structure HOL = 

struct

type 'a eq = {eq : 'a -> 'a -> bool};

fun eq (A_:'a eq) = #eq A_;

type 'a ord = {less_eq : 'a -> 'a -> bool, less : 'a -> 'a -> bool};

fun less_eq (A_:'a ord) = #less_eq A_;

fun less (A_:'a ord) = #less A_;

fun eqop A_ a = eq A_ a;

end; (*struct HOL*)

structure Orderings = 

struct

type 'a preorder = {Orderings__ord_preorder : 'a HOL.ord};

fun ord_preorder (A_:'a preorder) = #Orderings__ord_preorder A_;

type 'a order = {Orderings__preorder_order : 'a preorder};

fun preorder_order (A_:'a order) = #Orderings__preorder_order A_;

type 'a linorder = {Orderings__order_linorder : 'a order};

fun order_linorder (A_:'a linorder) = #Orderings__order_linorder A_;

end; (*struct Orderings*)

structure Nat = 

struct

datatype nat = Suc of nat | Zero_nat;

fun eq_nat (Suc a) Zero_nat = false

  | eq_nat Zero_nat (Suc a) = false

  | eq_nat (Suc nat) (Suc nat') = eq_nat nat nat'

  | eq_nat Zero_nat Zero_nat = true;

val eq_nata = {eq = eq_nat} : nat HOL.eq;

fun less_nat m (Suc n) = less_eq_nat m n

  | less_nat n Zero_nat = false

and less_eq_nat (Suc m) n = less_nat m n

  | less_eq_nat Zero_nat n = true;

val ord_nat = {less_eq = less_eq_nat, less = less_nat} : nat HOL.ord;

val preorder_nat = {Orderings__ord_preorder = ord_nat} :

  nat Orderings.preorder;

val order_nat = {Orderings__preorder_order = preorder_nat} :

  nat Orderings.order;

val linorder_nat = {Orderings__order_linorder = order_nat} :

  nat Orderings.linorder;

end; (*struct Nat*)

structure Codegen = 

struct

datatype ('a, 'b) searchtree =

  Branch of ('a, 'b) searchtree * 'a * ('a, 'b) searchtree |

  Leaf of 'a * 'b;

fun update (A1_, A2_) (it, entry) (Leaf (key, vala)) =

  (if HOL.eqop A1_ it key then Leaf (key, entry)

    else (if HOL.less_eq

               ((Orderings.ord_preorder o Orderings.preorder_order o

                  Orderings.order_linorder)

                 A2_)

               it key

           then Branch (Leaf (it, entry), it, Leaf (key, vala))

           else Branch (Leaf (key, vala), it, Leaf (it, entry))))

  | update (A1_, A2_) (it, entry) (Branch (t1, key, t2)) =

    (if HOL.less_eq

          ((Orderings.ord_preorder o Orderings.preorder_order o

             Orderings.order_linorder)

            A2_)

          it key

      then Branch (update (A1_, A2_) (it, entry) t1, key, t2)

      else Branch (t1, key, update (A1_, A2_) (it, entry) t2));

val example : (Nat.nat, (Nat.nat list)) searchtree =

  update (Nat.eq_nata, Nat.linorder_nat)

    (Nat.Suc (Nat.Suc (Nat.Suc (Nat.Suc Nat.Zero_nat))),

      [Nat.Suc (Nat.Suc Nat.Zero_nat), Nat.Suc (Nat.Suc Nat.Zero_nat)])

    (update (Nat.eq_nata, Nat.linorder_nat)

      (Nat.Suc (Nat.Suc (Nat.Suc Nat.Zero_nat)),

        [Nat.Suc (Nat.Suc (Nat.Suc Nat.Zero_nat))])

      (update (Nat.eq_nata, Nat.linorder_nat)

        (Nat.Suc (Nat.Suc Nat.Zero_nat), [Nat.Suc (Nat.Suc Nat.Zero_nat)])

        (Leaf (Nat.Suc Nat.Zero_nat, []))));

end; (*struct Codegen*)