NDLI: Non-parametric parametricity

Content Provider	ACM Digital Library
Author	Rossberg, Andreas Neis, Georg Dreyer, Derek
Abstract	Type abstraction and intensional type analysis are features seemingly at odds-type abstraction is intended to guarantee parametricity and representation independence, while type analysis is inherently non-parametric. Recently, however, several researchers have proposed and implemented "dynamic type generation" as a way to reconcile these features. The idea is that, when one defines an abstract type, one should also be able to generate at run time a fresh type name, which may be used as a dynamic representative of the abstract type for purposes of type analysis. The question remains: in a language with non-parametric polymorphism, does dynamic type generation provide us with the same kinds of abstraction guarantees that we get from parametric polymorphism? Our goal is to provide a rigorous answer to this question. We define a step-indexed Kripke logical relation for a language with both non-parametric polymorphism (in the form of type-safe cast) and dynamic type generation. Our logical relation enables us to establish parametricity and representation independence results, even in a non-parametric setting, by attaching arbitrary relational interpretations to dynamically-generated type names. In addition, we explore how programs that are provably equivalent in a more traditional parametric logical relation may be "wrapped" systematically to produce terms that are related by our non-parametric relation, and vice versa. This leads us to a novel "polarized" form of our logical relation, which enables us to distinguish formally between positive and negative notions of parametricity.
Starting Page	135
Ending Page	148
Page Count	14
File Format	PDF MP4
ISSN	03621340 15581160
DOI	10.1145/1631687.1596572
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	44
Issue Number	9
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Parametricity Representation independence Type-safe cast Step-indexed logical relations Intensional type analysis
Content Type	Audio Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

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