Communicating Formal Proofs: The Case of Flyspeck

  • Carst Tankink
  • Cezary Kaliszyk
  • Josef Urban
  • Herman Geuvers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7998)


We introduce a platform for presenting and cross-linking formal and informal proof developments together. The platform supports writing natural language ‘narratives’ that include islands of formal text. The formal text contains hyperlinks and gives on-demand state information at every proof step. We argue that such a system significantly lowers the threshold for understanding formal development and facilitates collaboration on informal and formal parts of large developments. As an example, we show the Flyspeck formal development (in HOL Light) and the Flyspeck informal mathematical text as a narrative linked to the formal development. To make this possible, we use the Agora system, a MathWiki platform developed at Nijmegen which has so far mainly been used with the Coq theorem prover: we show that the system itself is generic and easily adapted to the HOL Light case.


Formal Proof Formal Text Formal Development Source Text Proof Assistant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gonthier, G.: Engineering mathematics: the odd order theorem proof. In: Giacobazzi, R., Cousot, R. (eds.) POPL, pp. 1–2. ACM (2013)Google Scholar
  2. 2.
    Gonthier, G.: The four colour theorem: Engineering of a formal proof. In: Kapur, D. (ed.) ASCM 2007. LNCS (LNAI), vol. 5081, pp. 333–333. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Hales, T.C., Harrison, J., McLaughlin, S., Nipkow, T., Obua, S., Zumkeller, R.: A revision of the proof of the Kepler conjecture. Discrete & Computational Geometry 44(1), 1–34 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Tankink, C., Geuvers, H., McKinna, J., Wiedijk, F.: Proviola: A tool for proof re-animation. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. (eds.) AISC 2010. LNCS, vol. 6167, pp. 440–454. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Tankink, C.: Proof in context — Web editing with rich, modeless contextual feedback. To appear in Proceedings of UITP 2012 (2012)Google Scholar
  6. 6.
    Tankink, C., McKinna, J.: Dynamic proof pages. In: ITP Workshop on Mathematical Wikis (MathWikis). Number 767 in CEUR Workshop Proceedings (2011)Google Scholar
  7. 7.
    Tankink, C., Lange, C., Urban, J.: Point-and-write – documenting formal mathematics by reference. In: Jeuring, J., Campbell, J.A., Carette, J., Dos Reis, G., Sojka, P., Wenzel, M., Sorge, V. (eds.) CICM 2012. LNCS, vol. 7362, pp. 169–185. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  8. 8.
    Harrison, J.: HOL Light: An overview. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 60–66. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Hales, T.C.: Dense Sphere Packings - a blueprint for formal proofs. Cambridge University Press (2012)Google Scholar
  10. 10.
    Sauer, C., Smith, C., Benz, T.: Wikicreole: A common wiki markup. In: WikiSym 2007, pp. 131–142. ACM, New York (2007)Google Scholar
  11. 11.
    Wenzel, M., Paulson, L.: Isabelle/isar. In: Wiedijk, F. (ed.) The Seventeen Provers of the World. LNCS (LNAI), vol. 3600, pp. 41–49. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Alama, J., Brink, K., Mamane, L., Urban, J.: Large formal wikis: Issues and solutions. In: Davenport, J.H., Farmer, W.M., Urban, J., Rabe, F. (eds.) Calculemus/MKM 2011. LNCS, vol. 6824, pp. 133–148. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Corbineau, P., Kaliszyk, C.: Cooperative repositories for formal proofs. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS (LNAI), vol. 4573, pp. 221–234. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  14. 14.
    Kaliszyk, C., Urban, J.: Learning-assisted automated reasoning with Flyspeck. CoRR abs/1211.7012 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Carst Tankink
    • 1
  • Cezary Kaliszyk
    • 2
  • Josef Urban
    • 1
  • Herman Geuvers
    • 1
    • 3
  1. 1.ICISRadboud Universiteit NijmegenNetherlands
  2. 2.Institut für InformatikUniversität InnsbruckAustria
  3. 3.Technical University EindhovenNetherlands

Personalised recommendations