A Path to Faithful Formalizations of Mathematics

  • Gueorgui Jojgov
  • Rob Nederpelt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3119)


In this paper we are interested in the process of formalizing a mathematical text written in Common Mathematical Language (CML) into type theory using intermediate representations in Weak Type Theory [8] and in type theory with open terms. We demonstrate that this method can be reliable not only in the sense that eventually we get formally verified mathematical texts, but also in the sense that we can have a fairly high confidence that we have produced a ‘faithful’ formalization (i.e. that the formal text is as close as possible to the intentions expressed in the informal text).

A computer program that assists a human along the formalization path should create enough “added value” to be useful in practice. We also discuss some problems that such an implementation needs to solve and possible solutions for them.


Type Theory Proof Obligation Open Term Proof Assistant Strong Typing 
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.
    Barendregt, H.: Lambda calculi with types. In: Abramsky, et al. (eds.) Handbook of Logic in Computer Science, pp. 117–309. Oxford University Press, Oxford (1992)Google Scholar
  2. 2.
    Barendregt, H., Geuvers, H.: Proof assistants using dependent type systems. In: Handbook of Automated Reasoning. Elsevier Science Publishers B.V., Amsterdam (1999)Google Scholar
  3. 3.
    van Benthem Jutting, L.S.: Checking Landau’s “Grundlagen” in the Automath System. In: Nederpelt, R.P., Geuvers, J.H., de Vrijer, R.C. (eds.) Selected Papers on Automath. Studies in Logic and Foundations of Mathematics, vol. 133, pp. 701–732. North-Holland, Amsterdam (1994)CrossRefGoogle Scholar
  4. 4.
    de Bruijn, N.G.: The mathematical language Automath, its usage and some of its extensions. In: Nederpelt, R.P., Geuvers, J.H., de Vrijer, R.C. (eds.) Selected Papers on Automath. Studies in Logic and Foundations of Mathematics, vol. 133. North-Holland, Amsterdam (1994)Google Scholar
  5. 5.
    The Coq Development Team, The Coq Proof Assistant Reference Manual - Version V7.4 (February 2003),
  6. 6.
    Jojgov, G.I.: Incomplete Proofs and Terms and Their Use in Interactive Theorem Proving, PhD thesis. Eindhoven University of Technology (2004)Google Scholar
  7. 7.
    Jojgov, G.I., Nederpelt, R.P., Scheffer, M.: Faithfully reflecting the structure of informal mathematical proofs into formal type theories. In: Proceedings of the MKM Symposium 2003. Elsevier, Amsterdam (2003)Google Scholar
  8. 8.
    Kamareddine, F., Nederpelt, R.: A refinement of de Bruijn’s formal language of mathematics. Journal of Logic, Language and Information (to appear)Google Scholar
  9. 9.
    Nederpelt, R.: Weak Type Theory: A formal language for mathematics, Technical report. Eindhoven University of Technology (May 2002)Google Scholar
  10. 10.
    Pollack, R.: The LEGO Proof Assistant,
  11. 11.
    Rudnicki, P.: An overview of the Mizar project. In: Proceedings of the 1992 Workshop on Types for Proofs and Programs (1992),

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Gueorgui Jojgov
    • 1
  • Rob Nederpelt
    • 1
  1. 1.Eindhoven University of TechnologyThe Netherlands

Personalised recommendations