Subtype polymorphism in Haskell

Question

Building a hierarchy of GUI widget classes is pretty much a standard exercise in object-oriented programming. You have some sort of abstract Widget class, with an a

Answer 1

The wxHaskell GUI library makes excellent use of phantom types to model a widget hierarchy.

The idea is the following: all widgets share the same implementation, namely they are foreign pointers to C++ objects. However, this doesn't mean that all widgets need to have the same type. Instead, we can build a hierarchy like this:

type Object a = ForeignPtr a

data CWindow a
data CControl a
data CButton a

type Window  a = Object  (CWindow a)
type Control a = Window  (CControl a)
type Button  a = Control (CButton a)

This way, a value of the type Control A also matches the type Window b, so you can use controls as windows, but not the other way round. As you can see, subtyping is implemented via a nested type parameter.

For more on this technique, see section 5 in Dan Leijen's paper on wxHaskell.

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Note that this technique appears to be limited to the case where the actual representation of widgets is uniform, i.e. always the same. However, I am confident that with some thought, it can be extended to the case where widgets have different representations.

In particular, the observation is that object-orientation can be modeled by including the methods in the data type, like this

data CWindow a = CWindow
    { close   :: IO ()
    , ...
    }
data CButton a = CButton
    { onClick :: (Mouse -> IO ()) -> IO ()
    , ...
    }

Subtyping may save some boilerplate here, but it's not required.