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Importing HOL Light into Coq

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Interactive Theorem Proving (ITP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6172))

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Abstract

We present a new scheme to translate mathematical developments from HOL Light to Coq, where they can be re-used and re-checked. By relying on a carefully chosen embedding of Higher-Order Logic into Type Theory, we try to avoid some pitfalls of inter-operation between proof systems. In particular, our translation keeps the mathematical statements intelligible. This translation has been implemented and allows the importation of the HOL Light basic library into Coq.

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References

  1. Our implementation, http://perso.ens-lyon.fr/chantal.keller/Recherche/hollightcoq.html

  2. Dedukti, a universal proof checker, http://www.lix.polytechnique.fr/dedukti

  3. The Flyspeck project, http://www.flyspeck-blog.blogspot.com

  4. Aagaard, M., Harrison, J. (eds.): TPHOLs 2000. LNCS, vol. 1869. Springer, Heidelberg (2000)

    MATH  Google Scholar 

  5. Aydemir, B., Charguéraud, A., Pierce, B., Pollack, R., Weirich, S.: Engineering formal metatheory. In: Necula, G., Wadler, P. (eds.) POPL, pp. 3–15. ACM, New York (2008)

    Google Scholar 

  6. Barras, B., Boutin, S., Cornes, C., Courant, J., Filliatre, J., Gimenez, E., Herbelin, H., Huet, G., Munoz, C., Murthy, C., et al.: The Coq proof assistant: reference manual. Rapport technique - INRIA (2000)

    Google Scholar 

  7. Berger, U., Schwichtenberg, H.: An inverse of the evaluation functional for typed lambda-calculus. In: LICS, pp. 203–211. IEEE Computer Society, Los Alamitos (1991)

    Google Scholar 

  8. Berghofer, S., Nipkow, T.: Proof terms for simply typed higher order logic. In: Aagaard, Harrison: [4], pp. 38–52

    Google Scholar 

  9. Denney, E.: A prototype proof translator from hol to coq. In: Aagaard, Harrison: [4], pp. 108–125

    Google Scholar 

  10. Filliâtre, J.C., Conchon, S.: Type-safe modular hash-consing. In: Kennedy, A., Pottier, F. (eds.) ML, pp. 12–19. ACM, New York (2006)

    Chapter  Google Scholar 

  11. Furbach, U., Shankar, N. (eds.): IJCAR 2006. LNCS (LNAI), vol. 4130. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  12. Garillot, F., Werner, B.: Simple types in type theory: Deep and shallow encodings. In: Schneider, K., Brandt, J. (eds.) TPHOLs 2007. LNCS, vol. 4732, pp. 368–382. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Gonthier, G., Mahboubi, A.: A Small Scale Reflection Extension for the Coq system. Tech. rep., INRIA (2007)

    Google Scholar 

  14. Gordon, M., Melham, T.: Introduction to HOL: A theorem proving environment for higher order logic. Cambridge University Press, New York (1993)

    MATH  Google Scholar 

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

    Chapter  Google Scholar 

  16. Harrison, J.: Towards self-verification of HOL Light. In: Furbach, Shankar: [11], pp. 177–191

    Google Scholar 

  17. Hurd, J.: OpenTheory: Package Management for Higher Order Logic Theories. In: PLMMS’09, p. 31 (2009)

    Google Scholar 

  18. Leroy, X.: The OCaml Programming Language (1998)

    Google Scholar 

  19. Obua, S., Skalberg, S.: Importing HOL into Isabelle/HOL. In: Furbach, Shankar: [11], pp. 298–302

    Google Scholar 

  20. Wiedijk, F.: Encoding the HOL Light logic in Coq. Unpublished notes (2007)

    Google Scholar 

  21. Wong, W.: Recording and checking HOL proofs. In: Schubert, E., Windley, P., Alves-Foss, J. (eds.) TPHOLs 1995. LNCS, vol. 971, pp. 353–368. Springer, Heidelberg (1995)

    Google Scholar 

  22. Zammit, V.: A comparative study of Coq and HOL. In: Gunter, E., Felty, A. (eds.) TPHOLs 1997. LNCS, vol. 1275, pp. 323–337. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

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Keller, C., Werner, B. (2010). Importing HOL Light into Coq. In: Kaufmann, M., Paulson, L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14052-5_22

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  • DOI: https://doi.org/10.1007/978-3-642-14052-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14051-8

  • Online ISBN: 978-3-642-14052-5

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