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Subtyping and Parametricity (1993)

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by Gordon Plotkin , Luca Cardelli
Citations:11 - 2 self
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BibTeX

@MISC{Plotkin93subtypingand,
    author = {Gordon Plotkin and Luca Cardelli},
    title = {Subtyping and Parametricity},
    year = {1993}
}

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Abstract

In this paper we study the interaction of subtyping and parametricity. We describe a logic for a programming language with parametric polymorphism and subtyping. The logic supports the formal definition and use of relational parametricity. We give two models for it, and compare it with other formal systems for the same language. In particular, we examine the "Penn interpretation" of subtyping as implicit coercion. Without subtyping, parametricity yields, for example, an encoding of abstract types and of initial algebras, with the corresponding proof principles of simulation and induction. With subtyping, we obtain partially abstract types and certain initial order-sorted algebras, and may derive proof principles for them. 1 Introduction A function is polymorphic if it works on inputs of several types. We may distinguish various notions of polymorphism, particularly parametric polymorphism (e.g. [Rey83]) and subtype polymorphism (e.g. [CW85]). These may exist in isolation, as in ML [MT...

Citations

1497 The Definition of Standard ML - Milner, Tofte, et al. - 1997
727 On understanding types, data abstraction, and polymorphism - Cardelli, Wegner - 1985
267 G.D.: Abstract types have existential types - Mitchell, Plotkin - 1988
237 Inheritance is not subtyping - Cook, Hill, et al. - 1990
221 Interprétation fonctionnelle et élimination des coupures de l’arithmétique d’ordre supérieur. Thèse de Doctorat d’ État, Université de Paris VII - Girard - 1972
203 Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance - Goguen, Meseguer - 1987
112 A logic for parametric polymorphism - Plotkin, Abadi - 1993
107 An extension of System F with subtyping - Cardelli, Martini, et al. - 1994
104 Inheritance as implicit coercion - Breazu-Tannen, Coquand, et al. - 1991
85 A modest model of records, inheritance and bounded quantification - Bruce, Longo - 1990
53 Types, abstraction, and parametric polymorphism, part 2 - Ma, Reynolds - 1992
44 Functorial polymorphism - Bainbridge, Freyd, et al. - 1990
37 Proof Theoretic Studies about a Minimal Type System Integrating Inclusion and Parametric Polymorphism - Ghelli - 1990
35 Extensible records in a pure calculus of subtyping - Cardelli - 1994
26 Categorical data types in parametric polymorphism - Hasegawa - 1994
13 Pierre-Louis Curien. Formal parametric polymorphism - Abadi, Cardelli - 1993
7 Parametricity as subtyping - Ma - 1992
3 The maximum consistent theory of the second order fij-lambda calculus - Moggi - 1986
1 type checking in a staticallytyped object-oriented programming language - Safe - 1993
1 Decidability and confluence of βηtop≤ reduction - Curien, Ghelli - 1994
1 Decidability and confluence of fijtop reduction - Curien, Ghelli - 1994
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