Parametricity as isomorphism

Parametricity as Isomorphism

We investigatea simple form of parametricity, based on adding \abstract" copies of pre-existing types. Connections are made with the Reynolds-Ma theory of parametricity by logical relations, with the theory of parametricity via dinaturality, and with the categorical notion of equivalence.

Parametricity as Subtyping (preliminary Report)

A polymorphic function is parametric if it has uniform behavior for all type parameters. This property is useful when writing, reasoning about, and compiling functional programs. We show how to syntactically deene and reason about parametricity in a language with intersection types and bounded polymorphism. Within this framework, parametricity is subtyping, and reasoning about para-metricity be...

Relational Parametricity for Control Considered as a Computational Effect

This paper investigates parametric polymorphism in the presence of control operators. Our approach is to specialise a general type theory combining polymorphism and computational effects, by extending it with additional constants expressing control. By defining relationally parametric models of this extended calculus, we capture the interaction between parametricity and control. As a worked exa...

Parametricity as a Notion of Uniformity in Reflexive Graphs

Subtyping and Parametricity

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 a...