Summary: Page 1
Formal Parametric Polymorphism
Martín Abadi Luca Cardelli Pierre­Louis Curien
Digital Equipment Corporation Digital Equipment Corporation CNRS
Systems Research Center Systems Research Center Ecole Normale Supérieure
Abstract
A polymorphic function is parametric if its behavior does not depend on the type at which it is instanti ­
ated. Starting with Reynolds's work, the study of parametricity is typically semantic. In this paper, we de ­
velop a syntactic approach to parametricity, and a formal system that embodies this approach, called system
R . Girard's system F deals with terms and types; R is an extension of F that deals also with relations be ­
tween types.
In R , it is possible to derive theorems about functions from their types, or ``theorems for free'', as
Wadler calls them. An easy ``theorem for free'' asserts that the type "(X)X®Bool contains only constant
functions; this is not provable in F. There are many harder and more substantial examples. Various
metatheorems can also be obtained, such as a syntactic version of Reynolds's abstraction theorem.

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1. Explicit relations
A polymorphic function is parametric if its behavior does not depend on the type at which it is instanti ­
ated [Strachey 1967] . A function that reverses lists, for example, is parametric because it does not look at

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

Collections: Computer Technologies and Information Sciences