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International Conference on Mathematical Knowledge Management

MKM 2006: Mathematical Knowledge Management pp 17–30Cite as

Structured Induction Proofs in Isabelle/Isar

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4108))

Abstract

Isabelle/Isar is a generic framework for human-readable formal proof documents, based on higher-order natural deduction. The Isar proof language provides general principles that may be instantiated to particular object-logics and applications. We discuss specific Isar language elements that support complex induction patterns of practical importance. Despite the additional bookkeeping required for induction with local facts and parameters, definitions, simultaneous goals and multiple rules, the resulting Isar proof texts turn out well-structured and readable. Our techniques can be applied to non-standard variants of induction as well, such as co-induction and nominal induction. This demonstrates that Isar provides a viable platform for building domain-specific tools that support fully-formal mathematical proof composition.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Makarius Wenzel

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  1. Makarius Wenzel
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science, Dalhousie University, 6050 University Avenue, Halifax, B3H 1W5, Nova Scotia, Canada

    Jonathan M. Borwein

  2. Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

    William M. Farmer

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© 2006 Springer-Verlag Berlin Heidelberg

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Wenzel, M. (2006). Structured Induction Proofs in Isabelle/Isar. In: Borwein, J.M., Farmer, W.M. (eds) Mathematical Knowledge Management. MKM 2006. Lecture Notes in Computer Science(), vol 4108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11812289_3

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  • DOI: https://doi.org/10.1007/11812289_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37104-5

  • Online ISBN: 978-3-540-37106-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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