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Lemma Discovery for Induction

A Survey

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Book cover Intelligent Computer Mathematics (CICM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11617))

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Abstract

Automating proofs by induction can be challenging, not least because proofs might need auxiliary lemmas, which themselves need to be proved by induction. In this paper we survey various techniques for automating the discovery of such lemmas, including both top-down techniques attempting to generate a lemma from an ongoing proof attempt, as well as bottom-up theory exploration techniques trying to construct interesting lemmas about available functions and datatypes, thus constructing a richer background theory.

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Notes

  1. 1.

    A small program executing one or several proof steps automatically.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Chalmers University of Technology, Gothenburg, Sweden

    Moa Johansson

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  1. Moa Johansson
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Correspondence to Moa Johansson .

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Editors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. University of St. Andrews, St. Andrews, UK

    Edwin Brady

  3. University of Applied Sciences, Neu-Ulm, Germany

    Andrea Kohlhase

  4. University of Bologna, Bologna, Italy

    Claudio Sacerdoti Coen

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Johansson, M. (2019). Lemma Discovery for Induction. In: Kaliszyk, C., Brady, E., Kohlhase, A., Sacerdoti Coen, C. (eds) Intelligent Computer Mathematics. CICM 2019. Lecture Notes in Computer Science(), vol 11617. Springer, Cham. https://doi.org/10.1007/978-3-030-23250-4_9

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  • DOI: https://doi.org/10.1007/978-3-030-23250-4_9

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