Formalizing O Notation in Isabelle/HOL

  • Jeremy Avigad
  • Kevin Donnelly
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3097)


We describe a formalization of asymptotic O notation using the Isabelle/HOL proof assistant.


Theorem Prove Automate Reasoner Proof Assistant Equality Symbol Subset Relation 
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.
    Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete mathematics: a foundation for computer science, 2nd edn. Addison-Wesley Publishing Company, Reading (1994)zbMATHGoogle Scholar
  2. 2.
    Kammüller, F., Wenzel, M., Paulson, L.C.: Locales – a sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, p. 149. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  3. 3.
    Krueger, R., Rudnicki, P., Shelley, P.: Asymptotic notation. Part I: theory. Journal of Formalized Mathematics 11 (1999),
  4. 4.
    Krueger, R., Rudnicki, P., Shelley, P.: Asymptotic notation. Part II: examples and problems. Journal of Formalized Mathematics 11 (1999),
  5. 5.
    Nathanson, M.B.: Elementary Methods in Number Theory. Springer, New York (2000)zbMATHGoogle Scholar
  6. 6.
    Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)zbMATHCrossRefGoogle Scholar
  7. 7.
    Shapiro, H.N.: Introduction to the theory of numbers. Pure and Applied Mathematics. John Wiley & Sons Inc., New York (1983), A Wiley-Interscience PublicationzbMATHGoogle Scholar
  8. 8.
    Wenzel, M.: Using axiomatic type classes in Isabelle (1995),
  9. 9.
    Type classes and overloading in higher-order logic. In: Gunther, E., Felty, A. (eds.) TPHOLs 1997, pp. 307–322. Murray Hill, New Jersey (1997)Google Scholar
  10. 10.
    Wenzel, M., Bauer, G.: Calculational reasoning revisited (an Isabelle/ Isar experience). In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, pp. 75–90. Springer, Heidelberg (2001)Google Scholar
  11. 11.
    The Coq proof assistant. Developed by the LogiCal project,
  12. 12.
    The Isabelle theorem proving environment. Developed by Larry Paulson at Cambridge University and Tobias Nipkow at TU Munich,

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jeremy Avigad
    • 1
  • Kevin Donnelly
    • 1
  1. 1.Carnegie Mellon University 

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