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


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Aczel. A notion of class for theory development in algebra in a predicative type theory. Talk presented at the Workshop on Types for Proofs and Programs, June 1994.Google Scholar
  2. 2.
    H. Barendregt. Lambda calculi with types. In S. Abramsky, D. M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 3. Oxford science publications, 1994.Google Scholar
  3. 3.
    Henk Barendregt. The quest of correctness. Images of SMC research, Stichting Mathematisch Centrum, P.O. Box 94079, 1090 GB Amsterdam, 39–58.Google Scholar
  4. 4.
    A. Church. A formulation of the simple theory of types. Journal of Symbolic Logic, 5:56–68, 1940.MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    R.L. Constable et al. Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall, 1986.Google Scholar
  6. 6.
    T. Coquand. Metamathematical Investigations of a Calculus of Constructions. In P. Odifreddi, editor, Logic and Computer Science, volume 31 of The APIC series, pages 91–122. Academic Press, 1990.Google Scholar
  7. 7.
    T. Coquand. On the analogy between propositions and types. In G. Huet, editor, Logical Foundations of Functional Programming, pages 399–417. Addison-Wesley, 1990.Google Scholar
  8. 8.
    Th. Coquand and G. Huet. Constructions: A higher order proof system for mechanizing mathematics. In EUROCAL'85, volume 203 of LNCS, Linz, 1985. Springer-Verlag.Google Scholar
  9. 9.
    C. Cornes and D. Terrasse. Automatizing Inversion Predicates in Coq. In Workshop on Types for Proofs on Programs, number 1152 in LNCS. Springer-Verlag, 1995.Google Scholar
  10. 10.
    EC Types Working Group. First Workshop on Formal Topology, Padova, October 1997.Google Scholar
  11. 11.
    E. Giménez. An application of co-Inductive types in Coq: verification of the Alternating Bit Protocol. In Workshop on Types for Proofs and Programs, number 1158 in LNCS, pages 135–152. Springer-Verlag, 1995.Google Scholar
  12. 12.
    J.-Y. Girard. Proceedings of the 2nd scandinavian logic symposium. In J.E. Fenstad, editor, Une extension de l'interprétation de Gödel à l'analyse, et son application à l'élimination des coupures dans l'analyse et la téorie des types, pages 63–92. North-Holland, 1971.Google Scholar
  13. 13.
    J.-Y. Girard, Y. Lafont, and P. Taylor. Proofs and Types. Cambridge Tracts in Theoretical Computer Science 7. Cambridge University Press, 1989.Google Scholar
  14. 14.
    M.J. Gordon, R. Milner, and C. Wadsworth. Edinburgh LCF, volume 78 of LNCS. Springer-Verlag, 1979.Google Scholar
  15. 15.
    M.J.C. Gordon and T. F. Melham. Introduction to HOL. A theorem proving environment for higher order logic. University of Cambridge, 1993.Google Scholar
  16. 16.
    L. Helmink, M.P.A. Sellink, and F.W. Vaandrager. Proof-Checking a Data Link Protocol. In Henk Barendregt, Tobias Nipkow, editor, Workshop on Types for Proofs and Programs, volume 806 of LNCS, pages 127–165. Springer-Verlag, 1993.Google Scholar
  17. 17.
    A. Heyting. Intuitionism: An Introduction. North-Holland, 1971.Google Scholar
  18. 18.
    W.A. Howard. The formulae-as-types notion of constructions. In J.P. Seldin and J.R. Hindley, editors, to H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980. Unpublished 1969 Manuscript.Google Scholar
  19. 19.
    G. Huet and G. Plotkin, editors. Logical Frameworks. Cambridge University Press, May 1991.Google Scholar
  20. 20.
    Z. Luo. Computation and Reasoning: A Type Theory for Computer Science, volume 11 of International Series of Monographs on Computer Science. Oxford Science Publications, 1994.Google Scholar
  21. 21.
    L. Magnusson. The implementation of ALF-a Proof Editor based on Martin-Löf's Monomorphic Type Theory with Explicit Substitution. PhD thesis, Chalmers University of Göteborg, 1994.Google Scholar
  22. 22.
    C. McLarty. Elementary Categories, Elementary Toposes. Oxford University Press, 1992.Google Scholar
  23. 23.
    P.-A. Melliès. Typed γ-calculi with explicit substitutions may not terminate. In Typed Lambda Calculi and Applications, number 902 in LNCS. Second International Conference TLCA'95, Springer-Verlag, 1995.Google Scholar
  24. 24.
    P. Nederpelt, J.H. Geuvers, and R.C. de Vrijer, editors. Selected Papers on Automath. North-Holland, 1994.Google Scholar
  25. 25.
    T. Nipkow, and K. Slind. IO Automata in Isabelle/HOL. In P Dybjer, B. Nordström, and J. Smith, editors, Workshop on Types for Proofs and Programs, number 996 in LNCS, pages 101–119. Springer-Verlag, 1994.Google Scholar
  26. 26.
    B. Nordström, K. Petersson, and J. Smith. Programming in Martin-Löf's Type Theory: An Introduction, volume 7 of International Series of Monographs on Computer Science. Oxford Science Publications, 1990.Google Scholar
  27. 27.
    S. Owre, S. Rajan, J.M. Rushby, N. Shankar, and M.K. Srivas. PVS: Combining specification, proof checking, and model checking. In Rajeev Alur and Thomas A. Henzinger, editors, Computer-Aided Verification, CAV '96, volume 1102 of Lecture Notes in Computer Science, pages 411–414, New Brunswick, NJ, July/August 1996. Springer-Verlag.Google Scholar
  28. 28.
    P. Martin-Löf. Intuitionistic Type Theory. Studies in Proof Theory. Bibliopolis, 1984.Google Scholar
  29. 29.
    C. Paulin-Mohring and B. Werner. Synthesis of ML programs in the system Coq. Journal of Symbolic Computation, 15:607–640, 1993.MATHMathSciNetGoogle Scholar
  30. 30.
    L. Paulson. Set theory for verification: from foundations to functions. Journal of Automatic Reasoning, 11(2):353–389, 1993.MATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    L. Paulson. The Isabelle reference manual. Technical Report 283, Computer Laboratory, University of Cambridge, 1993.Google Scholar
  32. 32.
    L. Paulson. Set theory for verification: induction and recursion. Journal of Automatic Reasoning, 15(3), 1995.Google Scholar
  33. 33.
    A. Ranta. Type-theoretical grammar. Oxford: Clarendon, 1994.MATHGoogle Scholar
  34. 34.
    P. Rudnicki. An overview of the Mizar project, 1992.Google Scholar
  35. 35.
    G. Sambin and J. Smith, editors. Twenty-Five Years of Constructive Type Theory. Oxford University Press, 1998.Google Scholar
  36. 36.
    A. Whitehead and B. Russel. Principia Mathematica. Cambridge University Press, 1910.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Personalised recommendations