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An Interpretation of Isabelle/HOL in HOL Light

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Automated Reasoning (IJCAR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

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Abstract

We define an interpretation of the Isabelle/HOL logic in HOL Light and its metalanguage, OCaml. Some aspects of the Isabelle logic are not representable directly in the HOL Light object logic. The interpretation thus takes the form of a set of elaboration rules, where features of the Isabelle logic that cannot be represented directly are elaborated to functors in OCaml. We demonstrate the effectiveness of the interpretation via an implementation, translating a significant part of the Isabelle standard library into HOL Light.

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References

  1. http://www.cs.cmu.edu/~seanmcl/projects/logosphere/isabelle-holl

  2. Avigad, J., Donnelly, K., Gray, D., Raff, P.: A formally verified proof of the prime number theorem. To appear in the ACM Transactions on Computational Logic

    Google Scholar 

  3. Ballarin, C.: Locales and locale expressions in Isabelle/Isar. In: B., S., et al. (eds.) Types for Proofs and Programs: International Workshop (2003)

    Google Scholar 

  4. Bertot, Y., Castéran, P.: CoqÁrt: The Calculus of Inductive Constructions. In: Texts in Theoretical Computer Science, Springer, Heidelberg (2004)

    Google Scholar 

  5. de Bruijn, N.G.: A survey of the project AUTOMATH. In: Seldin, J.P., Hindley, J.R. (eds.) To H. B. Curry: Essays in Combinatory Logic, Lambda Calculus, and Formalism, pp. 589–606. Academic Press, London (1980)

    Google Scholar 

  6. Constable, R.: Implementing Mathematics with The Nuprl Proof Development System. Prentice-Hall, Englewood Cliffs (1986)

    Google Scholar 

  7. Howe, D.J.: Importing mathematics from HOL into Nuprl. In: Von Wright, J., Grundy, J., Harrison, J. (eds.) TPHOLs 1996. LNCS, vol. 1125, pp. 267–282. Springer, Heidelberg (1996)

    Google Scholar 

  8. Felty, A.P., Howe, D.J.: Hybrid interactive theorem proving using Nuprl and HOL. In: WebDB 2000. LNCS, pp. 351–365. Springer, Heidelberg (1997)

    Google Scholar 

  9. Gonthier, G.: A computer-checked proof of the four colour theorem (2005), Available on the Web via http://research.microsoft.com/~gonthier/

  10. 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 

  11. Hales, T.: The Flyspeck Project fact sheet. Project description (2005), available at http://www.math.pitt.edu/~thales/flyspeck/

  12. Hales, T.: The Jordan Curve Theorem in HOL Light. Source code (2005), available at http://www.math.pitt.edu/~thales/

  13. Hales, T.C.: A proof of the the Kepler conjecture. Annals of Mathematics 162, 1065–1185 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  14. Harper, R., Honsell, F., Plotkin, G.: A framework for defining logics. In: Proceedings of the Second Annual Symposium on Logic in Computer Science, Ithaca, NY, pp. 194–204. IEEE Computer Society Press, Los Alamitos (1987)

    Google Scholar 

  15. Harper, R., Pierce, B.C.: Design issues in advanced module systems. In: Pierce, B.C. (ed.) Advanced Topics in Types and Programming Languages, MIT Press, Cambridge (2005)

    Google Scholar 

  16. Harrison, J.: HOL Light: A tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)

    Google Scholar 

  17. Landau, E.: Grundlagen der Analysis. Leipzig, 1930. English translation by F. Steinhardt: Foundations of analysis: the arithmetic of whole, rational, irrational, and complex numbers. A supplement to textbooks on the differential and integral calculus, published by Chelsea; 3rd edition (1966)

    Google Scholar 

  18. McLaughlin, S., Barrett, C., Ge, Y.: Cooperating theorem provers: A case study combining CVC Lite and HOL Light. In: Armando, A., Cimatti, A. (eds.) Proceedings of the Third Workshop on Pragmatics of Decision Procedures in Automated Reasoning, vol. 144, pp. 43–51 (2005)

    Google Scholar 

  19. Milner, R., Tofte, M., Harper, R.: The Definition of Standard ML. MIT Press, Cambridge (1990)

    Google Scholar 

  20. Naumov, P.: Importing Isabelle formal mathematics into Nuprl. Technical Report TR99-1734, Cornell University, 26 (1999)

    Google Scholar 

  21. Naumov, P., Stehr, M.-O., Meseguer, J.: The HOL/NuPRL proof translator - a practical approach to formal interoperability. In: Boulton, R.J., Jackson, P.B. (eds.) TPHOLs 2001. LNCS, vol. 2152, Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  22. Nipkow, T., Bauer, G., Schultz, P.: Flyspeck I: Tame Graphs. Technical report, Institut für Informatik, TU München (January 2006)

    Google Scholar 

  23. Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL (submitted, 2006)

    Google Scholar 

  24. Owre, S., Rushby, J.M., Shankar, N.: PVS: A prototype verification system. In: Kapur, D. (ed.) CADE 1992. LNCS, vol. 607, pp. 748–752. Springer, Heidelberg (1992)

    Google Scholar 

  25. Paulson, L.C.: Isabelle. LNCS, vol. 828. Springer, Heidelberg (1994)

    MATH  Google Scholar 

  26. Pfenning, F.: Logical frameworks. In: Handbook of Automated Reasoning, pp. 1063–1147. MIT Press, Cambridge (2001)

    Chapter  Google Scholar 

  27. Pfenning, F., Schürmann, C.: System description: Twelf - a meta-logical framweork for deductive systems. In: Ganzinger, H. (ed.) Proceedings of the 16th International Conference on Automated Deduction, pp. 202–206 (1999)

    Google Scholar 

  28. Pfenning, F., Schürmann, C., Kohlhase, M., Shankar, N., Owre, S.: The Logosphere Project (2005), Project description available at http://www.logosphere.org

  29. Schürmann, C., Stehr, M.-O.: An Executable Formalization of the HOL/NuPRL Connection in Twelf. In: 11th International Conference on Logic for Programming Artificial Intelligence and Reasoning (2005)

    Google Scholar 

  30. Stehr, M.-O., Naumov, P., Meseguer, J.: A proof-theoretic approach to the HOL-NuPRL connection with applications to proof-translation. In: WADT/CoFI (2001)

    Google Scholar 

  31. Weis, P., Leroy, X.: Le langage Caml. InterEditions (1993), see also the CAML Web page: http://pauillac.inria.fr/caml/

  32. Wenzel, M.: Type Classes and Overloading in Higher-Order Logic. In: Gunter, E.L., Felty, A.P. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 307–322. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  33. Whitehead, A.N., Russell, B.: Principia Mathematica, vol. 3. Cambridge University Press, Cambridge (1910)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Carnegie Mellon University,  

    Sean McLaughlin

Authors
  1. Sean McLaughlin
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Artificial Intelligence Research Group, University of Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz

    Ulrich Furbach

  2. SRI International, MS EL256,, 333 Ravenswood Avenue, 94025-3493, Menlo Park, CA, USA

    Natarajan Shankar

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© 2006 Springer-Verlag Berlin Heidelberg

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McLaughlin, S. (2006). An Interpretation of Isabelle/HOL in HOL Light. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_18

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  • DOI: https://doi.org/10.1007/11814771_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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