Lambda the Ultimate

Variance and Generalized Constraints for C# Generics. Burak Emir, Andrew J. Kennedy, Claudio Russo, Dachuan Yu. July 2006

Generic types in C# behave invariantly with respect to sub-typing. We propose a system of type-safe variance for C# that supports the declaration of covariant and contravariant type parameters on generic types. To support more widespread application of variance we also generalize the existing constraint mechanism with arbitrary subtype assertions on classes and methods. This extension is useful even in the absence of variance, and subsumes equational constraints proposed for Generalized Algebraic Data Types (GADTs). We formalize the subtype relation in both declarative and syntax-directed style, and describe and prove the correctness of algorithms for constraint closure and subtyping. Finally, we formalize and prove a type safety theorem for a featherweight language with variant classes and generalized constraints.

Discussion of previous C# GADT paper on LtU.

I am unsure about use-site versus definition-site variance declerations. It would be interesting to hear what others think.

Also check out the LtU discussion on wildcards in Java.