> To fix that, you need to start supporting error polymorphism.

  > map :: List a -> (a -> b -[err]) -> List b -[err]

FWIW, Haskell has this already; it's called[0] Traversable:

  ghci> :t mapA
  mapA :: (Traversable t,Applicative f) => (a -> f b) -> t a -> f (t b)
  ghci> :t mapA @(Error ||) @[]
  mapA :: (a -> Error || b) -> [a] -> Error || [b]

0: The default prelude calls it `traverse` instead of `mapA` (which is terrible for reasons that should be obvious[1]) and `Either Error a` instead of `Error || a` (which is a matter of taste).

1: Especially if you rename the method of Functor from `fmap` to:

  map :: Functor t => (a ->   b) -> t a ->    t b
  -- for comparison:
  mapA :: ...      => (a -> f b) -> t a -> f (t b)