module LexicographicOrder =
    functor (Ord1: sig type t val equal: t->t->bool val less: t->t->bool end)
    functor (Ord2: sig type t val equal: t->t->bool val less: t->t->bool end)
      struct
        type t = Ord1.t * Ord2.t
        val equal p q =
          if Ord1.equal (fst p) (fst q)
          then Ord2.equal (snd p) (snd q)
          else false
        val less p q =
          if Ord1.less (fst p) (fst q) then true
          else if Ord1.equal (fst p) (fst q) then Ord2.less (snd p) (snd q)
          else false
      end
;;
module NatOrder =
    struct
      type t = nat
      val equal x y = x == y
      val less  x y = x < y 
    end

;;

module NatPairOrder = LexicographicOrder(NatOrder)(NatOrder)