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Verification of the interface of a small proof system in coq

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Types for Proofs and Programs (TYPES 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1512))

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Abstract

This article describes the formalization of the interface of a proof-checker. The latter is based on a kernel consisting of type-checking functions for the Calculus of Constructions, but it seems the ideas can generalize to other type systems, as far as they are based on the proofsas-terms principle. We suppose that the metatheory of the corresponding type system is proved (up to type decidability). We specify and certify the toplevel loop, the system invariant, and the error messages.

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References

  1. Barendregt, H.: Lambda Calculi with Types. In Handbook of Logic in Computer Science, Vol II, Elsevier, 1992.

    Google Scholar 

  2. Barras, B.: Coq en Coq. Rapport de Recherche INRIA 3026. Octobre 1996.

    Google Scholar 

  3. Barras, B., Werner, B.: Coq in Coq. Submitted to publication. http://pauillac.inria.fr/~barras/coqincoq.ps.gz

    Google Scholar 

  4. Barras, B., Boutin, S., Cornes, C., Courant, J., Filliâtre, J.-C., Giménez, E., Herbelin, H., Huet, G., Muñoz, C., Murthy, C., Parent, C., Paulin-Mohring, C., Saïbi, A., Werner, B.: The Coq Proof Assistant Reference Manual Version 6.1. Technical Report 0203. Coq Project-INRIA Rocquencourt-ENS Lyon. May 97.

    Google Scholar 

  5. Boyer, R.S., Dowek, G.: Towards Checking Proof-Checkers. In Herman Geuvers, editor, Informal Proceedings of the Nijmegen Workshop on Types for Proofs and Programs, May 1993.

    Google Scholar 

  6. De Bruijn, N.J.: Lambda-Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem. Indag. Math. Vol. 34 (5), pp 381–392, 1972.

    Google Scholar 

  7. Coquand, T., Huet, G.: The Calculus of Constructions. In: Information and Computation Vol. 76, February/March 1988 (ed. A.R. Meyer), Academic Press, London, 95–120.

    Google Scholar 

  8. Coscoy, Y., Khan, G., Théry, L.: Extracting text from proofs. INRIA Research Report 2459. January 1995.

    Google Scholar 

  9. Courant, J.: A Module Calculus for Pure Type Systems. In: Proceedings of the Third International Conference on Typed Lambda Calculi and Applications, TLCA'97, Nancy (ed. Ph. de Groote and J. R. Hindley), Springer-Verlag, LNCS 1210, April 1997.

    Google Scholar 

  10. Girard, J.-Y., Lafont, Y., Taylor, P.: Proofs and Types. Cambridge Tracts in Theoretical Computer Science 7. Cambridge University Press.

    Google Scholar 

  11. Geuvers, H., Nederhof, M.-J.: A Modular Proof of Strong Normalization for the Calculus of Constructions. Journal of Functional Programming, 1(2):155–189, April 1991.

    MATH  MathSciNet  Google Scholar 

  12. Gordon, M., Milner, R., Wadsworth, C.: Edinburgh LCF: A Mechanized Logic of Computation. Springer-Verlag, LNCS 78, 1979.

    Google Scholar 

  13. Huet, G.: The Constructive Engine. In R. Narasimhan, editor, A Perspective in Theoretical Computer Science. WorldScientific Publishing, 1989. Commemorative Volume for Gift Siromoney.

    Google Scholar 

  14. Leroy, X.: Applicative Functors and Fully Transparent Higher-Order Modules. In: 22nd Symposium on Principles of Programming Languages, pp. 142–153. ACM Press, 1995.

    Google Scholar 

  15. Martin-Löf, P.: A Theory of Types. Technical Report 71-3, University of Stockholm, 1971.

    Google Scholar 

  16. Paulin-Mohring, C., Werner, B.: Synthesis of ML programs in Coq. Journal of Symbolic Computation-special issue on automated programming, 1993.

    Google Scholar 

  17. Pollack, R.: Closure Under Alpha-Conversion. In: Types for Proofs and Programs: International Workshop TYPES'93, Nijmegen, May 1993, Selected Papers, file://ftp.dcs.ed.ac.uk/pub/lego/alpha-closure.ps.gz (ed. H. Barendregt and T. Nipkow), Springer-Verlag, pp. 313–332, LNCS 806, 1994.

    Google Scholar 

  18. Pollack, R.: A Proof Checker for the Extended Calculus of Constructions. Ph. D. Thesis, ftp://ftp.dcs.ed.ac.uk/pub/lego/thesis-pollack.ps.Z University of Edinburgh, 1994.

    Google Scholar 

  19. Pollack, R.: A Verified Typechecker. In: Proceedings of the Second International Conference on Typed Lambda Calculi and Applications, TLCA'95, Edinburgh, (ed. M. Dezani-Ciancaglini and G. Plotkin), Springer-Verlag, LNCS 902, April 1995.

    Google Scholar 

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Authors and Affiliations

  1. INRIA-Rocquencourt Domaine de Voluceau, B.P. 105, 78153, Le Chesnay Cedex, France

    Bruno Barras

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  1. Bruno Barras
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Eduardo Giménez Christine Paulin-Mohring

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© 1998 Springer-Verlag Berlin Heidelberg

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Barras, B. (1998). Verification of the interface of a small proof system in coq. In: Giménez, E., Paulin-Mohring, C. (eds) Types for Proofs and Programs. TYPES 1996. Lecture Notes in Computer Science, vol 1512. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097785

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  • DOI: https://doi.org/10.1007/BFb0097785

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65137-6

  • Online ISBN: 978-3-540-49562-8

  • eBook Packages: Springer Book Archive

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