In 2008, three years after the introduction of associated types, they were subsumed by type families. Associated types are special type families where the type function is attached to a type-class.
In contrast to associated types, we have top-level type-families that are not associated with a type-class, for example:
type family RepF d type instance RepF (List' a) = (RList a)
The type family RepF represents a type function, with each instance declaring a value. Put another way, a type family represents a set of types, and each instance represents a set member.
In our example, GenericF simply uses the top-level type function in its type signatures:
class GenericF d where fromF :: d -> (RepF d) toF :: (RepF d) -> d instance GenericF (List' a) where fromF Nil' = L U fromF (Cons' x xs) = R (Combo x xs) toF (L U) = Nil' toF (R (Combo x xs)) = (Cons' x xs) main = print $ fromF (Cons' 1 Nil')
With associated types, we...