structure ROOT = 

struct

structure Orderings = 

struct

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_;

end; (*struct Orderings*)

structure Code_Generator = 

struct

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

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

end; (*struct Code_Generator*)

structure Nat = 

struct

datatype nat = Zero_nat | Suc of nat;

fun eq_nat Zero_nat (Suc m) = false

  | eq_nat (Suc n) Zero_nat = false

  | eq_nat (Suc n) (Suc m) = eq_nat n m

  | eq_nat Zero_nat Zero_nat = true;

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

fun less_nat n (Suc m) = less_eq_nat n m

  | less_nat n Zero_nat = false

and less_eq_nat (Suc n) m = less_nat n m

  | less_eq_nat Zero_nat m = true;

val ord_nat = {less_eq = less_eq_nat, less = less_nat} :

  nat Orderings.ord;

end; (*struct Nat*)

structure Codegen = 

struct

datatype ('a, 'b) searchtree = Leaf of 'a * 'b |

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

fun update (C1_, C2_) (it, entry) (Branch (t1, key, t2)) =

  (if Orderings.less_eq C2_ it key

    then Branch (update (C1_, C2_) (it, entry) t1, key, t2)

    else Branch (t1, key, update (C1_, C2_) (it, entry) t2))

  | update (C1_, C2_) (it, entry) (Leaf (key, vala)) =

    (if Code_Generator.eq C1_ it key then Leaf (key, entry)

      else (if Orderings.less_eq C2_ it key

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

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

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

  update (Nat.eq_nata, Nat.ord_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.ord_nat)

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

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

      (update (Nat.eq_nata, Nat.ord_nat)

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

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

end; (*struct Codegen*)

end; (*struct ROOT*)