A modification of the λ-calculus as a base for functional programming languages

  • K. J. Berkling
  • E. Fehr
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)


Church's λ-calculus is modified by introducing a new mechanism, the lambda-bar operator “#”, which neutralizes the effect of one preceeding λ-binding. This operator can be used in such a way that renaming of bound variables in any reduction sequence can be avoided, with the effect that efficient interpreters with comparatively simple machine organization can be designed.

Any semantic model of the pure λ-calculus also serves as a model for this modified reduction calculus, which guarantees smooth semantical theories.

The Berkling Reduction Language BRL is a new functional programming language based upon this modification.


Denotational Semantic Reduction Term Functional Programming Language Substitution Operator Variable Conflict 
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]
    Backus, J.: “Can Programming Be Liberated from the von Neumann Style ?”, CACM 21 (8), pp. 613–641, (1978)MathSciNetCrossRefGoogle Scholar
  2. [2]
    Berkling, K. J.: “A symmetric complement to the Lambda calculus”, Interner Bericht ISF-76-7, GMD, D-5205 St. Augustin 1, 1976Google Scholar
  3. [3]
    Berkling, K. J.: “Reduction languages for reduction machines”, Interner Bericht ISF-76-8, GMD, D-5205 St. Augustin 1, 1976Google Scholar
  4. [4]
    De Bruijn, N. G.: “Lambda-calculus notation with nameless dummies, a tool for automatic formula manipulation”, Indag. Math. 34Google Scholar
  5. [5]
    Fehr, E.: “The lambda-semantics of LISP”, Schriften zur Informatik und Mathematik, Bericht Nr. 72, RWTH Aachen, Mai 1981Google Scholar
  6. [6]
    Gordon, M.: “Operational reasoning and denotational semantics” Stanford Artificial Intelligence Laboratory, Memo AIM-264, 1975Google Scholar
  7. [7]
    Mc Gowan, C.:“The modified SECD-machine” Second ACM Symposium on Theory of Computing, 1970Google Scholar
  8. [8]
    Hommes, F.: “The internal structure of the reduction machine”, Interner Bericht ISF-77-3, GMD, D-5205 St. Augustin 1, 1977Google Scholar
  9. [9]
    Hommes, F., Schlütter, H.: “Reduction machine system. User's guide” GMD-ISF, D-5205 St. Augustin 1, 1979Google Scholar
  10. [10]
    Kluge, W.E.: “The architecture of a reduction language machine hardware model,” Interner Bericht ISF-79-3, GMD, 5205 St. Augustin-1, 1979Google Scholar
  11. [11]
    Scott, D.: “Continuous lattices”, Proc. of Dalhousie Conf., Springer LNM No. 274, pp. 97–134, 1972Google Scholar
  12. [12]
    Scott, D.: “Data types as lattices”, SIAM J. Computing, Vol. 5.3, 1976MathSciNetCrossRefGoogle Scholar
  13. [13]
    Turner, D.A.: “A new Implementation Technique for Applicative Languages”, Software-Practice and Experience, Vol. 9, 31–49, (1979)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • K. J. Berkling
    • 1
  • E. Fehr
    • 2
  1. 1.Institut für InformationssystemforschungGMD-BonnDeutschland
  2. 2.Lehrstuhl für Informatik IIRWTH AachenDeutschland

Personalised recommendations