(* This code extends 'mini_prelude'. *)

Dtype
  [(["a"],"heap",
    [("Tree",[Tvar "a"; Tapp [Tapp [Tvar "a"] "heap"] "list"]);
     ("Empty",[])])]

Dlet (Pvar "empty") (Con "Empty" [])

Dlet (Pvar "is_empty")
  (Fun "v3"
     (Mat (Var "v3")
        [(Pcon "Empty" [],Val (Lit (Bool T)));
         (Pcon "Tree" [Pvar "v2"; Pvar "v1"],Val (Lit (Bool F)))]))

Dlet (Pvar "merge")
  (Fun "v8"
     (Fun "v9"
        (Fun "v10"
           (Fun "v7"
              (Mat (Var "v10")
                 [(Pcon "Empty" [],
                   Mat (Var "v7")
                     [(Pcon "Empty" [],Con "Empty" []);
                      (Pcon "Tree" [Pvar "v2"; Pvar "v1"],
                       Con "Tree" [Var "v2"; Var "v1"])]);
                  (Pcon "Tree" [Pvar "v6"; Pvar "v5"],
                   Mat (Var "v7")
                     [(Pcon "Empty" [],Con "Tree" [Var "v6"; Var "v5"]);
                      (Pcon "Tree" [Pvar "v4"; Pvar "v3"],
                       If
                         (App Opapp
                            (App Opapp (Var "v9")
                               (App Opapp (Var "v8") (Var "v6")))
                            (App Opapp (Var "v8") (Var "v4")))
                         (Con "Tree"
                            [Var "v6";
                             Con "Cons"
                               [Con "Tree" [Var "v4"; Var "v3"];
                                Var "v5"]])
                         (Con "Tree"
                            [Var "v4";
                             Con "Cons"
                               [Con "Tree" [Var "v6"; Var "v5"];
                                Var "v3"]]))])])))))

Dlet (Pvar "insert")
  (Fun "v1"
     (Fun "v3"
        (Fun "v4"
           (Fun "v2"
              (App Opapp
                 (App Opapp
                    (App Opapp (App Opapp (Var "merge") (Var "v1"))
                       (Var "v3"))
                    (Con "Tree" [Var "v4"; Con "Nil" []]))
                 (Var "v2"))))))

Dletrec
  [("merge_pairs","v5",
    Fun "v6"
      (Fun "v7"
         (Mat (Var "v7")
            [(Pcon "Nil" [],Con "Empty" []);
             (Pcon "Cons" [Pvar "v4"; Pvar "v3"],
              Mat (Var "v3")
                [(Pcon "Nil" [],Var "v4");
                 (Pcon "Cons" [Pvar "v2"; Pvar "v1"],
                  App Opapp
                    (App Opapp
                       (App Opapp (App Opapp (Var "merge") (Var "v5"))
                          (Var "v6"))
                       (App Opapp
                          (App Opapp
                             (App Opapp
                                (App Opapp (Var "merge") (Var "v5"))
                                (Var "v6")) (Var "v4")) (Var "v2")))
                    (App Opapp
                       (App Opapp
                          (App Opapp (Var "merge_pairs") (Var "v5"))
                          (Var "v6")) (Var "v1")))])])))]

Dlet (Pvar "find_min")
  (Fun "x1"
     (Mat (Var "x1")
        [(Pcon "Empty" [],Raise Bind_error);
         (Pcon "Tree" [Pvar "v2"; Pvar "v1"],Var "v2")]))

Dlet (Pvar "delete_min")
  (Fun "x1"
     (Fun "x2"
        (Fun "x3"
           (Mat (Var "x3")
              [(Pcon "Empty" [],Raise Bind_error);
               (Pcon "Tree" [Pvar "v2"; Pvar "v1"],
                App Opapp
                  (App Opapp (App Opapp (Var "merge_pairs") (Var "x1"))
                     (Var "x2")) (Var "v1"))]))))