A Calculus for Overloaded Functions with Subtyping

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 crucia...

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Bibliographic Details
Published in:Information and computation Vol. 117; no. 1; pp. 115 - 135
Main Authors: Castagna, G., Ghelli, G., Longo, G.
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 15.02.1995
Elsevier
Subjects:
Applied sciences
Computer Science
Computer science; control theory; systems
Exact sciences and technology
Mathematics
Programming theory
Theoretical computing
Functional language
Typing
Overload
Branch
Lambda calculus
Object oriented
Selection rule
ISSN:0890-5401, 1090-2651
Online Access:Get full text
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Summary: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 it 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 to 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 extensive stressed. We show that this calculus provides a foundation for types object-oriented languages which solves some of the problems of the standard record-based approach.
ISSN:0890-5401
1090-2651
DOI:10.1006/inco.1995.1033