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Formalisation vs. Understanding

A Case Study in Isabelle

  • Conference paper
  • First Online:
Unconventional Computation and Natural Computation (UCNC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9252))

Abstract

We discuss how formalisation using proof assistants, an unconventional way of doing mathematics which seems to disregard Gödel’s celebrated Incompleteness Theorems, interacts with ideas of understanding. Our experience is based on a formalisation carried out in the Isabelle generic proof assistant.

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Notes

  1. 1.

    Our thanks to a reviewer for highlighting this unconventional view of proofs.

  2. 2.

    http://www.jedit.org/.

References

  1. Isabelle hompage. http://isabelle.in.tum.de/

  2. Ballarin, C., Belgrade 2008 - Tutorial: Introduction to the proof assistant. http://www21.in.tum.de/ ballarin/belgrade08-tut/

  3. Calude, C.S., Desfontaines, D.: Universality and almost decidability. Fundamenta Informaticae 21, 1001–1006 (2014)

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  5. Gordon, M.: From LCF to HOL: a short history. In: Plotkin, G., Stirling, C.P., Tofte, M. (eds.) Proof, Language, and Interaction, pp. 169–186. MIT Press, Cambridge (2000)

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  6. Nipkow, T.: Programming and proving in Isabelle/HOL (2013)

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  7. OED Online. proof, n. http://www.oed.com/view/Entry/152578?rskey=bJkM38, October 2014

  8. Xu, J., Zhang, X., Urban, C.: Mechanising turing machines and computability theory in Isabelle/HOL. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 147–162. Springer, Heidelberg (2013)

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Acknowledgements

Special thanks is given to Cris Calude for his generous advice, guidance and help. Thanks is also given to Robert Drummond, Mostafa Raziebrahimsaraei and Marcus Triplett for useful discussions on issues encountered during formalisation, and to the anonymous reviewers for helpful comments.

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Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Auckland, New Zealand

    Declan Thompson

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  1. Declan Thompson
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Correspondence to Declan Thompson .

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Editors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Cristian S. Calude

  2. University of Auckland, Auckland, New Zealand

    Michael J. Dinneen

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Thompson, D. (2015). Formalisation vs. Understanding. In: Calude, C., Dinneen, M. (eds) Unconventional Computation and Natural Computation. UCNC 2015. Lecture Notes in Computer Science(), vol 9252. Springer, Cham. https://doi.org/10.1007/978-3-319-21819-9_22

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  • DOI: https://doi.org/10.1007/978-3-319-21819-9_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21818-2

  • Online ISBN: 978-3-319-21819-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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