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Uniformly applicative structures, a theory of computability and polyadic functions

  • Patrick Bellot
  • Véronique Jay
Session 9 Semantics
Part of the Lecture Notes in Computer Science book series (LNCS, volume 338)

Abstract

This article describes a Computability theory developed from the theory of URS described by E.G. Wagner and H.R. Strong and a Combinatory theory named TGE presented by the authors. Its main contribution is that the theory handles polyadicity as a primitive notion and allows a natural representation of functions with variable arity, that is functions which can be applied to sequences of arguments of any length. Aside from classical computability results, we prove a General Abstraction theorem which allows us to construct representations for a large class of functions with variable arity.

Keywords

computability recursive function algorithmic abstraction definability representability polyadicity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Patrick Bellot
    • 1
  • Véronique Jay
    • 2
  1. 1.Centre Scientifique de Paris, Compagnie IBM-FranceParis Cedex 01France
  2. 2.LITP - Paris 6, Université Pierre et Marie CurieParis Cedex 05France

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