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Subtyping and Parametricity Gordon Plotkin \Lambda Mart'in Abadi y Luca Cardelli y

Summary: Subtyping and Parametricity
Gordon Plotkin \Lambda Mart'in Abadi y Luca Cardelli y
In this paper we study the interaction of subtyping
and parametricity. We describe a logic for a program­
ming language with parametric polymorphism and sub­
typing. 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 exam­
ple, an encoding of abstract types and of initial alge­
bras, with the corresponding proof principles of simu­
lation and induction. With subtyping, we obtain par­
tially abstract types and certain initial order­sorted al­
gebras, 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 no­


Source: Abadi, Martín - Department of Computer Science, University of California at Santa Cruz


Collections: Computer Technologies and Information Sciences