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A Calculus for Overloaded Functions with Subtyping

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Fully Integrated Data Environments

Part of the book series: Esprit Basic Research Series ((ESPRIT BASIC))

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Abstract

We present a simple extension of typed λ-calculus where functions can be overloaded by putting different “branches of code” together. When the function is applied, the branch to execute is chosen according to a particular selection rule which depends on the type of the argument. The crucial feature of the present approach is that the branch selection depends on the “run-time type” of the argument, which may differ from its compile-time type, because of the existence of a subtyping relation among types. Hence overloading cannot be eliminated by a static analysis of code, but is an essential feature to be dealt with during computation. We obtain in this way a type-dependent calculus, which differs from the various λ-calculi where types do not play any role during computation. We prove Confluence and a generalized Subject-Reduction theorem for this calculus. We prove Strong Normalization for a “stratified” subcalculus. The definition of this calculus is guided by the understanding of object-oriented features and the connections between our calculus and object-orientedness are extensively stressed. We show that this calculus provides a foundation for typed object- oriented languages which solves some of the problems of the standard record-based approach.

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Authors and Affiliations

  1. LIENS(CNRS)-DMI, 45 rue d’Ulm, Paris, France

    Giuseppe Castagna & Giuseppe Longo

  2. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125, Pisa, Italy

    Giorgio Ghelli

Authors
  1. Giuseppe Castagna
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  2. Giorgio Ghelli
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  3. Giuseppe Longo
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Editor information

Editors and Affiliations

  1. Department of Computing Science, University of Glasgow, 8-17 Lilybank Gardens, G12 8RZ, Glasgow, UK

    Malcolm P. Atkinson  & Ray Welland  & 

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Castagna, G., Ghelli, G., Longo, G. (2000). A Calculus for Overloaded Functions with Subtyping. In: Atkinson, M.P., Welland, R. (eds) Fully Integrated Data Environments. Esprit Basic Research Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59623-0_11

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  • DOI: https://doi.org/10.1007/978-3-642-59623-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-64055-1

  • Online ISBN: 978-3-642-59623-0

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