Completeness results for a polymorphic type system

  • M. Coppo
  • E. Giovannetti
Contributed Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 159)


An interesting notion of polymorphism is the one introduced in the language ML (/GMW/). Its soundness has been proved in /MIL/ for a subset of ML based on λ-calculus plus constants. A partial completeness result for the same language has been given in /COP/. The aim of this paper is to extend the above results to a language including also Cartesian product and disjoint sum. The extension is not trivial, owing to difficulties introduced mainly by disjoint sum. Moreover a semantic characterization of typed terms is given.


Induction Hypothesis Type Variable Denotational Semantic Assignment Rule Type Assignment 
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  1. /BEN/.
    C. Ben-Yelles, Type Assignment in the Lambda-Calculus: Syntax and Semantics, Ph.D. Thesis, University of Wales, Swansea, 1979.Google Scholar
  2. /COP/.
    M. Coppo, On the semantics of Polymorphism, Internal Report of I.S.I., University of Turin, 1982 (to appear in Acta Informatica).Google Scholar
  3. /DM/.
    L. Damas and R. Milner, Principal Type-Schemes for Functional Programs, Proc. 9th ACM Symposium on Principles of Programming Languages, Albuquerque, 1982.Google Scholar
  4. /GMW/.
    M.J. Gordon, A. J. Milner and C.P. Wadsworth, Edinburgh LCF, LNCS 78, Springer-Verlag, 1979.Google Scholar
  5. /MIL/.
    R. Milner, A Theory of Type Polymorphism in Programming, J. Comput. Sys. Sci. 17 (1978), 348–375.CrossRefGoogle Scholar
  6. /PLO/.
    G. Plotkin, Tω as a Universal Domain, J. Comput. Sys. Sci. 17 (1978), 209–236.CrossRefGoogle Scholar
  7. /STO/.
    J. Stoy, Denotational Semantics, MIT Press, 1977.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • M. Coppo
    • 1
  • E. Giovannetti
    • 2
  1. 1.I.S.I. — Università di TorinoTorino
  2. 2.CSELTTorino

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