An extensional partial combinatory algebra based on λ-terms

  • Ramón Pino Perez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 520)


We build an extensional partial combinatory algebra on λ-terms. The main tool for our construction is the equality between two relations ∼c and ∼ on λ-terms. The first relation has been defined by Plotkin in [13]. The second relation looks like the bisimulation relation of Abramsky [1] but in the setting of eager evaluation. One consequence of this equality is that the algebra obtained is monotonic.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Abramsky, A., (1989), The Lazy Lambda Calculus. In ”Declarative Programming”. David Turner, editor. Addison-Wesley. To appear.Google Scholar
  2. [2]
    Abramsky, A., Ong C.-H. L. (1989), Full Abstraction in the Lazy Lambda Calculus. To appear.Google Scholar
  3. [3]
    Barendregt, H. (1984), ”The Lambda Calculus: Its Syntax and Semantics”. North-Holland. Amsterdam. 1984.Google Scholar
  4. [4]
    Beeson, M. (1985), “Foundations of Constructive Mathematics”. Springer-Verlag. 1985Google Scholar
  5. [5]
    Berry, G. (1981) ”Some Syntactic and Categorical Constructions of Lambda Calculus Models”. Rapport de Recherche de L'Institut National de Recherche en Informatique et Automatique (INRIA). Rocquancourt. 1981.Google Scholar
  6. [6]
    Bethke, I. (1988), ”Notes on Partial Combinatory Algebras”. Ph.D. Thesis. University of Amsterdam. 1988.Google Scholar
  7. [7]
    Hoofman, R., Schellinx, H. (1991) Collapsing Graph Models by Preorders. ITLI Prepublication Series ML-91-04. Amsterdam. 1991.Google Scholar
  8. [8]
    Egidi, L., Honsell, F., Ronchi de la Rocca, S. The for Lazy call-by-value λ-calculus. Presented at Jumelage on typed lambda calculus, Paris, 1–5 February 1991.Google Scholar
  9. [9]
    Moggi, E. (1986), Categories of partial morphisms and the Partial Lambda Calculus. In ”Proceedings of the Workshop on Category Theory and Computer Programming”. Guilford 1985. Lecture Notes in Computer Science vol. 240. Springer-Verlag, 1986.Google Scholar
  10. [10]
    Moggi, E. (1988), The Partial Lambda Calculus, Ph.D. Thesis, University of Edinburgh. 1988.Google Scholar
  11. [11]
    Pino Pérez, R. (1990), Contribution à l'étude du Lambda Calcul Partiel. Forthcoming thesis (draft). Université Paris 7.Google Scholar
  12. [12]
    Pino Pérez, R. (1991), Semantics of the partial lambda calculus. Rapport de recherche LIFL. Université Lille I. 1991.Google Scholar
  13. [13]
    Plotkin, G. (1975), Call-by-name, call-by-value and the λ-calculus. Theoretical Computer Science (1), 1975.Google Scholar
  14. [14]
    Tarski, A. (1955) A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics. Vol. 5, pp 285–309.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Ramón Pino Perez
    • 1
  1. 1.Université Lille I and LIFL U.A. 369 du CNRS Cité ScientifiqueVilleneuve d'Ascq CedexFrance

Personalised recommendations