On Feb 20, 2010, at 6:32 PM, Nick Rudnick wrote:
A simple example: class Show el=> ExceptionNote el where comment:: Show exception=> exception-> el-> String
instance ExceptionNote Int where comment exception refId = show refId ++ ": " ++ show exception
Here you don't need to constrain «exception» to be of «Show» at the instance declaration. So it does not appear wrong for Sjoerd to expect f and g to already be of Suitable2...
There really are instances missing. The context is coming from here:
The instance for Suitable2 restricts objects to IsProduct, and requires the Fst and Snd parts of the objects to be suitable in c1 resp. c2:
instance (IsProduct a, IsProduct b, Suitable2 c1 (Fst a) (Fst b), Suitable2 c2 (Snd a) (Snd b)) => Suitable2 (c1 :***: c2) a b where data Constraints (c1 :***: c2) a b = (IsProduct a, IsProduct b, Suitable2 c1 (Fst a) (Fst b), Suitable2 c2 (Snd a) (Snd b)) => ProdConstraints constraints _ = ProdConstraints
Given types A and B, the product A x B has a type Fst which is A, and a type Snd which is B -- by construction:
class IsProduct p where type Fst p :: * type Snd p :: * fst :: p -> Fst p snd :: p -> Snd p
So, if we have two products named a and b, and a = A + B, b = C + D (letting the first type in the addition be Fst, and the latter be Snd in each), a x b has four "components": (A x C) + (B x C) + (A x D) + (B x D). a x b = (A | B) x (C | D) = (Fst a | Snd a) x (Fst b | Snd b) = (Fst a, Fst b) + (Snd a, Fst b) + (Fst a, Snd b) + (Snd a, Snd b) This really comes down to the semantics of Suitability2, but I think Sjoerd made a logic mistake, and is trying to make a product out of a pair of products, in stead of a pair of categories.