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An abstract notion of application

  • Pietro Di Gianantonio
  • Furio Honsell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)

Abstract

Many concrete notions of function application, suitable for interpreting typed lambda calculi with recursive types, have been introduced in the literature. These arise in different fields such as set theory, multiset theory, type theory and functor theory and are apparently unrelated. In this paper we introduce the general concept of applicative exponential structure and show that it subsumes all these notions. Our approach is based on a generalization of the notion of intersection type. We construe all these structures in a finitary way, so as to be able to utilize uniformly a general form of type assignment system for defining the interpretation function. Applicative exponential structures are just combinatory algebras, in general. Our approach suggests a wide variety of entirely new concrete notions of function application: e.g. in connection with boolean sets. Applicative exponential structures can be used for modeling various forms of non-deterministic operators.

Keywords

Boolean Algebra Combinatory Structure Heyting Algebra Filter Model Denotational Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Pietro Di Gianantonio
    • 1
  • Furio Honsell
    • 1
  1. 1.Dipartimento di Matematica e InfonnaticaUniversità di UdineUdineItaly

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