stanford btree problems: hasPathSum

I decided to go through some of the Stanford Btree problems. Today I wrote a solution to the hasPathSum problem and part of the printPaths problem in SML. My solution will take a binary tree and return a list of all the paths that will sum to the given sum. A path starts at the root and ends at the descendant whose integer value adds to the sum.

datatype itree = Node of itree * int * itree
        | Leaf

val mytree = Node(
        Node(
         Node(
   Node(Leaf,~3,Leaf),
   2,
   Node(Leaf,12,Leaf)),
  4,
  Leaf),
        1,
        Node(Node(Leaf,15,Leaf),
      3,
      Leaf))

(*
 -should handle positive/negative weights
 -should find all paths in the tree that are equal to this sum
*)
fun hasPathSum root sum =
    let
      fun search (Node(left,i,right)) path accum all_paths =
   let
     val new_path = (i::path)
     val new_accum = (accum + i)
     val get_left_paths = search (left) (new_path) (new_accum)
     val get_right_paths = search (right) (new_path) (new_accum)
     val new_all_paths = if sum = new_accum then 
      ((rev new_path)::all_paths)
    else
      all_paths
   in
     get_right_paths (get_left_paths new_all_paths)
   end
 | search (Leaf) (_) (_) (all_paths) = all_paths
    in
      search (root) ([]) (0) ([])
    end

hasPathSum (mytree) (4) (*result: [[1,3], [1, 4, 2, ~3]] *)
hasPathSum (mytree) (1) (*result: [[1]]*)
hasPathSum (mytree) (1024) (*result: [] *)