Inductively defined types

  • Thierry Coquand
  • Christine Paulin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 417)


Positive Operator Type Theory Elimination Rule Inductive Type Computation Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Aczel. “The strength of Martin-Löf's intuitionistic type theory with one universe.” In the Proceedings of the Symposium on Mathematical Logic, Helsinki, 1977.Google Scholar
  2. [2]
    R. Backhouse. “On the meaning and construction of the rules in Martin-Löf's theory of types.” Technical Report CS 8606, University of Groningen, 1986.Google Scholar
  3. [3]
    E. Bishop. “Foundations of Constructive Analysis.” McGraw-Hill, New-York, 1967.Google Scholar
  4. [4]
    C. Böhm and A. Berarducci. “Automatic synthesis of typed A-programs on term algebras.” Theoretical Computer Science, 39, 1985.Google Scholar
  5. [5]
    A. Church. “A formulation of the simple theory of types.” Journal of Symbolic Logic 5, 1940.Google Scholar
  6. [6]
    Th. Coquand. “An introduction to type theory.” Course notes, Albi, 1989.Google Scholar
  7. [7]
    Th. Coquand. “An Analysis of Girard's Paradox.” Proceedings of the first Logic in Computer Science, Boston, 1986.Google Scholar
  8. [8]
    P. Dybjer. “Inductively Defined Types in Martin-Löf's Set Theory.” Unpublished manuscript, 1987.Google Scholar
  9. [9]
    P. Dybjer. “An inversion principle for Martin-Löf's type theory.” To appear in the proceedings of Bastad, 1989.Google Scholar
  10. [10]
    K. Gödel. “On a hitherto unexploited extension of the finitist viewpoint.” Translation by W. Hodge, appeared in Journal of Philosophical Logic 9 (1980).Google Scholar
  11. [11]
    D. Hilbert. “On the Infinite.” Published in Van Heijenoort.Google Scholar
  12. [12]
    P. Martin-Löf. “Notes on Constructive Mathematics.” Almqvist & Wiksell, Stockholm.Google Scholar
  13. [13]
    P. Martin-Löf. “Intuitionistic Type Theory.” Bibliopolis, 1980.Google Scholar
  14. [14]
    P. F. Mendler. “Inductive Definition in Type Theory.” Ph. D. Thesis, Cornell, 1987.Google Scholar
  15. [15]
    P.J. Landin. “The mechanical evaluation of expressions.” Comput. J. 6, 1964.Google Scholar
  16. [16]
    Z. Luo. “CC and its meta Theory.” LFCS report ECS-LFCS-88-57, Dept. of Computer Science, University of Edinburgh.Google Scholar
  17. [17]
    Z. Luo. “ECC, an Extended calculus of Constructions.” Proc. of the Fourth IEEE Symposium on Logics in Computer Science, June 1989, Asilomar, California, U.S.A.Google Scholar
  18. [18]
    Ch. Paulin-Mohring. “Extraction de programmes dans le Calcul des Constructions.” Thèse, Université Paris 7, 1989.Google Scholar
  19. [19]
    D. Normann. “Inductively and recursively defined types.” A seminar report, Department of Mathematics, University of Oslo, 1987.Google Scholar
  20. [20]
    L. C. Paulson. “A formulation of the Simple Theory of Types (for Isabelle).” Unpublished manuscript, Cambridge, 1989.Google Scholar
  21. [21]
    F. Pfenning and Ch. Paulin-Mohring. “Inductively Defined Types in the Calculus of Constructions.” To appear in the proceedings of MFPLS'89, 1989.Google Scholar
  22. [22]
    J.C. Reynolds. “Polymorphism is not Set-Theoretic.” Lecture Notes in Computer Science 173, Springer-Verlag, 1984.Google Scholar
  23. [23]
    B. Russell and A.N. Whitehead. “Principia Mathematica.” Volume 1,2,3 Cambridge University Press, 1912.Google Scholar
  24. [24]
    J.R. Shoenfield. “Mathematical Logic.” Addison-Wesley, 1967.Google Scholar
  25. [25]
    S.S. Wainer. “Slow Growing Versus Fast Growing.” Journal of Symbolic Logic, Volume 54, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Thierry Coquand
  • Christine Paulin

There are no affiliations available

Personalised recommendations