Comparing Mathematical Provers

  • Freek Wiedijk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2594)


We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Agerholm, I. Beylin, and P. Dybjer. A Comparison of HOL and ALF Formalizations of a Categorical Coherence Theorem. In TPHOLs’96, volume 1125 of LNCS, pages 17–32. Springer-Verlag, 1996.Google Scholar
  2. 2.
    S. Agerholm and M.J.C. Gordon. Experiments with ZF Set Theory in HOL and Isabelle. In 8th International Workshop on Higher Order Logic Theorem Proving and its Applications, volume 971, pages 32–45. Springer-Verlag, 1995.Google Scholar
  3. 3.
    Henk Barendregt. The impact of the lambda calculus. Bulletin of Symbolic Logic, 3(2), 1997.Google Scholar
  4. 4.
    Henk Barendregt and Herman Geuvers. Proof-Assistants Using Dependent Type Systems. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers B.V., 2001.Google Scholar
  5. 5.
    D. Basin and M. Kaufmann. The Boyer-Moore Prover and NuPRL: An experimental comparison. In Proceedings of the First Workshop on ‘Logical Frameworks’, Antibes, France, pages 89–119. Cambridge University Press, 1991.Google Scholar
  6. 6.
    R. Boyer et al. The QED Manifesto. In A. Bundy, editor, Automated Deduction-CADE 12, volume 814 of LNAI, pages 238–251. Springer-Verlag, 1994. <>.
  7. 7.
    B. Buchberger, T. Jebelean, F. Kriftner, M. Marin, and D. Vasaru. An Overview on the Theorema project. In W. Kuechlin, editor, Proceedings of ISSAC’97 (International Symposium on Symbolic and Algebraic Computation), Maui, Hawaii, 1997. ACM Press.Google Scholar
  8. 8.
    Robert L. Constable, Stuart F. Allen, H.M. Bromley, W.R. Cleaveland, J.F. Cremer, R.W. Harper, Douglas J. Howe, T.B. Knoblock, N.P. Mendler, P. Panangaden, James T. Sasaki, and Scott F. Smith. Implementing Mathematics with the Nuprl Development System. Prentice-Hall, NJ, 1986.Google Scholar
  9. 9.
    Ingo Dahn and Christoph Wernhard. First Order Proof Problems Extracted from an Article in the MIZAR Mathematical Library. In Proceedings of the International Workshop on First order Theorem Proving, number 97–50 in RISC-Linz Report Series, pages 58–62, Linz, 1997. Johannes Kepler Universität.Google Scholar
  10. 10.
    G.P. Goold, editor. Selections illustrating the history of Greek mathematics, with an English translation by Ivor Thomas. Harvard University Press, London, 1939.Google Scholar
  11. 11.
    David Griffioen and Marieke Huisman. A comparison of PVS and Isabelle/HOL. In Jim Grundy and Malcolm Newey, editors, Theorem Proving in Higher Order Logics: 11th International Conference, TPHOLs’98, volume 1479 of LNCS, pages 123–142. Springer-Verlag, 1998.CrossRefGoogle Scholar
  12. 12.
    L. Jakubiec, S. Coupet-Grimal, and P. Curzon. A Comparison of the Coq and HOL Proof Systems for Specifying Hardware. In E. Gunter and A. Felty, editors, International Conference on Theorem Proving in Higher Order Logics: B-Track, pages 63–78, 1997.Google Scholar
  13. 13.
    Matt Kaufmann, Panagiotis Manolios, and J. Strother Moore. Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, Boston, 2000.CrossRefGoogle Scholar
  14. 14.
    Norman D. Megill. Metamath, A Computer Language for Pure Mathematics. <>, 1997.
  15. 15.
    M. Muzalewski. An Outline of PC Mizar. Fondation Philippe le Hodey, Brussels, 1993. <>.
  16. 16.
    P. Naumov, M.-O. Stehr, and J. Meseguer. The HOL/NuPRL Proof Translator: A Practical Approach to Formal Interoperability. In R.J. Boulton and P.B. Jackson, editors, The 14th International Conference on Theorem Proving in Higher Order Logics, volume 2152 of LNCS, pages 329–345. Springer-Verlag, 2001.zbMATHGoogle Scholar
  17. 17.
    R.P. Nederpelt, J.H. Geuvers, and R.C. de Vrijer. Selected Papers on Automath, volume 133 of Studies in Logic and the Foundations of Mathematics. Elsevier Science, Amsterdam, 1994.CrossRefGoogle Scholar
  18. 18.
    S. Owre, J. Rushby, and N. Shankar. PVS: A prototype verification system. In D. Kapur, editor, 11th International Conference on Automated Deduction (CADE), volume 607 of LNAI, pages 748–752, Berlin, Heidelberg, New York, 1992. Springer-Verlag.Google Scholar
  19. 19.
    Henri Poincaré. La Science et l’Hypothèse. Flammarion, Paris, 1902.Google Scholar
  20. 20.
    A. Quaife. Automated Development of Fundamental Mathematical Theories. Kluwer Academic, 1992.Google Scholar
  21. 21.
    N. Shankar. Metamathematics, Machines and Gödel’s Proof. Number 38 in Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1994.Google Scholar
  22. 22.
    Otto Töplitz. The Calculus: A Genetic Approach. University of Chicago Press, Chicago, 1963. Translated by Luise Lange.Google Scholar
  23. 23.
    F. Wiedijk. Mizar: An Impression. < >, 1999.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Freek Wiedijk
    • 1
  1. 1.University of NijmegenNijmegenThe Netherlands

Personalised recommendations