Advertisement

Limits of ML-definability

  • Stefan Kahrs
Typing and Structuring Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1140)

Abstract

It is well-known that the type system of ML is overly restrictive in its handling of recursion: certain intuitively sound terms do not pass ML's type-check. We formalise this intuition and show that the restriction is semantical: there are computable (semantical) functions which cannot be expressed by well-typed (syntactical) terms.

Keywords

definability polymorphism recursion ML completeness 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Cardone and M. Coppo. Two extensions of Curry's type inference system. In P. Odifreddi, editor, Logic and Computer Science, pages 19–76. Academic Press, 1990.Google Scholar
  2. 2.
    N. G. de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation. Indagationes Mathematicae, 34:381–392, 1972.Google Scholar
  3. 3.
    Nachum Dershowitz and Jean-Pierre Jouannaud. Rewrite systems. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 6, pages 244–320. Elsevier, 1990.Google Scholar
  4. 4.
    Fritz Henglein. Type inference with polymorphic recursion. ACM Transactions on Programming Languages and Systems, 15(2):253–289, 1993.Google Scholar
  5. 5.
    Stefan Kahrs. About the completeness of type systems. In Proceedings ESSLLI Workshop on Observational Equivalence and Logical Equivalence, 1996. (to appear).Google Scholar
  6. 6.
    Robin Milner, Mads Tofte, and Robert Harper. The Definition of Standard ML. MIT Press, 1990.Google Scholar
  7. 7.
    Mads Tofte. Operational Semantics and Polymorphic Type Inference. PhD thesis, University of Edinburgh, 1988. CST-52-88.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Stefan Kahrs
    • 1
  1. 1.Laboratory for Foundations of Computer ScienceUniversity of EdinburghEdinburghUK

Personalised recommendations