Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

HOL Light: An Overview

  • Conference paper
Theorem Proving in Higher Order Logics (TPHOLs 2009)

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

Included in the following conference series:

  • 1756 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Andrews, P.B.: An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof. Academic Press, London (1986)

    MATH  Google Scholar 

  2. Church, A.: A formulation of the Simple Theory of Types. Journal of Symbolic Logic 5, 56–68 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  3. Diaconescu, R.: Axiom of choice and complementation. Proceedings of the American Mathematical Society 51, 176–178 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  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. Gordon, M.J.C., Melham, T.F.: Introduction to HOL: a theorem proving environment for higher order logic. Cambridge University Press, Cambridge (1993)

    MATH  Google Scholar 

  6. Gordon, M.J.C., Milner, R., Wadsworth, C.P.: Edinburgh LCF. LNCS, vol. 78. Springer, Heidelberg (1979)

    MATH  Google Scholar 

  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. Hales, T.C.: The Jordan curve theorem, formally and informally. The American Mathematical Monthly 114, 882–894 (2007)

    MathSciNet  MATH  Google Scholar 

  9. Harrison, J.: Proof style. In: Giménez, E., Paulin-Mohring, C. (eds.) TYPES 1996. LNCS, vol. 1512, pp. 154–172. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Harrison, J.: Theorem Proving with the Real Numbers. Springer, Heidelberg (1998); Revised version of author’s PhD thesis

    Book  MATH  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Lambek, J., Scott, P.J.: Introduction to higher order categorical logic. Cambridge studies in advanced mathematics, vol. 7. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  15. Loveland, D.W.: Mechanical theorem-proving by model elimination. Journal of the ACM 15, 236–251 (1968)

    Article  MATH  Google Scholar 

  16. Scott, D.: A type-theoretical alternative to ISWIM, CUCH, OWHY. Theoretical Computer Science 121, 411–440 (1993); Annotated version of a 1969 manuscript

    Article  MathSciNet  MATH  Google Scholar 

  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

Download references

Author information

Authors and Affiliations

  1. Intel Corporation, JF1-13, 2111 NE 25th Avenue, Hillsboro, OR, 97124

    John Harrison

Authors
  1. John Harrison
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Stefan Berghofer , Tobias Nipkow , Christian Urban  & Makarius Wenzel , ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Harrison, J. (2009). HOL Light: An Overview. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03359-9_4

  • 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)

Publish with us

Policies and ethics

Search

Navigation