Actually, doing arbitrary arity with type classes turns out to be incredibly easy:
module Pred where
class Predicate a where
complement :: a -> a
instance Predicate Bool where
complement = not
instance (Predicate b) => Predicate (a -> b) where
complement f = \a -> complement (f a)
-- if you want to be mysterious, then
-- complement = (complement .)
-- also works
ge :: Ord a => a -> a -> Bool
ge = complement (<)
Thanks for pointing out this cool problem. I love Haskell.