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A mizar mode for HOL

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Theorem Proving in Higher Order Logics (TPHOLs 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1125))

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Abstract

The HOL theorem prover is implemented in the LCF manner. All inference is ultimately reduced to a collection of very simple (forward) primitive inference rules, but by programming it is possible to build alternative means of proving theorems on top, while preserving security. Existing HOL proofs styles are, however, very different from those used in textbooks. Here we describe the addition of another style, inspired by Mizar. We believe the resulting system combines the secure extensibility and interactivity of HOL with Mizar’s readability and lack of logical prescriptiveness. Part of our work involves adding new facilities to HOL for first order automation, since this allows HOL to be more flexible, as Mizar is, over the precise logical connection between steps.

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References

  1. P. B. Andrews, M. Bishop, S. Issar, D. Nesmith, F. Pfenning, and H. Xi. TPS: A theorem proving system for classical type theory. Research report 94–166, Department of Mathematics, Carnegie-Mellon University, 1994.

    Google Scholar 

  2. Anonymous. The QED Manifesto. In A. Bundy, editor, 12th International Conference on Automated Deduction, volume 814 of Lecture Notes in Computer Science, pages 238–251, Nancy, France, 1994. Springer-Verlag.

    Google Scholar 

  3. M. Archer, J. J. Joyce, K. N. Levitt, and P. J. Windley, editors. Proceedings of the 1991 International Workshop on the HOL theorem proving system and its Applications, University of California at Davis, Davis CA, USA, 1991. IEEE Computer Society Press.

    Google Scholar 

  4. B. Beckert and J. Posegga. leanT A P: Lean, tableau-based deduction. Journal of Automated Reasoning, 15:339–358, 1995. Available on the Web from ftp://sonja.ira.uka.de/pub/posegga/LeanTaP.ps.Z.

    Article  MATH  MathSciNet  Google Scholar 

  5. P. E. Black and P. J. Windley. Automatically synthesized term denotation predicates: A proof aid. In P. J. Windley, T. Schubert, and J. Alves-Foss, editors, Higher Order Logic Theorem Proving and Its Applications: Proceedings of the 8th International Workshop, volume 971 of Lecture Notes in Computer Science, pages 46–57, Aspen Grove, Utah, 1995. Springer-Verlag.

    Google Scholar 

  6. R. J. Boulton. Efficiency in a fully-expansive theorem prover. Technical Report 337, University of Cambridge Computer Laboratory, New Museums Site, Pembroke Street, Cambridge, CB2 3QG, UK, 1993. Author's PhD thesis.

    Google Scholar 

  7. R. S. Boyer, E. Lusk, W. McCune, R. Overbeek, M. Stickel, and L. Wos. Set theory in first order logic: Clauses for Goedel's axioms. Journal of Automated Reasoning, 2:287–327, 1986.

    Article  MATH  Google Scholar 

  8. P. Curzon. Tracking design changes with formal machine-checked proof. The Computer Journal, 38:91–100, 1995.

    Article  Google Scholar 

  9. T. B. de la Tour. Minimizing the number of clauses by renaming. In Stickel [34], pages 558–572.

    Google Scholar 

  10. A. Degtyarev and A. Voronkov. Simultaneous rigid E-unification is undecidable. Technical report 105, Computing Science Department, Uppsala University, Box 311, S-751 05 Uppsala, Sweden, 1995. Also available on the Web as ftp://ftp.csd.uu.se/pub/papers/reports/0105.ps.gz.

    Google Scholar 

  11. G. Dowek. Collections, sets and types. Technical report 2708, INRIA Roquencourt, 1995.

    Google Scholar 

  12. A. J. M. van Gasteren. On the shape of mathematical arguments, volume 445 of Lecture Notes in Computer Science. Springer-Verlag, 1990. Foreword by E. W. Dijkstra.

    Google Scholar 

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

    Google Scholar 

  14. M. J. C. Gordon, R. Milner, and C. P. Wadsworth. Edinburgh LCF: A Mechanised Logic of Computation, volume 78 of Lecture Notes in Computer Science. Springer-Verlag, 1979.

    Google Scholar 

  15. J. Grundy. Window inference in the HOL system. In Archer et al. [3]. pages 177–189.

    Chapter  Google Scholar 

  16. J. Grundy. A browsable format for proof presentation. In C. Gefwert, P. Orponen, and J. Seppänen, editors, Proceedings of the Finnish Artificial Intelligence Society Symposium: Logic, Mathematics and the Computer, volume 14 of Suomen Tekoälyseuran julkaisuja, pages 171–178. Finnish Artificial Intelligence Society, 1996.

    Google Scholar 

  17. J. Harrison. Metatheory and reflection in theorem proving: A survey and critique. Technical Report CRC-053, SRI Cambridge, Millers Yard, Cambridge, UK, 1995. Available on the Web as http://www.cl.cam.ac.uk/users/jrh/papers/reflect.dvi.gz.

