Advertisement

Abstract

HOL Light is an interactive proof assistant for classical higher-order logic, intended as a clean and simplified version of Mike Gordon’s original HOL system. Theorem provers in this family use a version of ML as both the implementation and interaction language; in HOL Light’s case this is Objective CAML (OCaml). Thanks to its adherence to the so-called ‘LCF approach’, the system can be extended with new inference rules without compromising soundness. While retaining this reliability and programmability from earlier HOL systems, HOL Light is distinguished by its clean and simple design and extremely small logical kernel. Despite this, it provides powerful proof tools and has been applied to some non-trivial tasks in the formalization of mathematics and industrial formal verification.

Keywords

Inference Rule High Order Logic Prime Number Theorem Polymorphic Type Jordan Curve Theorem 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, London (1986)zbMATHGoogle Scholar
  2. 2.
    Church, A.: A formulation of the Simple Theory of Types. Journal of Symbolic Logic 5, 56–68 (1940)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Diaconescu, R.: Axiom of choice and complementation. Proceedings of the American Mathematical Society 51, 176–178 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Gordon, M.J.C.: Representing a logic in the LCF metalanguage. In: Néel, D. (ed.) Tools and notions for program construction: an advanced course, pp. 163–185. Cambridge University Press, Cambridge (1982)Google Scholar
  5. 5.
    Gordon, M.J.C., Melham, T.F.: Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, Cambridge (1993)zbMATHGoogle Scholar
  6. 6.
    Gordon, M.J.C., Milner, R., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)zbMATHGoogle Scholar
  7. 7.
    Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. (eds.) Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, vol. 05021. Internationales Begegnungs- und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany (2006)Google Scholar
  8. 8.
    Hales, T.C.: The Jordan curve theorem, formally and informally. The American Mathematical Monthly 114, 882–894 (2007)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Harrison, J.: Proof style. In: Giménez, E., Paulin-Mohring, C. (eds.) TYPES 1996. LNCS, vol. 1512, pp. 154–172. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  10. 10.
    Harrison, J.: Theorem Proving with the Real Numbers. Springer, Heidelberg (1998); Revised version of author’s PhD thesisCrossRefzbMATHGoogle Scholar
  11. 11.
    Harrison, J.: Floating-point verification using theorem proving. In: Bernardo, M., Cimatti, A. (eds.) SFM 2006. LNCS, vol. 3965, pp. 211–242. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Harrison, J.: Verifying nonlinear real formulas via sums of squares. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 102–118. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Harrison, J.: Formalizing an analytic proof of the Prime Number Theorem (dedicated to Mike Gordon on the occasion of his 60th birthday). Journal of Automated Reasoning (to appear, 2009)Google Scholar
  14. 14.
    Lambek, J., Scott, P.J.: Introduction to higher order categorical logic. Cambridge studies in advanced mathematics, vol. 7. Cambridge University Press, Cambridge (1986)zbMATHGoogle Scholar
  15. 15.
    Loveland, D.W.: Mechanical theorem-proving by model elimination. Journal of the ACM 15, 236–251 (1968)CrossRefzbMATHGoogle Scholar
  16. 16.
    Scott, D.: A type-theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science 121, 411–440 (1993); Annotated version of a 1969 manuscriptMathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Solovay, R.M., Arthan, R., Harrison, J.: Some new results on decidability for elementary algebra and geometry. ArXiV preprint 0904.3482 (2009); submitted to Annals of Pure and Applied Logic, http://arxiv.org/PS_cache/arxiv/pdf/0904/0904.3482v1.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • John Harrison
    • 1
  1. 1.Intel Corporation, JF1-13Hillsboro

Personalised recommendations