(* This code extends 'mini_prelude'. *)

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

let empty = Empty ;;

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

let rec merge v18 = 
  (fun v19 -> 
    (fun v16 -> 
      (fun v17 -> 
        (match v16 with 
            Empty -> 
              (match v17 with 
                  Empty -> Empty 
                | (Tree (v3, v2, v1)) -> (Tree (v3, v2, v1))) 
          | (Tree (v15, v14, v13)) -> 
              (match v17 with 
                  Empty -> (Tree (v15, v14, v13)) 
                | (Tree (v12, v11, v10)) -> 
                    (if ((v19 (v18 v15)) (v18 v12)) 
                    then 
                      (match v14 with 
                          Empty -> (Tree (v15, (Tree (v12, v11, v10)), v13)) 
                        | (Tree (v6, v5, v4)) -> (Tree (v15, Empty, ((((merge v18) v19) ((((merge v18) v19) (Tree (v12, v11, v10))) v14)) v13)))) 
                    else 
                      (match v11 with 
                          Empty -> (Tree (v12, (Tree (v15, v14, v13)), v10)) 
                        | (Tree (v9, v8, v7)) -> (Tree (v12, Empty, ((((merge v18) v19) ((((merge v18) v19) (Tree (v15, v14, v13))) v11)) v10)))))))))) ;;

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

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