(* This code extends 'mini_prelude'. *)

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

val empty = Empty ;

val is_empty = 
  (fn v4 => 
    (case v4 of 
        Empty => true 
      | (Tree (v3, v2, v1)) => false)) ;

fun partition v22 = 
  (fn v23 => 
    (fn v24 => 
      (fn v25 => 
        (case v25 of 
            Empty => (Pair (Empty, Empty)) 
          | (Tree (v21, v20, v19)) => 
              (if ((v23 (v22 v20)) (v22 v24)) 
              then 
                (case v19 of 
                    Empty => (Pair ((Tree (v21, v20, v19)), Empty)) 
                  | (Tree (v9, v8, v7)) => 
                      (if ((v23 (v22 v8)) (v22 v24)) 
                      then 
                        let val v3 = ((((partition v22) v23) v24) v7) 
                        in 
                          (case v3 of 
                              (Pair (v2, v1)) => (Pair ((Tree ((Tree (v21, v20, v9)), v8, v2)), v1))) 
                        end 
                      else 
                        let val v6 = ((((partition v22) v23) v24) v9) 
                        in 
                          (case v6 of 
                              (Pair (v5, v4)) => (Pair ((Tree (v21, v20, v5)), (Tree (v4, v8, v7))))) 
                        end )) 
              else 
                (case v21 of 
                    Empty => (Pair (Empty, (Tree (v21, v20, v19)))) 
                  | (Tree (v18, v17, v16)) => 
                      (if ((v23 (v22 v17)) (v22 v24)) 
                      then 
                        let val v12 = ((((partition v22) v23) v24) v16) 
                        in 
                          (case v12 of 
                              (Pair (v11, v10)) => (Pair ((Tree (v18, v17, v11)), (Tree (v10, v20, v19))))) 
                        end 
                      else 
                        let val v15 = ((((partition v22) v23) v24) v18) 
                        in 
                          (case v15 of 
                              (Pair (v14, v13)) => (Pair (v14, (Tree (v13, v17, (Tree (v16, v20, v19))))))) 
                        end ))))))) ;

val insert = 
  (fn v4 => 
    (fn v5 => 
      (fn v7 => 
        (fn v6 => 
          let val v3 = ((((partition v4) v5) v7) v6) 
          in 
            (case v3 of 
                (Pair (v2, v1)) => (Tree (v2, v7, v1))) 
          end )))) ;

fun merge v8 = 
  (fn v9 => 
    (fn v10 => 
      (fn v7 => 
        (case v10 of 
            Empty => v7 
          | (Tree (v6, v5, v4)) => 
              let val v3 = ((((partition v8) v9) v5) v7) 
              in 
                (case v3 of 
                    (Pair (v2, v1)) => (Tree (((((merge v8) v9) v2) v6), v5, ((((merge v8) v9) v1) v4)))) 
              end )))) ;

fun find_min x = 
  (case x of 
      Empty => (raise Bind) 
    | (Tree (v6, v5, v4)) => 
        (case v6 of 
            Empty => v5 
          | (Tree (v3, v2, v1)) => (find_min (Tree (v3, v2, v1))))) ;

fun delete_min x = 
  (case x of 
      Empty => (raise Bind) 
    | (Tree (v9, v8, v7)) => 
        (case v9 of 
            Empty => v7 
          | (Tree (v6, v5, v4)) => 
              (case v6 of 
                  Empty => (Tree (v4, v8, v7)) 
                | (Tree (v3, v2, v1)) => (Tree ((delete_min (Tree (v3, v2, v1))), v5, (Tree (v4, v8, v7))))))) ;