Simple Implementation of Binary Search Tree in Ocaml

type 'a tree = 
 | Node of 'a * 'a tree * 'a tree
 | Leaf;;

let empty = Leaf ;;

let rec mem x = function
 | Leaf -> false
 | Node (key, left, right) ->
  key = x || (x < key && mem x left) || (x > key && mem x right) ;;


(* insert function will ignore the key which has already existed *)
let rec insert x = function
 | Leaf -> Node (x, Leaf, Leaf)
 | Node (k, left, right) as node-> 
    if x < k then
    Node (k, insert x left, right)
   else if x > k then
    Node (k, left, insert x right)
   else
    node ;;


let rec tree_of_list = function
 | [] -> empty
 | h::t -> insert h (tree_of_list t) ;;


let rec insert x = function
 | Leaf -> Node (x, Leaf, Leaf)
 | Node (k, left, right) as node-> 
    if x < k then
    Node (k, insert x left, right)
   else if x > k then
    Node (k, left, insert x right)
   else
    node ;;


let my_tree = tree_of_list [2;3;4;1;7;6;4;8] ;;

let rec in_order_walk = function
 | Leaf -> ()
 | Node (k,left,right) ->
  in_order_walk left;
  let () = print_int k in
    print_newline ();
  in_order_walk right;;

let rec pre_order_walk = function
 | Leaf -> ()
 | Node (k, left, right) ->
  let () = print_int k in
   print_newline ();
  pre_order_walk left;
  pre_order_walk right ;;

let rec post_order_walk = function
 | Leaf -> ()
 | Node (k, left, right) ->
  post_order_walk left;
  post_order_walk right;
  let () = print_int k in
   print_newline () ;;
  
let rec height = function
 | Leaf -> 0
 | Node (k, left, right) ->
   1 + max (height left) (height right) ;;