Traf: A Graphical Proof Tree Viewer Cooperating with Coq Through Proof General

  • Hideyuki KawabataEmail author
  • Yuta Tanaka
  • Mai Kimura
  • Tetsuo Hironaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11275)


Traf is a graphical proof tree viewer that cooperates with the Coq proof assistant and is controlled through Proof General. Among other proof tree viewers and tools for browsing proof scripts, Traf is well suited for daily proving of Coq problems as it is easy to use, non-disturbing, and helpful. Proof trees dynamically updated by Traf during interactive sessions with Proof General are informative and as readable as Gentzen-style natural deduction proofs. Traf facilitates browsing and investigating tactic-based proof scripts, which are often burdensome to read. Traf can also be used for typesetting proof trees with Open image in new window . The current version of Traf was developed as an extension to the Prooftree proof tree viewer and makes use of many of its facilities. Traf provides functionalities that are useful to both novice Coq users and experienced Proof General users.


Proof tree viewer Interactive theorem prover Coq Proof General Readability of proof scripts 


  1. 1.
    The compcert project.
  2. 2.
  3. 3.
    Pcoq: a graphical user-interface for coq.
  4. 4.
    The sel4 microkernel.
  5. 5.
    Asperti, A., Coen, C.S., Tassi, E., Zacchiroli, S.: User interaction with the matita proof assistant. J. Autom. Reason. 39(2), 109–139 (2007)CrossRefGoogle Scholar
  6. 6.
    Bedford, A.: Coqatoo: generating natural language versions of coq proofs. In: 4th International Workshop on Coq for Programming Languages (2018)Google Scholar
  7. 7.
    Byrnes, J., Buchanan, M., Ernst, M., Miller, P., Roberts, C., Keller, R.: Visualizing proof search for theorem prover development. Electron. Notes Theor. Comput. Sci. 226, 23–38 (2009)CrossRefGoogle Scholar
  8. 8.
    Corbineau, P.: A declarative language for the coq proof assistant. In: Miculan, M., Scagnetto, I., Honsell, F. (eds.) TYPES 2007. LNCS, vol. 4941, pp. 69–84. Springer, Heidelberg (2008). Scholar
  9. 9.
    Coscoy, Y., Kahn, G., Théry, L.: Extracting text from proofs. In: Dezani-Ciancaglini, M., Plotkin, G. (eds.) TLCA 1995. LNCS, vol. 902, pp. 109–123. Springer, Heidelberg (1995). Scholar
  10. 10.
    Curzon, P.: Tracking design changes with formal machine-checked proof. Comput. J. 38(2), 91–100 (1995). Scholar
  11. 11.
    Dunchev, C., et al.: Prooftool: a GUI for the GAPT framework. In: Proceedings 10th International Workshop On User Interfaces for Theorem Provers (2013)CrossRefGoogle Scholar
  12. 12.
    Fiedler, A.: P.rex: an interactive proof explainer. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS, vol. 2083, pp. 416–420. Springer, Heidelberg (2001). Scholar
  13. 13.
    Giero, M., Wiedijk, F.: MMode, a Mizar Mode for the proof assistant coq. Technical report, Nijmegen Institute for Computing and Information Sciences (2003)Google Scholar
  14. 14.
    Gonthier, G.: A computer-checked proof of the four colour theorem (2006).
  15. 15.
    Gonthier, G., et al.: A machine-checked proof of the odd order theorem. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 163–179. Springer, Heidelberg (2013). Scholar
  16. 16.
    Gonthier, G., Mahboubi, A.: An introduction to small scale reflection in coq. J. Form. Reason. 3(2), 95–152 (2010)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Harrison, J.: A mizar mode for HOL. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 203–220. Springer, Heidelberg (1996). Scholar
  18. 18.
    Hendriks, M., Kaliszyk, C., van Raamsdonk, F., Wiedijk, F.: Teaching logic using a state-of-the-art proof assistant. Acta Didact. Napoc. 3, 35–48 (2010)Google Scholar
  19. 19.
    Libal, T., Riener, M., Rukhaia, M.: Advanced proof viewing in ProofTool. In: Eleventh Workshop on User Interfaces for Theorem Provers (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Sakurai, K., Asai, K.: MikiBeta : a general GUI library for visualizing proof trees. In: Alpuente, M. (ed.) LOPSTR 2010. LNCS, vol. 6564, pp. 84–98. Springer, Heidelberg (2011). Scholar
  21. 21.
    Tankink, C., Geuvers, H., McKinna, J., Wiedijk, F.: Proviola: a tool for proof re-animation. In: Autexier, S., et al. (eds.) CICM 2010. LNCS (LNAI), vol. 6167, pp. 440–454. Springer, Heidelberg (2010). Scholar
  22. 22.
    Tesson, J., Hashimoto, H., Hu, Z., Loulergue, F., Takeichi, M.: Program calculation in coq. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 163–179. Springer, Heidelberg (2011). Scholar
  23. 23.
  24. 24.
    Trac, S., Puzis, Y., Sutcliffe, G.: An interactive derivation viewer. Electron. Notes Theor. Comput. Sci. 174(2), 109–123 (2007)CrossRefGoogle Scholar
  25. 25.
    Wenzel, M., Wiedijk, F.: A comparison of Mizar and Isar. J. Autom. Reason. 29, 389–411 (2002)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wiedijk, F. (ed.): The Seventeen Provers of the World. LNCS (LNAI), vol. 3600. Springer, Heidelberg (2006). Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Hideyuki Kawabata
    • 1
    Email author
  • Yuta Tanaka
    • 1
  • Mai Kimura
    • 1
  • Tetsuo Hironaka
    • 1
  1. 1.Hiroshima City UniversityHiroshimaJapan

Personalised recommendations