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*)