Cartesian closed categories and lambda-calculus

  • Gérard Huet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 242)


Inference Rule Category Theory Equational Theory Sequent Calculus Combinatory Logic 
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]
    H. Barendregt “The Lambda-Calculus: Its Syntax and Semantics.” North-Holland (1980).Google Scholar
  2. [2]
    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
  3. [3]
    G. Cousineau, P.L. Curien and M. Mauny “The Categorical Abstract Machine.” In Functional Programming Languages and Computer Architecture, Ed. J. P. Jouannaud, Springer-Verlag LNCS 201 (1985) 50–64.Google Scholar
  4. [4]
    Th. Coquand, G. Huet “Constructions: A Higher Order Proof System for Mechanizing Mathematics.” EUROCAL85, Linz, Springer-Verlag LNCS 203 (1985).Google Scholar
  5. [5]
    P. L. Curien “Categorical Combinatory Logic.” ICALP 85, Nafplion, Springer-Verlag LNCS 194 (1985).Google Scholar
  6. [6]
    P. L. Curien “Categorical Combinators, Sequential Algorithms and Functional Programming.” Monography to appear, Pitman (1985).Google Scholar
  7. [7]
    G. Gentzen “The Collected Papers of Gerhard Gentzen.” Ed. E. Szabo, North-Holland, Amsterdam (1969).Google Scholar
  8. [8]
    M. J. Gordon, A. J. Milner, C. P. Wadsworth “Edinburgh LCF” Springer-Verlag LNCS 78 (1979).Google Scholar
  9. [9]
    G. Huet “Confluent Reductions: Abstract Properties and Applications to Term Rewriting Systems.” J. Assoc. Comp. Mach. 27,4 (1980) 797–821.Google Scholar
  10. [10]
    G. Huet “Initiation à la Théorie des Catégories.” Polycopié de cours de DEA, Université Paris VII (Nov. 1985).Google Scholar
  11. [11]
    G. Huet. “Deduction and Computation.” in Fundamentals in Artificial Intelligence, Eds. W. Bibel and Ph. Jorrand, Springer-Verlag Lecture Notes in Computer Science vol. 232 (1986) 39–74.Google Scholar
  12. [12]
    G. Huet. “Formal Structures for Computation and Deduction.” In preparation.Google Scholar
  13. [13]
    H. Huwig and A. Poigné “A note on inconsistencies caused by fixpoints in a cartesian closed category.” Personal communication (April 1986).Google Scholar
  14. [14]
    L.S. van Benthem Jutting “The language theory of A, a typed λ-calculus where terms are types.” Personal communication (1984).Google Scholar
  15. [15]
    S.C. Kleene “Introduction to Meta-mathematics.” North Holland (1952).Google Scholar
  16. [16]
    J.W. Klop “Combinatory Reduction Systems.” Ph. D. Thesis, Mathematisch Centrum Amsterdam (1980).Google Scholar
  17. [17]
    D. Knuth, P. Bendix “Simple word problems in universal algebras”. In: Computational Problems in Abstract Algebra, J. Leech Ed., Pergamon (1970) 263–297.Google Scholar
  18. [18]
    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
  19. [19]
    J. Lambek and P. J. Scott “Aspects of Higher Order Categorical Logic.” Contemporary Mathematics 30 (1984) 145–174.Google Scholar
  20. [20]
    F. W. Lawvere “Diagonal Arguments and Cartesian Closed Categories.” in Category Theory, Homology Theory and their Applications II, Springer-Verlag Lect. Notes in Math. 92 (1969).Google Scholar
  21. [21]
    S. Mac Lane “Categories for the Working Mathematician.” Springer-Verlag (1971).Google Scholar
  22. [22]
    C. Mann “The Connection between Equivalence of Proofs and Cartesian Closed Categories.” Proc. London Math. Soc. 31 (1975) 289–310.Google Scholar
  23. [23]
    A. Poigné “On Semantic Algebras.” Universitat Dortmund (March 1983).Google Scholar
  24. [24]
    D. Prawitz “Natural Deduction.” Almquist and Wiskell, Stockolm (1965).Google Scholar
  25. [25]
    D. Scott “Relating Theories of the Lambda-Calculus.” 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
  26. [26]
    S. Stenlund “Combinators λ-terms, and proof theory.” Reidel (1972).Google Scholar
  27. [27]
    M. E. Szabo “Algebra of Proofs.” North-Holland (1978).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Gérard Huet
    • 1
  1. 1.InriaFrance

Personalised recommendations