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2011-12-12T10:06:24Z

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'''Template Systems for Languages of the Future, Part III: Variance''' by Yannis Smaragdakis, based on "Taming the Wildcards: Combining Definition- and Use-Site Variance" (PLDI'11)

In a continuation of our recent work on advanced type systems for templates/generics (MorphJ, cJ), I'll talk about the topic of variance. "Variance" is the name for language mechanisms that integrate parametric and subtype polymorphism, i.e., ask "when is a template instantiation a subtype of another?". 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. We present a unifying framework for reasoning about variance. Our 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. This general framework can have multiple applications to combine the best of both worlds: for instance, it can be used to add use-site variance annotations to the Scala type system. We show one such application in detail: we extend the Java type system with a mechanism that modularly infers the definition-site variance of type parameters, while allowing use-site variance annotations on any type-instantiation.

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