    Google Scholar 

  18. J. Harrison. Optimizing proof search in model elimination. To appear in the proceedings of the 13th International Conference on Automated Deduction (CADE 13), Springer Lecture Notes in Computer Science, 1996.

    Google Scholar 

  19. J. Harrison and K. Slind. A reference version of HOL. Presented in poster session of 1994 HOL Users Meeting and only published in participants’ supplementary proceedings. Available on the Web from http://www.dcs.glasgow.ac.uk/~hug94/sproc.html, 1994.

    Google Scholar 

  20. G. Huet. A unification algorithm for typed λ-calculus. Theoretical Computer Science, 1:27–57, 1975.

    Article  MathSciNet  Google Scholar 

  21. R. Kumar, T. Kropf, and K. Schneider. Integrating a first-order automatic prover in the HOL environment. In Archer et al. [3], pages 170–176.

    Chapter  Google Scholar 

  22. W. McCune. Equality in automated deduction. In: T. Dietterich and W. Swartout, editors, Proceedings of the 8th National Conference on Artificial Intelligence, pages 246–252, Boston, MA, 1990. MIT Press.

    Google Scholar 

  23. T. F. Melham. Automating recursive type definitions in higher order logic. In G. Birtwistle and P. A. Subrahmanyam, editors, Current Trends in Hardware Verification and Automated Theorem Proving, pages 341–386. Springer-Verlag, 1989.

    Google Scholar 

  24. T. F. Melham. A package for inductive relation definitions in HOL. In Archer et al. [3], pages 350–357.

    Chapter  Google Scholar 

  25. L. C. Paulson. A higher-order implementation of rewriting. Science of Computer Programming, 3:119–149, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  26. L. C. Paulson. Isabelle: a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994. With contributions by Tobias Nipkow.

    Google Scholar 

  27. I. S. W. B. Prasetya. On the style of mechanical proving. In J. J. Joyce and C. Seger, editors, Proceedings of the 1993 International Workshop on the HOL theorem proving system and its applications, volume 780 of Lecture Notes in Computer Science, pages 475–488, UBC, Vancouver, Canada, 1993. Springer-Verlag.

    Google Scholar 

  28. J. A. Robinson. A note on mechanizing higher order logic. In B. Meltzer and D. Michie, editors, Machine Intelligence 5, pages 123–133. Edinburgh University Press, 1969.

    Google Scholar 

  29. P. J. Robinson and J. Staples. Formalizing a hierarchical structure of practical mathematical reasoning. Journal of Logic and Computation, 3:47–61, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  30. P. Rudnicki, Obvious inferences. Journal of Automated Reasoning, 3:383–393, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  31. K. Slind. Object language embedding in standard ml of new jersey. Technical Report 91-454-38, University of Calgary Computer Science Department, 2500 University Drive N. W., Calgary, Alberta, Canada, TN2 1N4, 1991. Also appeared in Proceedings of 2nd ML Workshop.

    Google Scholar 

  32. S. Sokolowski. A note on tactics in LCF. Technical Report CSR-140-83, University of Edinburgh, Department of Computer Science, 1983.

    Google Scholar 

  33. M. E. Stickel. A Prolog Technology Theorem Prover: Implementation by an extended Prolog compiler. Journal of Automated Reasoning, 4:353–380, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  34. M. E. Stickel, editor. 10th International Conference on Automated Deduction, volume 449 of Lecture Notes in Computer Science, Kaiserslautern, Federal Republic of Germany, 1990. Springer-Verlag.

    Google Scholar 

  35. M. Tarver. An examination of the Prolog Technology Theorem-Prover. In Stickel [34]. Springer-Verlag pages 322–335.

    Google Scholar 

  36. A. Trybulec and H. A. Blair. Computer aided reasoning. In R. Parikh, editor, Logics of Programs, volume 193 of Lecture Notes in Computer Science, pages 406–412, Brooklyn, 1985. Springer-Verlag.

    Google Scholar 

  37. J. G. Wiltink. A deficiency of natural deduction. Information Processing Letters, 25:233–234, 1987.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Åbo Akademi University, Lemminkäisenkatu 14a, 20520, Turku, Finland

    John Harrison

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  1. John Harrison
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Editor information

Gerhard Goos Juris Hartmanis Jan van Leeuwen Joakim von Wright Jim Grundy John Harrison

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© 1996 Springer-Verlag Berlin Heidelberg

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Harrison, J. (1996). A mizar mode for HOL. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105406

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  • DOI: https://doi.org/10.1007/BFb0105406

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  • Print ISBN: 978-3-540-61587-3

  • Online ISBN: 978-3-540-70641-0

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