How can I write test cases for instances in Haskell

Question

I have an instance of Num for a type I created called Vec:

instance Num Vec where
  (+) (Vec x) (Vec y) = Vec (zipWith (+) x y)

And I am trying to write a test case for it like I normally do. Normally, I test functions and not instances. I usually do it this way this way:

spec :: Spec
spec = do
  describe "(+)" $ do
    it "produces (Vec [2])" $
      Vec [1] + Vec [1] `shouldBe` Vec [2]

Since the code above doesn't produce any results, does this mean I'd have to create functions for (+) in order to test it? How can I do it for instances?

Answer 1

This is not an answer to the question but it is too long for a comment.

It seems like Vec uses pointwise lifting of Num.

This corresponds to using Applicative lifting (Ap) over ZipList:

{-# Language DerivingVia #-}

import Control.Applicative (ZipList(..))
import Data.Monoid         (Ap(..))

-- >> Vec [1] + Vec [1]
-- Vec [2]
newtype Vec = Vec [Int]
  deriving Num
  via Ap ZipList Int

You can also use deriving newtype IsList if you want to use list syntax for Vec.