How does scanr work? Haskell

scanr is to foldr what scanl is to foldl. foldr works from the right:

foldr (+) 0 [1,2,3] =
  (1 + (2 + (3 +   0))) =
  (1 + (2 +    3)) =
  (1 +    5) =
     6
-- [ 6,   5,   3,   0 ]

and scanr just shows the interim results in sequence: [6,5,3,0]. It could be defined as

scanr (+) z xs = foldr g [z] xs
  where
  g x ys@(y:_) = x+y : ys

scanl though should work like

scanl (+) 0 [1,2,3] =
  0 : scanl (+) (0+1) [2,3] =
  0 : 1 : scanl (+) (1+2) [3] =
  0 : 1 : 3 : scanl (+) (3+3) [] =
  0 : 1 : 3 : [6]

so it must be that

scanl (+) z xs = foldr f h xs z
   where h      z = [z]
         f x ys z = z : ys (z + x)

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