Type constraints on typeclass instances in Haskell?

Question

So I was playing around with Data.Set.Monad, which does not seem to be an instance of Data.Foldable like Data.Set is. I decided to try and add this instance myself as an experiment:

import Data.Foldable (Foldable, foldr)
import qualified Data.Set.Monad as S (Set, foldr)

instance Foldable S.Set where
  foldr = S.foldr

I get compilation error:

No instance for (Ord a) arising from a use of ‘S.foldr’
Possible fix:
  add (Ord a) to the context of
    the type signature for foldr :: (a -> b -> b) -> b -> Set a -> b
In the expression: S.foldr
In an equation for ‘foldr’: foldr = S.foldr
In the instance declaration for ‘Foldable Set’

Okay, this must be because S.foldr :: Ord a => (a -> b -> b) -> b -> Set a -> b. How do I express this constraint in the instance declaration? I tried this:

instance (Ord a) => Foldable (Set a) where
  foldr = S.foldr

And get another compilation error:

The first argument of ‘Foldable’ should have kind ‘* -> *’,
  but ‘Set a’ has kind ‘*’
In the instance declaration for ‘Foldable (Set a)’

What am I doing wrong? Or will Haskell even let me create this instance at all?

Answer 1

So, you need to define Foldable Set. Which means you can't depend on a, since foldr is required to work for any a.

So basically you would need constraint kinds to be embedded into the definition of Foldable to make this work, I think.

Note that Data.Set.foldr doesn't have the Ord a constraint so it can define a Foldable instance.