Question

Rookie question, why this is not correct in Haskell?

class BasicEq a where
    isEqual :: a -> a -> Bool
    isNotEqual :: a -> a -> Bool
    isNotEqual = not . isEqual

Answer 1

Let’s open up the GHC prompt and look at the types of things:

Prelude> :t not
not :: Bool -> Bool
Prelude> :t (not .)
(not .) :: (a -> Bool) -> a -> Bool

So you can see (not .) takes a a -> Bool, not an a -> a -> Bool. We can double up the function composition to get a working version:

Prelude> :t ((not .) .)
((not .) .) :: (a -> a1 -> Bool) -> a -> a1 -> Bool

So the correct definition is:

isNotEqual = (not .) . isEqual

Or equivalently,

isNotEqual x y = not $ isEqual x y
isNotEqual = curry $ not . uncurry isEqual

et cetera.