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Automated Theory Exploration for Interactive Theorem Proving:

An Introduction to the Hipster System

  • Conference paper
Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

Theory exploration is a technique for automatically discovering new interesting lemmas in a mathematical theory development using testing. In this paper I will present the theory exploration system Hipster, which automatically discovers and proves lemmas about a given set of datatypes and functions in Isabelle/HOL. The development of Hipster was originally motivated by attempts to provide a higher level of automation for proofs by induction. Automating inductive proofs is tricky, not least because they often need auxiliary lemmas which themselves need to be proved by induction. We found that many such basic lemmas can be discovered automatically by theory exploration, and importantly, quickly enough for use in conjunction with an interactive theorem prover without boring the user.

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Notes

  1. 1.

    This example can be found online: https://github.com/moajohansson/IsaHipster/blob/master/Examples/ITP2017/Tree.thy.

  2. 2.

    The source code is at: https://github.com/moajohansson/IsaHipster/blob/master/Examples/ITP2017/Qrev.thy.

  3. 3.

    The proof command metis (followed by a list of required library facts) in the proof of lemma_aa is produced by Sledgehammer. Metis is Isabelle’s built in first order prover used to reconstruct proofs from external provers.

  4. 4.

    The interested reader may consult the file Tactic_Data.ML in the Hipster source code repository for details of several pre-defined combinations of easy/hard reasoning tactics, as well as how to define additional ones.

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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 Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Johansson, M. (2017). Automated Theory Exploration for Interactive Theorem Proving:. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_1

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66106-3

  • Online ISBN: 978-3-319-66107-0

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