Re: [Caml-list] "map"-ing parameterized class types

[Jacques Garrigue <garrigue@math.nagoya-u.ac.jp>]

Hi Oleg,

The externalizing solution has been known since the beginning of
OCaml, but it is nice to know that it has such a cute name…

Jacques

On 2015/10/23 00:04, Oleg wrote:
> 
> The question was about creating a class of the following type
> 
>>     class type ['a] container : 'a ->
>>       object
>>         method map : 'b. ('a -> 'b) -> 'b container
>>       end
> 
> with a mapping method that makes a container of a different
> type. Jeremy Yallop has explained very well the class of exactly such
> type is not possible. The following is perhaps the simplest workaround
> requiring neither modules nor other higher-class artillery. It should
> have been possible even in OCaml 3.10 or earlier.
> 
> The idea was inspired by some high-falutin' Math, namely, left Kan
> extension from Category Theory. I actually don't know CT but I think I
> got the gist of the left Kan extension: rather than execute an an
> operation, just collect all the needed arguments and declare the
> operation performed. The recent paper on Freer monads (Haskell
> Symposium 2015) used two instances of this new kind of laziness.
> 
> Here is the whole solution
> 
>    type 'a cont_proxy = P of 'a
> 
>    class ['a] container (x : 'a) = object
>      method get_x = x
>      method map' : 'b. ('a -> 'b) -> 'b cont_proxy = fun f ->
>        P (f x)
>    end
> 
> The class container has one argument, which is the value needed to
> construct the container. The data type cont_proxy contains all the
> information needed to construct the container, but not the container
> itself (for one, the container type is not yet defined when we
> declared P). The method map' doesn't actually construct anything; it
> merely returns the data needed for the construction.
> 
> The map itself is then easy to define:
> 
>    let map : ('a -> 'b) -> ('a container -> 'b container) = fun f c ->
>      match c#map' f with
>        P x -> new container x
> 
> let c = new container 3
>    val c : int container = <obj>
> let _ = c#get_x
>    - : int = 3
> let c' = map string_of_int c
>    val c' : string container = <obj>
> let _ = c'#get_x
>    - : string = "3"