Functors

Functors là Functions dùng cho structure này với structure khác.

Functors cho phép viết code bất chấp cấu trúc dữ liệu cài đặt là gì, và cho phép tạo ra các hàm (functions) có thể thay đổi được.

(http://caml.inria.fr/pub/docs/manual-ocaml-4.00/manual004.html#toc15)

2.3  Functors

Functors are “functions” from structures to structures. They are used to express parameterized structures: a structure A parameterized by a structure B is simply a functor F with a formal parameter B (along with the expected signature for B) which returns the actual structure A itself. The functor F can then be applied to one or several implementations B₁ …B_n of B, yielding the corresponding structures A₁ …A_n.
For instance, here is a structure implementing sets as sorted lists, parameterized by a structure providing the type of the set elements and an ordering function over this type (used to keep the sets sorted):

# type comparison = Less | Equal | Greater;;
type comparison = Less | Equal | Greater

# module type ORDERED_TYPE =
    sig
      type t
      val compare: t -> t -> comparison
    end;;
module type ORDERED_TYPE = sig type t val compare : t -> t -> comparison end

# module Set =
    functor (Elt: ORDERED_TYPE) ->
      struct
        type element = Elt.t
        type set = element list
        let empty = []
        let rec add x s =
          match s with
            [] -> [x]
          | hd::tl ->
             match Elt.compare x hd with
               Equal   -> s         (* x is already in s *)
             | Less    -> x :: s    (* x is smaller than all elements of s *)
             | Greater -> hd :: add x tl
        let rec member x s =
          match s with
            [] -> false
          | hd::tl ->
              match Elt.compare x hd with
                Equal   -> true     (* x belongs to s *)
              | Less    -> false    (* x is smaller than all elements of s *)
              | Greater -> member x tl
      end;;
module Set :
  functor (Elt : ORDERED_TYPE) ->
    sig
      type element = Elt.t
      type set = element list
      val empty : 'a list
      val add : Elt.t -> Elt.t list -> Elt.t list
      val member : Elt.t -> Elt.t list -> bool
    end

By applying the Set functor to a structure implementing an ordered type, we obtain set operations for this type:

# module OrderedString =
    struct
      type t = string
      let compare x y = if x = y then Equal else if x < y then Less else Greater
    end;;
module OrderedString :
  sig type t = string val compare : 'a -> 'a -> comparison end

# module StringSet = Set(OrderedString);;
module StringSet :
  sig
    type element = OrderedString.t
    type set = element list
    val empty : 'a list
    val add : OrderedString.t -> OrderedString.t list -> OrderedString.t list
    val member : OrderedString.t -> OrderedString.t list -> bool
  end

# StringSet.member "bar" (StringSet.add "foo" StringSet.empty);;
- : bool = false