module type Sign = sig
  module type S
end

module type Nat =
  functor (S : Sign) -> functor (X : S.S) ->
    functor (F : (functor (M : S.S) -> S.S)) -> S.S

module Zero : Nat =
  functor (S : Sign) -> functor (X : S.S) ->
    functor (F : (functor (M : S.S) -> S.S)) -> X

module Succ (N : Nat) : Nat =
  functor (S : Sign) -> functor (X : S.S) ->
    functor (F : (functor (M : S.S) -> S.S)) -> N(S)(F(X))(F)

module One : Nat = Succ(Zero)

module type Fun = functor (N : Nat ) -> Nat

module NatS = struct
  module type S = Nat
end

module Aux (F : Fun) (N : Nat) : Nat = N(NatS)(F(One))(F)

module FunS = struct
  module type S = Fun
end

module A (N : Nat) = N(FunS)(Succ)(Aux)

module Ack (N : Nat) : Nat = A(N)(N)

module Four : Nat = Succ(Succ(Succ(One)))

let () = print_endline "Hello"

module M = Ack(Four)