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Beginners’ Quest to Formalize Mathematics: A Feasibility Study in Isabelle

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Intelligent Computer Mathematics (CICM 2019)

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

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Abstract

How difficult are interactive theorem provers to use? We respond by reviewing the formalization of Hilbert’s tenth problem in Isabelle/HOL carried out by an undergraduate research group at Jacobs University Bremen. We argue that, as demonstrated by our example, proof assistants are feasible for beginners to formalize mathematics. With the aim to make the field more accessible, we also survey hurdles that arise when learning an interactive theorem prover. Broadly, we advocate for an increased adoption of interactive theorem provers in mathematical research and curricula.

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Notes

  1. 1.

    In rest of the paper we write “Isabelle” to also mean “Isabelle/HOL”.

  2. 2.

    The actual source code has been made available at https://gitlab.com/hilbert-10/dprm under the GPLv3 license.

  3. 3.

    In rest of the text the authors use “we” to interchangeably refer to themselves as authors and as representatives of the workgroup.

  4. 4.

    This identification is, by no means, original. Many large open-source software projects are aware of this structure and routinely advocate for documentation that conforms to it. See for instance the Django documentation [8] and the Write the Docs project [2].

References

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Acknowledgements

We want to thank the entire workgroup [19], without whose involvement we wouldn’t be writing this paper; as well as Yuri Matiyasevich for initiating and guiding the project. Moreover, we would like to express our sincere gratitude to the entire welcoming and supportive Isabelle community. In particular we are indebted to Mathias Fleury for all his help with Isabelle. Thank you also to Christoph Benzmüller for mentoring us as well as Florian Rabe for suggesting this contribution and helping us prepare the final version. Furthermore, we thank everyone who replied to our small survey, sharing their experience and opinion on this topic with us. Finally, a big thank you to our supervisor Dierk Schleicher, for motivating us throughout the project, connecting us to many experts in the field, and all his comments on this article.

Author information

Authors and Affiliations

  1. Jacobs University Bremen, Campus Ring 1, 28759, Bremen, Germany

    Marco David, Abhik Pal & Benedikt Stock

  2. Institut für Mathematik, Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Jonas Bayer

Authors
  1. Jonas Bayer
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  2. Marco David
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  3. Abhik Pal
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  4. Benedikt Stock
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Corresponding author

Correspondence to Marco David .

Editor information

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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Bayer, J., David, M., Pal, A., Stock, B. (2019). Beginners’ Quest to Formalize Mathematics: A Feasibility Study in Isabelle. 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_2

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  • DOI: https://doi.org/10.1007/978-3-030-23250-4_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23249-8

  • Online ISBN: 978-3-030-23250-4

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