Haskell arbitrary typeclass instance return type

Question

From the Haskell Book chapter on Monoids, I am writing quickcheck tests for

semigroupAssoc :: (Eq m, S.Semigroup m) => m -> m -> m -> Bool
semigroupAssoc a b c =
    (a S.<> (b S.<> c)) == ((a S.<> b) S.<> c)

type IdentAssoc = Identity String -> Identity String -> Identity String -> Bool

, invoking with

quickCheck (semigroupAssoc :: IdentAssoc)

Here is the arbitrary typeclass instance

instance (Arbitrary a) => Arbitrary (Identity a) where
    arbitrary = do
        a <- Test.QuickCheck.arbitrary
        return (Identity a)

My question is that in my arbitrary instance, I can return either (Identity a) or just a. (Identity a) is correct, but just a gives no compiler error and causes an infinite loop when run. Why is this?

Answer 1

Type inference changes the arbitrary call to point at the same instance we are defining right now, causing an infinite loop.

instance (Arbitrary a) => Arbitrary (Identity a) where
   arbitrary = do
        x <- Test.QuickCheck.arbitrary  -- this calls arbitrary @ a
        return (Identity x)

instance (Arbitrary a) => Arbitrary (Identity a) where
   arbitrary = do
        x <- Test.QuickCheck.arbitrary  -- this calls arbitrary @ (Identity a)
        return x

Every time we call a class method, the compiler infers which instance to call.

In the former case, the compiler infers x :: a (only this type makes the code type check!), hence it calls arbitrary @ a.

In the latter case, the compiler infers x :: Identity a (only this type makes the code type check!), hence it calls arbitrary @ (Identity a), causing the infinite loop.