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Recording and checking HOL proofs

  • Wai Wong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 971)

Abstract

Formal proofs generated by mechanised theorem proving systems may consist of a large number of inferences. As these theorem proving systems are usually very complex, it is extremely difficult if not impossible to formally verify them. This calls for an independent means of ensuring the consistency of mechanically generated proofs. This paper describes a method of recording HOL proofs in terms of a sequence of applications of inference rules. The recorded proofs can then be checked by an independent proof checker. Also described in this paper is an efficient proof checker which is able to check a practical proof consisting of thousands of inference steps.

Keywords

Inference Rule Deductive System Inference Step Disk File Proof Checker 
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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References

  1. [BD93]
    Robert S. Boyer and Gilles Dowek. Towards checking proof checkers. In Workshop on types for proofs and programs (Type '93). 1993.Google Scholar
  2. [Bou92]
    R. J. Boulton. On efficiency in theorem provers which fully expand proofs into primitive inferences. Technical Report 248, University of Cambridge Computer Laboratory, 1992.Google Scholar
  3. [ea96]
    Constable et al. Implementing Mathematics with the Nuprl proof development system. Prentice-Hall, 1996.Google Scholar
  4. [GM93]
    M. J. C. Gordon and T. F. Melham, editors. Introduction to HOL—a theorem proving environment for higher order logic. Cambridge University Press, 1993.Google Scholar
  5. [Gor83]
    M. J. C. Gordon. LCF_LSM, A system for specifying and verifying hardware. Technical Report 41, University of Cambridge Computer Laborartory, 1983.Google Scholar
  6. [oD91]
    Ministry of Defence. Requirements for the procurement of safety-critical software in defence equipment. Interim Standard 00–55, April 1991.Google Scholar
  7. [Sym93]
    D. Syme. Reasoning with the formal definition of standard ML in HOL. In Higher Order Logic Theorem Proving and Its Applications, Lecture Notes in Computer Science No. 780, pages 43–58. Springer-Verlag, 1993.Google Scholar
  8. [VG93]
    M. VanInwegen and E. Gunter. HOL-ML, In Higher Order Logic Theorem Proving and Its Applications, Lecture Notes in Computer Science No. 780, pages 59–72. Springer-Verlag, 1993.Google Scholar
  9. [vW94]
    J. von Wright. Representing higher order logic proofs in HOL. In Thomas F. Melham and Juanito Camilleri, editors, Higher Order Logic Theorem Proving and Its Applications: 7th International Workshop, volume 859 of Lecture Notes in Computer Science, pages 456–470. Springer-Verlag, September 1994.Google Scholar
  10. [vW95]
    J. von Wright. Program refinement by theorem prover. In Proceedings of the 6th Refinement workshop, Lecture Notes in Computer Science. Springer-Verlag, 1995.Google Scholar
  11. [Won93a]
    W. Wong. Formal verification of VIPER's ALU. Technical Report 300, University of Cambridge Computer Laboratory, New Museums Site, Pembroke Street, Cambridge CB2 3QG, ENGLAND, May 1993.Google Scholar
  12. [Won93b]
    W. Wong. Recording HOL proofs. Technical Report 306, University of Cambridge Computer Laboratory, New Museums Site, Pembroke Street, Cambridge CB2 3QG, ENGLAND, July 1993.Google Scholar
  13. [Won94]
    W. Wong. The HOL record_proof Library. Computer Laboratory, University of Cambridge, 1994.Google Scholar
  14. [Won95]
    W. Wong. A proof checker for HOL proofs. Technical report, University of Cambridge Computer Laboratory, New Museums Site, Pembroke Street, Cambridge CB2 3QG, ENGLAND, 1995. to be published as technical report.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Wai Wong
    • 1
  1. 1.Department of Computing StudiesHong Kong Baptist UniversityKowloon TongHong Kong

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