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A Logic for Parametric Polymorphism Gordon Plotkin \Lambda Mart'in Abadi y
 

Summary: A Logic for Parametric Polymorphism
Gordon Plotkin \Lambda Mart'in Abadi y
Abstract
In this paper we introduce a logic for parametric polymorphism. Just as LCF is a
logic for the simply­typed –­calculus with recursion and arithmetic, our logic is a logic for
System F. The logic permits the formal presentation and use of relational parametricity.
Parametricity yields---for example---encodings of initial algebras, final co­algebras and
abstract datatypes, with corresponding proof principles of induction, co­induction and
simulation.
1 Introduction
In this paper we introduce a logic for parametric polymorphism, in the binary relational
sense of Reynolds [Rey83]. Just as LCF is a first­order logic for the simply­typed –­calculus,
with recursion and arithmetic, so our logic is a second­order logic for System F. It is intended
as a step towards a general logic of polymorphically typed programs. The terms are those
of the second­order –­calculus, and the formulae are built from equations and relations by
propositional operators and quantifiers over elements of types, or over types, or over relations
between types. The logic permits the formal presentation and use of relational parametricity,
which is expressed by an axiom schema. Parametricity yields---for example---encodings of
initial algebras, final co­algebras and abstract datatypes, with corresponding proof principles
of induction, co­induction and simulation.

  

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

 

Collections: Computer Technologies and Information Sciences