"SML 二叉搜索树插入函数"

Question

I am new to SML and am trying to implement a BST. I have figured out how to parse through the tree, but am struggling with creating an insert function. I want the function to be: insert(bst, key, value) of type BST * int * int -> BST where it inserts a key-value pair into a given tree and returns the resulting tree. I am struggling in the creation of this though, because I get a bit confused on making sure the function is of the right type.

(* left subtree, right subtree, key, value *)
datatype BST = Empty | Node of BST * BST * int * int;

fun parsePost [] = Empty
  | parsePost lst =
    let
      fun pP(stack, (0, k, v)::str) = pP(Node(Empty, Empty, k, v)::stack, str)
        | pP(L::stack, (1, k, v)::str) = pP(Node(L, Empty, k, v)::stack, str)
        | pP(R::stack, (2, k, v)::str) = pP(Node(Empty, R, k, v)::stack, str)
        | pP(R::L::stack, (3, k, v)::str) = pP(Node(L, R, k, v)::stack, str)
        | pP(T::stack, []) = T;
    in
      pP([], lst)
    end;

val exTree1 = [(0, 1, 1), (0, 3, 3), (3, 2, 2)];

Answer 1

If you insert a key and value pair into an empty tree, do you really expect to get an empty tree back? I very much doubt this is what you'd expect.

fun insert(Empty, x, y) = Node(Empty, Empty, x, y)