Notes in Computer Science(), vol 6167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14128-7_5

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  • DOI: https://doi.org/10.1007/978-3-642-14128-7_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14127-0

  • Online ISBN: 978-3-642-14128-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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