(* This code extends 'mini_prelude'. *)

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

let empty = Empty ;;

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

let merge = 
  (fun v8 -> 
    (fun v9 -> 
      (fun v10 -> 
        (fun v7 -> 
          (match v10 with 
              Empty -> 
                (match v7 with 
                    Empty -> Empty 
                  | (Tree (v2, v1)) -> (Tree (v2, v1))) 
            | (Tree (v6, v5)) -> 
                (match v7 with 
                    Empty -> (Tree (v6, v5)) 
                  | (Tree (v4, v3)) -> 
                      (if ((v9 (v8 v6)) (v8 v4)) 
                      then (Tree (v6, (Cons ((Tree (v4, v3)), v5)))) 
                      else (Tree (v4, (Cons ((Tree (v6, v5)), v3))))))))))) ;;

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

let rec merge_pairs v5 = 
  (fun v6 -> 
    (fun v7 -> 
      (match v7 with 
          Nil -> Empty 
        | (Cons (v4, v3)) -> 
            (match v3 with 
                Nil -> v4 
              | (Cons (v2, v1)) -> ((((merge v5) v6) ((((merge v5) v6) v4) v2)) (((merge_pairs v5) v6) v1)))))) ;;

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

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