How to get around the Coverage Condition for Functional Dependencies without using -XUndecidableInstances

Question

Wen using functional dependencies, I frequently hit the Coverage Condition. It is possible to lift it with UndecidableInstances, but I usually try to stay away from that extension.

Here is a somewhat contrived example, that works without UndecidableInstances:

{-# Language MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances #-}

data Result = Result String
  deriving (Eq, Show)

data Arguments a b = Arguments a b

class Applyable a b | a -> b where
  apply :: a -> b -> Result

instance Applyable (Arguments a b) (a -> b -> Result) where
  (Arguments a b) `apply` f = f a b

When I make the result type more generic, the Coverage Condition fails (hence requiring UndecidableInstances):

{-# Language MultiParamTypeClasses, FunctionalDependencies, FlexibleInstances, UndecidableInstances #-}

data Result a = Result a
  deriving (Eq, Show)

data Arguments a b = Arguments a b

class Applyable a b c | a -> b c where
  apply :: a -> b -> Result c

instance Applyable (Arguments a b) (a -> b -> Result c) c where
  (Arguments a b) `apply` f = f a b

I thought that because b and c are both determined by a, the more generic code should not cause any problems, so my questions:

1. Are there any possible issues with using UndecidableInstances here
2. Can I model the above scenario without relying on UndecidableInstances (maybe with type families?)

Answer 1

There's no big reason to stay away from UndecidableInstances. The worst that can happen is that the type checker starts looping (and tells you about it, I think). You can make the coverage condition more and more clever, but it will never do everything you could want since that's undecidable.