Integrated Semantic Browsing of the Mizar Mathematical Library for Authoring Mizar Articles

  • Grzegorz Bancerek
  • Josef Urban
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3119)


The Mizar system is equipped with a very large library containing tens of thousands of theorems and thousands of definitions, which often use overloaded notation. For efficient authoring of new Mizar articles it is necessary to have good tools for searching and browsing this library. It would be ideal if such tools were simple, intuitive and easy to access. Particularly, they should provide interactive and integrated support during authoring Mizar articles.

We describe an approach to this task which uses the extendable MML Query tools to generate a special representation of the Mizar library (MML). This representation, so called Generated Mizar Abstracts, contains human readable form of the MML, completed by additional information which is missing or hidden in regular Mizar abstracts and texts. It also includes semantic information necessary for implementing advanced browsing in the Mizar authoring environment for Emacs (Mizar mode). Together with other functions of the Mizar mode, this allows the authors of Mizar articles to disambiguate the meaning of overloaded Mizar notations, and thus helps to start browsing at an appropriate place.


Naming Scheme Proof Assistant Semantic Layer Human Presentation Interactive Query 
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.
    Bancerek, G.: Cardinal numbers. Formalized Mathematics 2(1), 377–382 (1990), Google Scholar
  2. 2.
    Bancerek, G.: MML Query, description,
  3. 3.
    Bancerek, G., Rudnicki, P.: Information retrieval in MML. In: Asperti, A., Buchberger, B., Davenport, J. (eds.) MKM 2003. LNCS, vol. 2594, pp. 119–132. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Borenstein, N.: The text/enriched MIME Content-type (09/23/1993),
  5. 5.
    Borenstein, N.: The text/enriched MIME Content-type (01/10/ 1994),
  6. 6.
  7. 7.
    Journal of Formalized Mathematics,
  8. 8.
    The Mizar Home Page,
  9. 9.
    Resnick, P., Walker, A.: The text/enriched MIME Content-type (January 1996),
  10. 10.
    Rudnicki, P.: An overview of the Mizar project. In: Proceedings of the 1992, Workshop on Types for Proofs and Programs. Chalmers University of Technology, Bastad (1992)Google Scholar
  11. 11.
    Rudnicki, P., Trybulec, A.: On Equivalents of Well-foundedness. An experiment in MIZAR. Journal of Automated Reasoning 23, 197–234 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Urban, J.: MizarMode: Emacs Authoring Environment for Mizar, available online at:
  13. 13.
    Urban, J.: MoMM – Fast interreduction and retrieval in large libraries of formalized mathematics. In: Sutcliffe, G., Schultz, S., Tammit, T. (eds.) Proceedings of the IJCAR 2004 Workshop on Empirically Successful First Order Reasoning, ENTCS (accepted, 2004), Available online at:
  14. 14.
    Urban, J.: MPTP – Motivation, implementation, first experiments. In: Dahn, I., Kapur, D., Vigneron, L. (eds.) Journal of Automated Reasoning, First-Order Theorem Proving Special Issue. Kluwer Academic Publishers, Dordrecht (supposed publication: end of 2004) (accepted), Available online at:

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Grzegorz Bancerek
    • 1
  • Josef Urban
    • 2
  1. 1.Faculty of Computer ScienceBialystok Technical UniversityBialystokPoland
  2. 2.Dept. of Theoretical Computer ScienceCharles UniversityPrahaCzech Republic

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