Bubble sort in SML

bSort.sml

(* sorted : int list -> bool
 * check if a list of ints is sorted *)
fun sorted []         = true
  | sorted [x]        = true
  | sorted (x::y::xs) = x < y andalso sorted (y::xs)

val sorted_test1 = sorted [1,2,3]
val sorted_test2 = not (sorted [2,1,3])
val sorted_test3 = not (sorted [2,3,1])
val sorted_test4 = sorted []

local
  (* bSort' : int list -> int list
   * sort a list of ints just a little *)
  fun bSort' [] = []
    | bSort' [x] = [x]
    | bSort' (x::y::xs) = case Int.compare (x,y) of
                               GREATER => y :: x :: xs
                             | EQUAL   => x :: y :: xs
                             | LESS    => x :: bSort' (y::xs)

  (* function for doing fix point iteration *)
  fun fix f x = if f x = x then x
                else fix f (f x)
in
  (* bSort : int list -> int list
     using bSort' and fix point interation, sort a list of ints *)
  fun bSort x = fix bSort' x
end

val bSort_test1 = bSort [5,3,4,2,1] = [1,2,3,4,5]
val bSort_test2 = bSort [] = []
val bSort_test3 = bSort [1,2,3] = [1,2,3]
val bSort_test4 = bSort [4,3,2,1] = [1,2,3,4]