C-CoRN, the Constructive Coq Repository at Nijmegen

  • Luís Cruz-Filipe
  • Herman Geuvers
  • Freek Wiedijk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3119)


We present C-CoRN, the Constructive Coq Repository at Nijmegen. It consists of a mathematical library of constructive algebra and analysis formalized in the theorem prover Coq. We explain the structure and the contents of the library and we discuss the motivation and some (possible) applications of such a library.

The development of C-CoRN is part of a larger goal to design a computer system where ‘a mathematician can do mathematics’, which covers the activities of defining, computing and proving. An important proviso for such a system to be useful and attractive is the availability of a large structured library of mathematical results that people can consult and build on. C-CoRN wants to provide such a library, but it can also be seen as a case study in developing such a library of formalized mathematics and deriving its requirements. As the actual development of a library is very much a technical activity, the work on C-CoRN is tightly bound to the proof assistant Coq.


Fundamental Theorem Proof Assistant Standard Library Constructive Mathematic Proof Term 
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.


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  1. 1.
    Asperti, A., Buchberger, B., Davenport, J.H. (eds.): MKM 2003. LNCS, vol. 2594. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  2. 2.
    Asperti, A., Wegner, B.: MOWGLI – A New Approach for the Content Description in Digital Documents. In: Proc. of the 9th Intl. Conference on Electronic Resources and the Social Role of Libraries in the Future, vol. 1, Autonomous Republic of Crimea, Ukraine (2002)Google Scholar
  3. 3.
    Bailey, A.: The machine-checked literate formalisation of algebra in type theory, PhD thesis. University of Manchester (1998)Google Scholar
  4. 4.
    Bishop, E.: Foundations of Constructive Analysis. McGraw-Hill, New York (1967)zbMATHGoogle Scholar
  5. 5.
    Buchberger, B., et al.: An Overview on the Theorema project. In: Kuechlin, W. (ed.) Proceedings of ISSAC 1997, Maui, Hawaii. ACM Press, New York (1997)Google Scholar
  6. 6.
    Constructive Coq Repository at Nijmegen,
  7. 7.
    Cairns, P., Gow, J.: A theoretical analysis of hierarchical proofs, In: Asperti, et al., [1], pp. 175–187Google Scholar
  8. 8.
    The CALCULEMUS Initiative,
  9. 9.
    Callaghan, P., Luo, Z., McKinna, J., Pollack, R. (eds.): TYPES 2000. LNCS, vol. 2277. Springer, Heidelberg (2002)Google Scholar
  10. 10.
    Caprotti, O., Carlisle, D.P., Cohen, A.M.: The OpenMath Standard, version 1.1 (2002),
  11. 11.
    Cohen, A., Cuypers, H., Sterk, H.: Algebra Interactive! Springer, Heidelberg (1999)zbMATHGoogle Scholar
  12. 12.
    Constable, R.L., et al.: Implementing Mathematics with the Nuprl Development System. Prentice-Hall, NJ (1986)Google Scholar
  13. 13.
    The Coq Development Team, The Coq Proof Assistant Reference Manual, Version 7.2 (January 2002),
  14. 14.
    Cruz-Filipe, L.: Formalizing real calculus in Coq, Technical report, NASA, Hampton, VA (2002)Google Scholar
  15. 15.
    Cruz-Filipe, L.: A constructive formalization of the Fundamental Theorem of Calculus. In: Geuvers, Wiedijk [20], pp. 108–126Google Scholar
  16. 16.
    Cruz-Filipe, L., Spitters, B.: Program extraction from large proof developments. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 205–220. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Filliâtre, J.-C.: CoqDoc: a Documentation Tool for Coq, Version 1.05, The Coq Development Team (September 2003),
  18. 18.
    Geuvers, H., Niqui, M.: Constructive reals in Coq: Axioms and categoricity. In: [9], pp. 79–95Google Scholar
  19. 19.
    Geuvers, H., Pollack, R., Wiedijk, F., Zwanenburg, J.: The algebraic hierarchy of the FTA Project. Journal of Symbolic Computation, pp. 271–286 (2002)Google Scholar
  20. 20.
    Geuvers, H., Wiedijk, F. (eds.): Types for Proofs and Programs. LNCS, vol. 2464. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  21. 21.
    Geuvers, H., Wiedijk, F., Zwanenburg, J.: Equational reasoning via partial reflection. In: Aagaard, M.D., Harrison, J. (eds.) TPHOLs 2000. LNCS, vol. 1869, pp. 162–178. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  22. 22.
    Geuvers, H., Wiedijk, F., Zwanenburg, J.: A constructive proof of the Fundamental Theorem of Algebra without using the rationals. In: [9], pp. 96–111Google Scholar
  23. 23.
    Guidi, F., Schena, I.: A query language for a metadata framework about mathematical resources. In: Asperti, et al., [1], pp. 105–118Google Scholar
  24. 24.
    Harrison, J.: The HOL Light manual (1.1) (2000),
  25. 25.
    Kohlhase, M.: OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of Mathematical Knowledge. In: Proceedings of Artificial Intelligence and Symbolic Computation. LNCS (LNAI). Springer, Heidelberg (2000)Google Scholar
  26. 26.
    Letouzey, P.: A new extraction for Coq. In: Geuvers, Wiedijk [20], pp. 200–219Google Scholar
  27. 27.
    Mayero, M.: Formalisation et automatisation de preuves en analyses réelle et numérique, PhD thesis, Université Paris VI (December 2001)Google Scholar
  28. 28.
    Muzalewski, M.: An Outline of PC Mizar, Fond. Philippe le Hodey, Brussels (1993),
  29. 29.
    Naumov, P., Stehr, M.-O., Meseguer, J.: The HOL/NuPRL Proof Translator: A Practical Approach to Formal Interoperability. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 329–345. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  30. 30.
    Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  31. 31.
    Shankar, N., Owre, S., Rushby, J.M., Stringer-Calvert, D.W.J.: The PVS System Guide, SRI International (December 2001),
  32. 32.
    Siekmann, J.: Proof Development with Omega. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, p. 144. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  33. 33.
    Slind, K.: HOL98 Draft User’s Manual, Cambridge UCL (January 1999),

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Luís Cruz-Filipe
    • 1
    • 2
  • Herman Geuvers
    • 1
  • Freek Wiedijk
    • 1
  1. 1.NIII, Radboud University NijmegenThe Netherlands
  2. 2.Center for Logic and ComputationLisbonPortugal

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