Haskell Overlapping/Incoherent Instances

Question

I know this is code is a bit silly, but can someone explain why this isList [42] returns True whereas isList2 [42] prints False

Answer 1

It's really quite simple. Let's ask GHCi what the type of isList2 is:

∀x. x ⊢ :t isList2
isList2 :: a -> Bool

This doesn't match the [a] instance (even though it could, via unification), but it does match the a instance immediately. Therefore, GHC selects the a instance, so isList2 returns False.

This behavior is precisely what IncoherentInstances means. Actually, this is a rather nice demonstration of it.

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Hilariously, if you simply disable IncoherentInstances, we get exactly the opposite effect, and GHCi now says this:

∀x. x ⊢ :t isList2
isList2 :: [Integer] -> Bool

This happens because isList2 is a top-level binding not defined using function syntax, and thus subject to the Dreaded Monomorphism Restriction. So it gets specialized to the instance it's actually used with.

Adding NoMonomorphismRestriction as well as disabling IncoherentInstances, we get this instead:

∀x. x ⊢ :t isList2
isList2 :: IsList a => a -> Bool
∀x. x ⊢ isList2 'a'
False
∀x. x ⊢ isList2 "a"
True
∀x. x ⊢ isList2 undefined

:19:1:
    Overlapping instances for IsList a0 arising from a use of `isList2'

Which is the expected overlapping behavior, with the instance chosen based on use and complaints if the choice is ambiguous.

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Regarding the edit to the question, I don't believe the desired result is possible without type annotations.

The first option is to give isList2 a type signature, which prevents IncoherentInstances from selecting an instance too early.

isList2 :: (IsList a) => a -> Bool
isList2 = isList

You'll probably need to do the same anywhere else isList is mentioned (even indirectly) without being applied to an argument.

The second option is to disambiguate the numeric literals and disable IncoherentInstances.

main = 
  print (isList (42 :: Integer)) >> 
  print (isList2 (42 :: Integer)) >> 
  print (isList [42]) >> 
  print (isList2 [42]) 

In this case, there's enough information to pick a most-specific instance, so OverlappingInstances does its thing.