Re: [Caml-list] composing functions...

["Daniel Bünzli" <daniel.buenzli@epfl.ch>]

Le 1 déc. 05 à 02:34, skaller a écrit :

> let h = compose f g
>
> You can of course fold 'compose' over a list if all the
> functions have the same type, if not, then you can't
> make the list in the first place :)

Unless you define your own type for lists of composable functions  
(see below). This was an example I wrote in this discussion [1] about  
encoding existential types in ocaml.

Best,

Daniel

[1] <http://sardes.inrialpes.fr/~aschmitt/cwn/2004.01.13.html#1>

module Funlist : sig

(* The funlist datatype *)
type ('a, 'b) t

(* Constructors *)
val nil : ('a, 'a) t
val cons : ('a -> 'b) -> ('b, 'c) t -> ('a, 'c) t

(* Applying a value to a composition *)
val apply : ('a, 'b) t -> 'a -> 'b

end = struct
(* List of composable functions.

    The intended type expressed by the four types below is :
    type ('a, 'b) t = Nil of ('a -> 'b)
                    | Cons of exists 'c. ('a -> 'c) * ('c, 'b) t
*)
type ('a, 'b) t = Nil of ('a -> 'b) | Cons of ('a, 'b) packed_list
and ('a, 'b, 'z) list_scope = { bind_list : 'c. ('a -> 'c) * ('c, 'b) t
-> 'z}
and ('a, 'b) packed_list = { open_list : 'z. ('a, 'b, 'z) list_scope ->
'z }

(* Packing and unpacking lists *)
let pack_list h t = { open_list = fun scope -> scope.bind_list (h,t) }
let with_packed_list p e = p.open_list e

(* Constructors *)
let nil = Nil (fun x -> x)
let cons h t = Cons (pack_list h t)

(* Type to handle the polymorphic recursion of the apply function *)
type poly_rec = { apply : 'a 'b. poly_rec -> ('a, 'b) t -> 'a -> 'b }
let apply' r l x = match l with
| Nil id -> id x
| Cons l ->
     with_packed_list l { bind_list = function h,t -> r.apply r t (h  
x) }

let poly_rec = { apply = apply' }
let apply l x = apply' poly_rec l x

end

(* Example of use *)
let twice x = 2*x
let double x = (x, x)
let list = Funlist.cons twice (Funlist.cons (( = ) 4) (Funlist.cons
double Funlist.nil))
let a, b = Funlist.apply list 2