Sharing in nondeterminism

  • Egidio Astesiano
  • Gerardo Costa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 71)


We consider a language of typed λ-expressions with primitives including nondeterministic choice operators. Starting from the natural idea that a first order nondeterministic procedure should define a one-many function, we give a reduction system in which ground arguments are shared, in order to avoid some unnatural consequences due to unrestricted application of the copy-rule. This is achieved by extending the language and modifying the usual β-rule. Then we discuss how to define a correspon ding denotational semantics, establishing in particular the existence of a model which is fully abstract w.r.t. the operational semantics.


Functional Model Operational Semantic Reduction System Reduction Rule Denotational Semantic 
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  1. A.
    A.Arnold, Schémas de programmes récursifs non déterministes avec appel syncrone, Proc. 3e Colloque International sur la Programmation, Paris 1978, Dunod, 126–140.Google Scholar
  2. AC1.
    E.Astesiano, G.Costa, On algebraic semantics of polyadic recursive schemas, Proc. 2e Colloque sur les Arbres an Algèbre et en Programmation, Lille 1977, Université de Lille, 29–83.Google Scholar
  3. AC2.
    = = = Nondeterminism and fully abstract models, 1978, submitted for publication.Google Scholar
  4. AC3.
    = = = Fully abstract semantics for nondeterministic typed λ-s-calculi, 1989, to appear.Google Scholar
  5. AN1.
    A.Arnold, M.Nivat,Non deterministic recursive program schemas, Proc. FCT 1977, Lecture Notes in C.S. 56, Springer, 12–21.Google Scholar
  6. AN2.
    = = = Interpretations métriques des schémas de programme, Proc. 1er Colloque AFCET-SMF de Math. Appliquées, Ecole Polytechnique, 1978, Vol.1, 191–208.Google Scholar
  7. B.
    G.Berry, Stable models of typed λ-calculi, Proc. 5th ICALP, Udine 1978, Lecture Notes in C.S. 62, Springer, 72–89.Google Scholar
  8. HA1.
    M.Hennessy, E.A.Ashcroft, The semantics of nondeterminism, Proc. 3rd ICALP, Edinburg 1976, Edinburg University Press, 478–493.Google Scholar
  9. HA2.
    = = = Parameter-passing mechanism and nondeterminism, Proc. 9th ACM Symp. on the Theory of Comput., 1977, 306–311.Google Scholar
  10. L.
    J.J.Lévy, Le problème du partage dans l'évaluation des λ-expressions, Proc. 1er Colloque AFCET-SMF de Math. Appliquées, Ecole Polytechnique, 1978.Google Scholar
  11. M1.
    R.Milner, Processes, a mathematical model for computing agents, Logic Coll. 1973, Studies in Logic and the Foundations of Mathematics 80, North-Holland & American Elsevier, 1975, 157–174.Google Scholar
  12. M2.
    = = =Fully abstract models of typed λ-calculi, T.C.S. 4 (1977) 1–22.Google Scholar
  13. P1.
    G. Plotkin, A powerdomain construction, Siam J. Comput. 5 (1976) 452–487.Google Scholar
  14. P2.
    = = =LCF as a programming language, T.C.S. 5 (1977) 223–255.Google Scholar
  15. PMT.
    G.Pacini, C.Montangero, F.Turini, Graph representation and computation rules for a typeless recursive language, Proc. 2nd ICALP, Saarbrücken, 1974, Lecture Notes in C.S. 14, Springer, 157–169.Google Scholar
  16. Sm.
    M.B. Smyth, Power domains, JCSS 16 (1978) 23–36.Google Scholar
  17. V.
    J. Vuillemin, Correct and optimal implementation of recursion in a simple programming language, JCSS 9 (1974) 332–354.Google Scholar
  18. W.
    C.P.Wadsworth, Semantics and pragmatics of the λ-calculus, Ph.D. Thesis, University of Oxford, 1971.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1979

Authors and Affiliations

  • Egidio Astesiano
    • 1
  • Gerardo Costa
    • 1
  1. 1.Istituto di Matematica dell'Università di GenovaGenovaItaly

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