haskell - Is there a better way to express the absolute error function in point-free notation?

Question

In pointful notation:

absoluteError x y = abs (x-y)

An unclear example in pointfree notation:

absoluteError' = curry (abs . uncurry (-))

Answer 1

Here's how you could derive it yourself, in small steps:

absoluteError x y = abs (x-y) = abs ((-) x y) = abs ( ((-) x) y) 
                  = (abs . (-) x) y = ( (abs .) ((-) x) ) y = 
                  = ( (abs .) . (-) ) x y

so, by eta-reduction, if f x y = g x y we conclude f = g.

Further, using _B = (.) for a moment,

(abs .) . (-) = _B (abs .) (-) = _B (_B abs) (-) = (_B . _B) abs (-)
              = ((.) . (.)) abs (-)