Re: [Caml-list] polymorphic lists, existential types and asorted other hattery

[Arnaud Spiwack <Arnaud.Spiwack@lix.polytechnique.fr>]

What you are describing is rather existential in essence. Existential 
type do not exist in OCaml but are encodable through interesting tricks 
(I know so because I kinda asked a similar question a few month ago :p 
). See discussion thread here (which was pointed to me this very time I 
asked the question) : http://tinyurl.com/2p5oan .

Here is your example refactored with this methodology :

type 'e show = { item : 'e; show: 'e-> string }
type 't show_scope = { bind_show : 'e. 'e show -> 't }
type showable = { open_showable : 't. 't show_scope -> 't }

let create_showable sh it =
  { open_showable = fun scope -> scope.bind_show { item = it ; show = sh } }

let use_showable shw f = shw.open_showable f

let show shw = use_showable shw { bind_show = fun sh -> sh.show sh.item }

let showable_int = create_showable string_of_int
let showable_bool = create_showable string_of_bool
let showable_float = create_showable string_of_float

let xs = [(showable_int 1); (showable_float 2.0); (showable_bool false)]

List.map show xs

Peng Zang a écrit :
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> Hi,
>
> Is there a way to create lists in which the elements may be of
> differing types but which all have some set of operations defined
> (eg. tostr) in common?  One can then imagine mapping over such lists
> with "generic" versions of those common operations.  Here's a concrete
> example of what I mean:
>
>   module Int = struct
>     type t = int
>     let show x = string_of_int x
>   end
>   module Float = struct
>     type t = float
>     let show x = string_of_float x
>   end
>   module Bool = struct
>     type t = bool
>     let show x = string_of_bool x
>   end
>
>   let xs = [`Int 1; `Float 2.0; `Bool false]
>   let showany x = match x with
>     | `Int x -> Int.show x
>     | `Float x -> Float.show x
>     | `Bool x -> Bool.show x
>   ;;
>   List.map showany xs;;
>
> Essentially we have ints, floats and bools.  All these types can be
> shown.  It would be nice to be able to create a list of them [1; 2.0;
> false] that you can then map a generalized show over.  In the above
> example, I used polymorphic variants in order to get them into the
> same list and then had to define my own generalized show function,
> "showany".  This is fine as there is only one shared operation but if
> there is a large set of these common operations, it becomes
> impractical to define a generalized version for each of them.
>
> I've come across a way to do this in haskell using what they call
> "existential types".
>
>   http://www.haskell.org/haskellwiki/Existential_type
>
> I don't really understand existential types however and don't know if
> OCaml has them nor how to use them.
>
> So.  How can one do this in OCaml?  Is there perhaps a camlp4
> extension that can do this?  Is there a possible functor trick that
> can take N modules as arguments and spit out a new module with a
> generalized type that can take on any of the types in the arguments
> and also make generalized versions of operations common to the N
> modules?  Are there existential types or equivalents in OCaml?  If so
> how does one go about using them?
>
> Thanks in advance to anyone who forays into this bundle of questions.
>
> Peng
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