Skip to main content

A Brief Overview of Mizar

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 5674)

Abstract

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.

Keywords

  • 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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-642-03359-9_5
  • Chapter length: 6 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-642-03359-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.00
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  4. Fitch, F.B.: Symbolic Logic. An Introduction. The Ronald Press Company (1952)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  6. Jaśkowski, S.: On the rules of supposition in formal logic. Studia Logica 1 (1934)

    Google Scholar 

  7. Matuszewski, R., Rudnicki, P.: Mizar: the first 30 years. Mechanized Mathematics and Its Applications 4(1), 3–24 (2005)

    Google Scholar 

  8. Mizar home page: http://mizar.org

  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. 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)

    CrossRef  Google Scholar 

  11. Ono, K.: On a practical way of describing formal deductions. Nagoya Mathematical Journal 21 (1962)

    Google Scholar 

  12. QED Manifesto: http://www.rbjones.com/rbjpub/logic/qedres00.htm

  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)

    CrossRef  Google Scholar 

  14. Trybulec, A.: Tarski Grothendieck set theory. Formalized Mathematics 1(1), 9–11 (1990)

    Google Scholar 

  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)

    CrossRef  Google Scholar 

  16. Wenzel, M., Wiedijk, F.: A comparison of Mizar and Isar. Journal of Automated Reasoning 29(3-4), 389–411 (2002)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Naumowicz, A., Korniłowicz, A. (2009). A Brief Overview of Mizar . In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03359-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03358-2

  • Online ISBN: 978-3-642-03359-9

  • eBook Packages: Computer ScienceComputer Science (R0)