Decidability of all minimal models

  • Vincent Padovani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1158)

Abstract

We consider a simply typed λ-calculus with constants of ground types, and assume that for one ground type o, there are finitely many constants of type o. We call minimal model the quotient by observational equivalence of the set of all closed terms whose type is of terminal subformula o. We show that this model is decidable: all classes of any given type are recursively representable, and observational equivalence on closed terms is a decidable relation. In particular, this result solves the question raised by R.Statman on the decidability of this model in the case of a unique ground type and two constants.

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References

  1. 1.
    Barendregt, H.: The Lambda Calculus, its Syntax and Semantics. North Holland (1981), (1984).Google Scholar
  2. 2.
    Dowek, G.: Third Order Matching is Decidable. Proceedings of Logic in Computer Science, Annals of Pure and Applied Logic (1993).Google Scholar
  3. 3.
    Hindley, J.R., Seldin, J.P.: Introduction to Combinators and λ-Calculus. Cambridge University Press, Oxford (1986).Google Scholar
  4. 4.
    Krivine J.L.: Lambda Calculus, Types and Models. Ellis Horwood series in computer and their applications (1993) 1–66.Google Scholar
  5. 5.
    Loader, R.: The undecidability of λ-definability. Manuscript (1993).Google Scholar
  6. 6.
    Padovani, V.: On Equivalence Classes of Interpolation Equations. Proceedings of the second international conference on typed lambda-calculi and applications, Lecture Notes in Computer Science 902 (1995) 335–349.Google Scholar
  7. 7.
    Padovani, V.: Filtrage d'Ordre Supérieur. Thèse de doctorat, Université Paris VII (1996).Google Scholar
  8. 8.
    Padovani, V.: Decidability of Fourth Order Matching. Manuscript (1996).Google Scholar
  9. 9.
    Statman, R.: Completeness, invariance and λ-definability. Journal of Symbolic Logic, 47, 1 (1982).Google Scholar
  10. 10.
    Statman, R., Dowek, G.: On Statman's completeness theorem. Technical Report, CMU-CS-92-152, University of Carnegie Mellon (1992).Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Vincent Padovani
    • 1
  1. 1.Equipe de Logique MathématiqueUniversité PARIS VII-C.N.R.S U.R.A. 753Paris Cedex 05France

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