Consider the following GHCi session:
>:set -XTypeApplications
>import Data.Map.Strict
>import GHC.Exts
>newtype MySet a = MySet (Map a ())
>let member' :: Ord a => a -> MySet a -> Bool; member' = coerce member
<interactive>:21:57: error:
* Couldn't match representation of type `a0' with that of `()'
arising from a use of `coerce'
* In the expression: coerce member
In an equation for member': member' = coerce member
>let member' :: Ord a => a -> MySet a -> Bool; member' = coerce (member @_ @())
I have a hunch of what's going on here: The type-checker needs to satisfy Coercible (Ord a => a -> Map a b -> Bool) (Ord a => a -> MySet a -> Bool) and isn't able to instantiate b in this constraint to ().
Is there a more elegant way than to do this with -XTypeApplications?
Edit: I'm especially looking for solutions that deal with many occurences of MySet a in the type, for example union :: Ord a => MySet a -> MySet a -> MySet a.
member :: Ord a => a -> Map a b -> Bool
member' :: Ord a => a -> MySet a -> Bool
GHC needs to accept
Coercible (Map a b) (MySet a)
It sees that
Coercible (MySet a) (Map a ())
which leaves it needing
Coercible (Map a ()) (Map a b)
which leads to
Coercible () b
But what is b? It's ambiguous. In this case, it doesn't matter what b is, because by parametricity, member can't possibly care. So it would be perfectly reasonable to choose b ~ () and resolve the coercion trivially. But GHC generally doesn't perform such a parametricity analysis in type inference. I suspect it might be tricky to change that. Most especially, any time the type inference "guesses", there's a risk it might guess wrong and block up inference somewhere else. It's a big can of worms.
As for your problem, I don't have a good solution. When you have several functions with similar patterns, you can abstract them out, but you'll still face significant annoyance.