Skip to main content
SpringerLink
Log in

Sur l'analogie entre les propositions et les types

  • Conference paper
  • First Online:
Combinators and Functional Programming Languages (LITP 1985)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 242))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.B. Andrews. “Resolution in Type Theory.” Journal of Symbolic Logic 36,3 (1971), 414–432.

    Google Scholar 

  2. R. Backhouse. “Algorithm development in Martin-Löf's type theory.” University of Essex (July 1984).

    Google Scholar 

  3. H. Barendregt “The lambda-Calculus: Its Syntax and Semantics.” North-Holland (1980).

    Google Scholar 

  4. E. Bishop. “Foundations of Constructive Analysis”. McGraw-Hill, New-York (1967).

    Google Scholar 

  5. N.G. de Bruijn “Lambda-Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem.” Indag. Math. 34,5 (1972), 381–392.

    Google Scholar 

  6. N.G. de Brujin “A survey of the project Automath.” in Curry Volume, Acc. Press (1980)

    Google Scholar 

  7. A. Church “A formulation of the simple theory of types” Journal of Symbolic Logic (1940), 56–68

    Google Scholar 

  8. R.L. Constable, J.L. Bates. “The Nearly Ultimate Pearl.” Dept. of Computer Science, Cornell University. (Dec. 1983).

    Google Scholar 

  9. Th. Coquand “Une Theorie des Constructions” Thèse de 3eme cycle, Paris VII (1985)

    Google Scholar 

  10. Th. Coquand “An analysis of Girard's Paradox” Submited to the Symposium on Logic and Computer Science, 86

    Google Scholar 

  11. Th. Coquand, G. Huet “Constructions: A Higher Order Proof System for Mechanizing Mathematics.” EUROCAL85, Linz, Springer-Verlag LNCS 203 (1985).

    Google Scholar 

  12. Th. Coquand, G. Huet “Concepts Mathématiques et Informatiques formalisés dans le Calcul des Constructions” Papier presente au Colloque de Logique d'Orsay (1985)

    Google Scholar 

  13. H. B. Curry, R. Feys. “Combinatory Logic Vol. I.” North-Holland, Amsterdam (1958).

    Google Scholar 

  14. L. Damas, R. Milner. “Principal type-schemas for functional programs.” Edinburgh University (1982).

    Google Scholar 

  15. J.Y. Girard “Interprétation fonctionnelle et élimination des coupures de l'arithmetique d'ordre supérieur” These d'Etat, Paris VII (1972)

    Google Scholar 

  16. S. Fortune, D. Leivant, M. O'Donnell. “The Expressiveness of Simple and Second-Order Type Structures.” Journal of the Assoc. for Comp. Mach., 30,1, (Jan. 1983) 151–185.

    Google Scholar 

  17. Ch. Goad “Computational uses of the manipulation of formal proofs” Ph. D., Stanford University (1980)

    Google Scholar 

  18. R. Harrop “Concerning formulas of the type A ⇒ A ⋁ B, A ⇒ ∃x.B(x) in intuitionnistic formal systems” Journal of Symbolic Logic, vol. 25 (1960), 27–32

    Google Scholar 

  19. W. A. Howard. “The formulæ-as-types notion of construction.” Unpublished manuscript (1969). Reprinted in to H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Eds J. P. Seldin and J. R. Hindley, Academic Press (1980).

    Google Scholar 

  20. S.C. Kleene. “Introduction to Meta-mathematics.” North Holland (1952).

    Google Scholar 

  21. S.C. Kleene “Realizability: a retrospective survey” L.N. 337, Cambridge Summer School in Mathematical Logic (1971)

    Google Scholar 

  22. G. Kreisel. “On the interpretation of nonfinitist proofs, Part I, II.” JSL 16 (1952, 1953).

    Google Scholar 

  23. J. Lambek. “From Lambda-calculus to Cartesian Closed Categories.” in To H. B. Curry: Essays on Combinatory Logic, Lambda-calculus and Formalism, Eds. J. P. Seldin and J. R. Hindley, Academic Press (1980).

    Google Scholar 

  24. P. Martin-Löf “intuitionistic Type Theory” Bibliopolis, (1980)

    Google Scholar 

  25. A.R. Meyer and J.C. Mitchell “Second-order Logical Relations” extended abstract (1985)

    Google Scholar 

  26. R. Milner “A theory of type polymorphism in programming” JCSS 17(3), 348–375 (1978)

    Google Scholar 

  27. G.C. Mints “E-Theorems” J. Soviet Math. 8, 323–329 (1978)

    Google Scholar 

  28. J.C. Mitchell “Lambda Calculus Models of Typed Programming langages” Ph. D. thesis, M.I.T. (1984)

    Google Scholar 

  29. C. Mohring. “Exemples de Développement de Programmes dans la Théorie des Constructions.” Rapport de DEA, Université d'Orsay (Sept 85).

    Google Scholar 

  30. J.C. Reynolds “Polymorphism is not Set-Theoretic” Lecture Notes in Computer Science 173, Springer-Verlag, 1984

    Google Scholar 

  31. B. Russel and A.N. Whitehead “Principia Mathematica” Volume 1,2,3 Cambridge University Press (1912)

    Google Scholar 

  32. J.R. Shoenfield “Mathematical Logic” Addison-Wesley (1967)

    Google Scholar 

  33. W. Tait. “Intensional interpretations of functionals of finite type I.” J. of Symbolic Logic 32 (1967) 198–212.

    Google Scholar 

  34. G. Werner “Méthodes et Problèmes de la synthèse de programmes dans un univers typé” Université de Lille I (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CMU and INRIA, France

    Thierry Coquand

Authors
  1. Thierry Coquand
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Guy Cousineau Pierre-Louis Curien Bernard Robinet

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Coquand, T. (1986). Sur l'analogie entre les propositions et les types. In: Cousineau, G., Curien, PL., Robinet, B. (eds) Combinators and Functional Programming Languages. LITP 1985. Lecture Notes in Computer Science, vol 242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17184-3_40

Download citation

  • DOI: https://doi.org/10.1007/3-540-17184-3_40

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17184-3

  • Online ISBN: 978-3-540-47253-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation