Closed Freyd- and κ-categories

  • John Power
  • Hayo Thielecke
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1644)


We give two classes of sound and complete models for the computational λ-calculus, or λc-calculus. For the first, we generalise the notion of cartesian closed category to that of closed Freyd-category. For the second, we generalise simple indexed categories. The former gives a direct semantics for the computational λ-calculus. The latter corresponds to an idealisation of stack-based intermediate languages used in some approaches to compiling.


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  1. [1]
    R. Douence and P. Fradet. A Taxonomy of Functional Language Implementations Part I: Call-by-Value, INRIA Research Report No 2783, 1995.Google Scholar
  2. [2]
    M. Hasegawa. Decomposing typed lambda calculus into a couple of categorical programming languages, Proc. CTCS, Lect. Notes in Computer Science 953 (1995).Google Scholar
  3. [3]
    A. Jeffrey. Premonoidal categories and a graphical view of programs.
  4. [4]
    G.M. Kelly. The basic concepts of enriched categories. CUP (1982).Google Scholar
  5. [5]
    X. Leroy. The ZINC experiment: an economical implementation of the ML language. Technical Report RT-0117, INRIA, Institut National de Recherche en Informatique et en Automatique, 1990.Google Scholar
  6. [6]
    P.B. Levy. Call-by-push-value: a subsuming paradigm (extended abstract). In J.-Y Girard, editor, Typed Lambda-Calculi and Applications, Lecture Notes in Computer Science, April 1999.Google Scholar
  7. [7]
    E. Moggi. Computational Lambda calculus and Monads, Proc. LICS 89, IEEE Press (1989) 14–23.Google Scholar
  8. [8]
    E. Moggi. Notions of computation and monads, Information and Computation 93 (1991) 55–92.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    A.J. Power. Premonoidal categories as categories with algebraic structure (submitted).Google Scholar
  10. [10]
    A.J. Power and E.P. Robinson. Premonoidal categories and notions of computation, Proc. LDPL’ 96, Math Structures in Computer Science.Google Scholar
  11. [11]
    A.J. Power and H. Thielecke. Environments, Continuation Semantics and Indexed Categories, Proc. Theoretical Aspects of Computer Science, Lecture Notes in Computer Science (1997) 391–414.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • John Power
    • 1
  • Hayo Thielecke
    • 2
  1. 1.University of EdinburghEdinburghScotland
  2. 2.QMW, University of LondonLondonUK

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