Is it possible to write a functor Interface for .NET?

Question

Functional languages often have Functor types/interfaces.

In .NET a Functor interface would be an Interface implementable by generic types (T)

Answer 1

The difficulty of giving a type to fmap is that it is parameterized by a higher-kinded type variable, the container type. So beyond being a simple polymorphic function, like say, map on lists:

map :: (a -> b) -> List a -> List b

fmap generalizes this to work on any container, as well as any element type:

fmap :: Functor (f :: * -> *) => (a -> b) -> f a -> f b

The problem in C# is that f is a higher-kinded type variable (it is a type function). Since C# doesn't support higher kinds, you'll be out of luck writing this directly, think.