In the new type, the parameter 'a' is misleading. It has no connection to the 'a's on the right of the equals sign. You might as well write:
type CB = forall a. a -> a -> a
On Tue, Jun 1, 2010 at 12:40 PM, Cory Knapp
Ah! That makes sense. Which raises a new question: Is this type "too general"? Are there functions which are semantically non-boolean which fit in that type
Actually, this type is *less* general, in that it has less members. Consider, what boolean is represented by this? q :: CB Int q = (+) Whereas the (forall a. a -> a -> a) must work on *any* type, so it has far less freedom to decide what to do, and therefore there are less possible implementations. In fact, if we treat all bottoms as equal, I believe these are all of the distinguishible implementations of this function: t a _ = a f _ a = a a1 = undefined a2 _ = undefined a3 _ _ = undefined a4 a b = seq b a a5 a b = seq a b a6 a = seq a (\_ -> a) a7 a = seq a (\b -> b) Without allowing bottoms, "t" and "f" are the only implementations. Here's some discriminators that are bottom if the passed in function is the first and not in the group of second: disc_t_f b = b undefined () disc_f_t b = b () undefined disc_6_t b = seq (b undefined) () disc_1_any b = seq b () disc_2_34567tf b = seq (b ()) () disc_3_4567tf b = seq (b () ()) () disc_4_6t b = b () undefined disc_5_f b = b undefined () disc_7_6 b = b () undefined disc_6_5 = seq (b undefined) () -- ryan