Hspec & QuickCheck - Ambiguous type variable a0?

I have written a function in Haskell that takes a list of arbitrary elements and returns (mapped) a list of tuples. Each tuple contains the original element and a fraction, with all the fractions in the list adding to 1 (therefore I simply calculate the fraction once using 1 ``div`` length xs and apply it all elements). This is the code:

uniform :: [a] -> [(a, Int)]
uniform xs = map (\x -> (x, prob)) xs
  where prob = 1 `div` (length xs)

(Disclaimer: This is actually a slightly simplified version, but I am producing the exact same behaviour, so hopefully this suffices).

I am trying to cover this with a property based test using Hspec and Quickcheck:

spec = do
    describe "uniform" $ do

        it "produces a uniform distribution summing to 1" $ property $
            let totalProbability ((_, p):xs) = p + (totalProbability xs)
            in (\xs -> (totalProbability $ uniform xs) `shouldBe` 1)

However when I run this I get this error:

• Ambiguous type variable ‘a0’ arising from a use of ‘property’
  prevents the constraint ‘(Arbitrary a0)’ from being solved.
  Probable fix: use a type annotation to specify what ‘a0’ should be.
  These potential instances exist:
    instance (Arbitrary a, Arbitrary b) => Arbitrary (Either a b)
      -- Defined in ‘Test.QuickCheck.Arbitrary’
    instance Arbitrary Ordering
      -- Defined in ‘Test.QuickCheck.Arbitrary’
    instance Arbitrary Integer
      -- Defined in ‘Test.QuickCheck.Arbitrary’
    ...plus 19 others
    ...plus 62 instances involving out-of-scope types
    (use -fprint-potential-instances to see them all)
• In the second argument of ‘($)’, namely
    ‘property
       $ let totalProbability ((_, p) : xs) = p + (totalProbability xs)
         in (\ xs -> (totalProbability $ uniform xs) `shouldBe` 1)’
  In a stmt of a 'do' block:
    it "produces a uniform distribution summing to 1"
      $ property
          $ let totalProbability ((_, p) : xs) = p + (totalProbability xs)
            in (\ xs -> (totalProbability $ uniform xs) `shouldBe` 1)
  In the second argument of ‘($)’, namely
    ‘do it "produces a uniform distribution summing to 1"
          $ property
              $ let totalProbability ((_, p) : xs) = ...
                in (\ xs -> (totalProbability $ uniform xs) `shouldBe` 1)’

| 12 | it "produces a uniform distribution summing to 1" $ property $ | ^^^^^^^^^^...

I am guessing that somewhere I have not given QuickCheck enough information about how to generate the test value, but I am not sure where to go from here.

Any help would be greatly appreciated.

Thanks!

Solution

You need to specify a type for xs: is that a list of strings? ints? booleans? This is so that QuickCheck can generate a random sample in that type.

You can write, for instance:

...
in (\xs -> (totalProbability $ uniform (xs :: [Int])) `shouldBe` 1)