(* This code extends 'mini_prelude'. *)

type ('a) heap = 
    Tree of int * 'a * ('a) heap * ('a) heap 
  | Empty ;;

let rank = 
  (fun v5 -> 
    (match v5 with 
        Empty -> 0 
      | (Tree (v4, v3, v2, v1)) -> v4)) ;;

let make_node = 
  (fun v3 -> 
    (fun v1 -> 
      (fun v2 -> 
        (if ((rank v1) > (rank v2)) 
        then (Tree (((rank v2) + 1), v3, v1, v2)) 
        else (Tree (((rank v1) + 1), v3, v2, v1)))))) ;;

let empty = Empty ;;

let is_empty = 
  (fun v5 -> 
    (match v5 with 
        Empty -> true 
      | (Tree (v4, v3, v2, v1)) -> false)) ;;

let rec merge v13 = 
  (fun v14 -> 
    (fun v15 -> 
      (fun v16 -> 
        (match v15 with 
            Empty -> 
              (match v16 with 
                  Empty -> Empty 
                | (Tree (v4, v3, v2, v1)) -> (Tree (v4, v3, v2, v1))) 
          | (Tree (v12, v11, v10, v9)) -> 
              (match v16 with 
                  Empty -> (Tree (v12, v11, v10, v9)) 
                | (Tree (v8, v7, v6, v5)) -> 
                    (if ((v14 (v13 v11)) (v13 v7)) 
                    then (((make_node v11) v10) ((((merge v13) v14) v9) (Tree (v8, v7, v6, v5)))) 
                    else (((make_node v7) v6) ((((merge v13) v14) (Tree (v12, v11, v10, v9))) v5)))))))) ;;

let insert = 
  (fun v1 -> 
    (fun v3 -> 
      (fun v4 -> 
        (fun v2 -> ((((merge v1) v3) (Tree (1, v4, Empty, Empty))) v2))))) ;;

let find_min = 
  (fun x1 -> 
    (match x1 with 
        Empty -> (raise (Match_failure (string_of_bool true, 0, 0))) 
      | (Tree (v4, v3, v2, v1)) -> v3)) ;;

let delete_min = 
  (fun x1 -> 
    (fun x2 -> 
      (fun x3 -> 
        (match x3 with 
            Empty -> (raise (Match_failure (string_of_bool true, 0, 0))) 
          | (Tree (v4, v3, v2, v1)) -> ((((merge x1) x2) v2) v1))))) ;;