The disjunctive constrained lambda calculus

  • Luis Mandel
  • María Victoria Cengarle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1181)


In previous works a calculus which extends the traditional lambda calculus by the addition of constraints was presented. The constraints can be used passively for restricting the range of variables and actively for computing solutions of goals. Here an extension of that calculus is presented, which is obtained by adding existential quantifiers and new rules for handling disjunctive terms and multiple solutions. The problem of shared variables is avoided by choosing a call-by-value application policy. The overall result is a very smoothly working language. The calculus satisfies the Church-Rosser property; the normal forms are given. Finally typical examples are presented.


lambda calculus constraints multiple solutions denotational semantics functional programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Astesiano and G. Costa. Sharing in Nondeterminism. In Proc. of the 6th Int. Conference on Automata, Languages and Programming, pages 1–15, July 1979.Google Scholar
  2. 2.
    H. P. Barendregt. Lambda Calculi with Types. In Handbook of Logic in Computer Science, chapter 13, pages 117–309. Oxford University Press, 1992.Google Scholar
  3. 3.
    M. V. Cengarle and L. Mandel. Finite Domains in the Constrained Lambda Calculus. In Proc. of the Post-Conference Workshop on Constraints, Databases and Logic Programming. Int. Logic Programming Symposium, pages 75–89, Dec 1995.Google Scholar
  4. 4.
    J. N. Crossley, L. Mandel, and M. Wirsing. Untyped Constrained Lambda Calculus. Technical Report Number 9318, Ludwig-Maximilians-Universität München, October 1993. 48 pages.Google Scholar
  5. 5.
    J. N. Crossley, L. Mandel, and M. Wirsing. First Order Constrained Lambda Calculus. In Proceedings of the Conference Frontiers on Combining Systems (FroCoS), March 27–29 1996. 17 pages.Google Scholar
  6. 6.
    A. Knapp and L. Mandel. A Rewriting System with Explicit Substitutions for the First Order Constrained Lambda Calculus. Interne Reports der FG Programmier-systeme FR I-Passau-1994-094, FORWISS (Universität Passau), 1994.Google Scholar
  7. 7.
    H. C. Lock, A. Mück, and T. Streicher. A tiny functional logic constraint language and its continuation semantics. In ESOP '94, Edinburgh, LNCS 788, April 1994.Google Scholar
  8. 8.
    M. G. Main. A Powerdomain Primer. Bulletin of the EATCS, 33, Oct 1987.Google Scholar
  9. 9.
    L. Mandel. Constrained Lambda Calculus. PhD thesis, Ludwig-Maximilians-Universität München, December 1995. 213 pages.Google Scholar
  10. 10.
    R. Paterson. A Tiny Functional Language with Logical Features. In Declarative Programming, Sasbachwalden, 1991.Google Scholar
  11. 11.
    G. D. Plotkin. A powerdomain construction. Theoretical Computer Science, 5(3):452–487, September 1976.Google Scholar
  12. 12.
    M. Smyth. Power Domains. Journal of Computing and System Sciences, 16(1):23–26, 1978.Google Scholar
  13. 13.
    H. Søndergaard and P. Sestoft. Nondeterminism in Functional Languages. The Computer Journal, 35(5):514–523, July 1992.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Luis Mandel
    • 1
  • María Victoria Cengarle
    • 1
  1. 1.Institut für InformatikLudwig-Maximilians-Universität MünchenMunichGermany

Personalised recommendations