Software

Taming the Wildcards: Combining Definition-And Use-Site Variance

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Executive Summary

Variance allows the safe integration of parametric and subtype polymorphism. Two flavors of variance, definition-site versus use-site variance, have been studied and have had their merits hotly debated. Definition-site variance (as in Scala and C#) offers simple type-instantiation rules, but causes fractured definitions of naturally invariant classes; Use-site variance (as in Java) offers simplicity in class definitions, yet complex type-instantiation rules that elude most programmers. The authors present a unifying framework for reasoning about variance. Their framework is quite simple and entirely denotational, that is, it evokes directly the definition of variance with a small core calculus that does not depend on specific type systems.

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