Coercible should be higher-kinded
Just discussed with SJP: The Coercible should be higher kinded, and it seems to be straight forward.
data T f = T (f Int) newtype List a = [a]
we want to be able to derive
Coercible (T (Either Int)) (T (Either Age)) Coercible (T List) (T )
We now allow
Coercible at a kind
* -> k, with the following intuition:
Coercible A B ⇐⇒ (forall a. Coercible (A a) (B a))
Note that this is ok independent of the role of
A’s parameter, as we are not modifying that parameter here.
Allowing such constraints, we therefore, we need these constraints exist in theory (but are in fact generated on demand, so only those of the rind kindnessare visible to the constraint solver) for
instance (Coercible a b, Coercible c d) => Coercible (Either a c) (Either b d) -- old instance Coercible a b => Coercible (Either a) (Either b) -- new instance Coercible [a] b => Coercible (List a) b -- old instance Coercible b [a] => Coercible b (List a) -- old instance Coercible a b => Coercible (List a) (List b) -- old instance Coercible  b => Coercible List b -- new instance Coercible b  => Coercible b List -- new
This solves the cases above. It does not solve all cases, though. Consider
newtype NT1 a = NT1 (a -> Int) newtype NT2 a = NT2 (a -> Int)
and we want to solve
Coercible (T NT1) (T NT2). Although, by the definition above,
Coercible NT1 NT2 should hold, such a coercion cannot be created (as far as I can see).