A Brief Overview of Mizar

  • Adam Naumowicz
  • Artur Korniłowicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5674)


Mizar is the name of a formal language derived from informal mathematics and computer software that enables proof-checking of texts written in that language. The system has been actively developed since 1970s, growing into a popular proof assistant accompanied with a huge repository of formalized mathematical knowledge. In this short overview, we give an outline of the key features of the Mizar language, the ideas and theory behind the system, its main applications, and current development.


Proof Assistant Inaccessible Cardinal Jordan Curve Theorem Mizar Mathematical Library Syntactic Construct 
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.
    Bancerek, G., Rudnicki, P.: Information retrieval in MML. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds.) MKM 2003. LNCS, vol. 2594, pp. 119–132. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  2. 2.
    Borak, E., Zalewska, A.: Mizar course in logic and set theory. In: Kauers, M., Kerber, M., Miner, R., Windsteiger, W. (eds.) MKM/CALCULEMUS 2007. LNCS, vol. 4573, pp. 191–204. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Fitch, F.B.: Symbolic Logic. An Introduction. The Ronald Press Company (1952)Google Scholar
  5. 5.
    Harrison, J.: A Mizar Mode for HOL. In: von Wright, J., Harrison, J., Grundy, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 203–220. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  6. 6.
    Jaśkowski, S.: On the rules of supposition in formal logic. Studia Logica 1 (1934)Google Scholar
  7. 7.
    Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mechanized Mathematics and Its Applications 4(1), 3–24 (2005)Google Scholar
  8. 8.
    Mizar home page:
  9. 9.
    Naumowicz, A.: Teaching How to Write a Proof. In: Formed 2008: Formal Methods in Computer Science Education, pp. 91–100 (2008)Google Scholar
  10. 10.
    Naumowicz, A., Byliński, C.: Improving Mizar texts with properties and requirements. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 290–301. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Ono, K.: On a practical way of describing formal deductions. Nagoya Mathematical Journal 21 (1962)Google Scholar
  12. 12.
  13. 13.
    Syme, D.: Three tactic theorem proving. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 203–220. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  14. 14.
    Trybulec, A.: Tarski Grothendieck set theory. Formalized Mathematics 1(1), 9–11 (1990)Google Scholar
  15. 15.
    Urban, J.: XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy. In: Kohlhase, M. (ed.) MKM 2005. LNCS, vol. 3863, pp. 346–360. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Wenzel, M., Wiedijk, F.: A comparison of Mizar and Isar. Journal of Automated Reasoning 29(3-4), 389–411 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Wiedijk, F.: Formal Proof Sketches. In: Berardi, S., Coppo, M., Damiani, F. (eds.) TYPES 2003. LNCS, vol. 3085, pp. 378–393. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Wiedijk, F.: Mizar Light for HOL Light. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 378–393. Springer, Heidelberg (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Adam Naumowicz
    • 1
  • Artur Korniłowicz
    • 1
  1. 1.Institute of InformaticsUniversity of BiałystokPoland

Personalised recommendations