(* This code extends 'mini_prelude'. *)

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

val empty = Empty ;

val is_empty = 
  (fn v3 => 
    (case v3 of 
        Empty => true 
      | (Tree (v2, v1)) => false)) ;

val merge = 
  (fn v8 => 
    (fn v9 => 
      (fn v10 => 
        (fn v7 => 
          (case v10 of 
              Empty => 
                (case v7 of 
                    Empty => Empty 
                  | (Tree (v2, v1)) => (Tree (v2, v1))) 
            | (Tree (v6, v5)) => 
                (case v7 of 
                    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))))))))))) ;

val insert = 
  (fn v1 => 
    (fn v3 => 
      (fn v4 => 
        (fn v2 => ((((merge v1) v3) (Tree (v4, Nil))) v2))))) ;

fun merge_pairs v5 = 
  (fn v6 => 
    (fn v7 => 
      (case v7 of 
          Nil => Empty 
        | (Cons (v4, v3)) => 
            (case v3 of 
                Nil => v4 
              | (Cons (v2, v1)) => ((((merge v5) v6) ((((merge v5) v6) v4) v2)) (((merge_pairs v5) v6) v1)))))) ;

val find_min = 
  (fn x1 => 
    (case x1 of 
        Empty => (raise Bind) 
      | (Tree (v2, v1)) => v2)) ;

val delete_min = 
  (fn x1 => 
    (fn x2 => 
      (fn x3 => 
        (case x3 of 
            Empty => (raise Bind) 
          | (Tree (v2, v1)) => (((merge_pairs x1) x2) v1))))) ;