Sure. Here's an example. {-# LANGUAGE TypeFamilies #-} module Mail where class C1 a where data T1 a :: * f1 :: T1 a -> T1 a instance C1 Bool where data T1 Bool = A | B deriving Show f1 A = B f1 B = A class C2 a where type T2 a :: * f2 :: T2 a -> T2 a data D2 = C | D deriving Show instance C2 Bool where type T2 Bool = D2 f2 C = D f2 D = C If you try to evaluate (f1 A) it works fine, whereas (f2 C) gives a type error. In fact, the f2 function is impossible to use. -- Lennart On Wed, Dec 10, 2008 at 1:40 PM, Jules Bean <jules@jellybean.co.uk> wrote:
Lennart Augustsson wrote:
For an associated data type D, we know that the type function D is injective, i.e., for different indicies given to D we'll get different data types. This makes much more powerful reasoning possible in the type checker. If associated data types are removed there has to be some new mechanism to declare an associated type as injective, or the type system will lose power.
Interesting.
Are you able to give an example which exploits this "known distinct types" effect?