quicksort with a single scan

-- quicksort
quicksort :: Ord a => [a] -> [a]
quicksort [] = []
quicksort (x1:xs) = let
  -- split xs: ( [x >= x1] , [x < x1] ) for x <- xs
  --- splitter: auxiliary function
  auxSplitter x0 geq_lt = let (geq, lt) = geq_lt
    in if x0 >= x1 then (x0:geq, lt)
       else (geq, x0:lt)

  --- split tail of list via foldr and auxSplitter
  (geq_x1, lt_x1) = foldr auxSplitter ([], []) xs

  -- do quicksort
  in quicksort lt_x1 ++ [x1] ++ quicksort geq_x1


-- test
testQuicksort = (quicksort [1, -2, 3, 4, 1, 2] == [-2, 1, 1, 2, 3, 4]) && (quicksort [3] == [3])
-- test1 = quicksort [] == []