Re: [Caml-list] Question about polymorphic variants

[Xavier Clerc <xcforum@free.fr>]

Le 29 oct. 05 à 02:26, Jacques Garrigue a écrit :

[...]

>> In this counter-example, it is not clear to me whether the possible
>> problem is type-related or runtime-related. I mean, would this
>> counter-example still hold if arrays were both boxed or both  
>> unboxed ?
>>
>
> No, the difference in representation is essential here.
>
> But at the type level, this problem can be expressed a bit
> differently: whether it is safe to add a "top" to the type system,
> allowing any type to be coerced to it. While some languages might
> allow that, there is no fundamental reason it should be so (an this is
> indeed not the case in ocaml.)
> If we cannot assume the existence of such a type, then we cannot prove
> that polymorphism in this case would be safe.

I must admit that I don't grasp the link between the existence of a  
"top" type and the inference of a polymorphic type in the given  
examples. I would expect inference of 'a array in arrays example and  
'a in "List.map (fun (x, y) -> x + 1)" and don't see in what  
circumstances such types would not be safe (modulo the array  
representation issue discussed above).
Could you exhibit an example where such inference would be false/ 
unsafe ?


>>> Actually, since this counter-example wouldn't apply to the above  
>>> case
>>> of polymorphic variants, this would probably be safe to leave the
>>> polymorphic variant type as polymorphic...
>>>
>>
>> Does this mean that inferring "[< `Off | `On] list -> int list" would
>> be perfectly safe in the example above ?
>> (by saying so, I am not pleading for any compiler change, I am just
>> trying to organize my thoughts)
>>
>
> I believe so, but I don't have a proof ready for that.
> One way to do it would be to prove that any instance of [< `Off | `On]
> is a subtype of [ `Off | `On ], which sounds trivial in this case.
> So I would say this should apply to both [< ... ] types (closed
> polymorphic variants, including the [< ... > ...] case) and <...; ..>
> types (extensible object types.) But not to [> ...] types (open
> polymorphic variants.)


Well, the only way to get rid of the leading underscore in inferred  
type is to "use" all the tags of the type (that is "converge" toward  
the upper bound of the variant), as in the following toplevel session :

# let f = function
   | `Off -> 0
   | `On -> 1;;
val f : [< `Off | `On ] -> int = <fun>
# let mf = List.map f;;
val mf : _[< `Off | `On ] list -> int list = <fun>
# mf [`On];;
- : int list = [1]
# mf;;
- : _[< `Off | `On > `On ] list -> int list = <fun>
# mf [`Off];;
- : int list = [0]
# mf;;
- : [ `Off | `On ] list -> int list = <fun>

Does this mean that [`Off | `On] list -> int list could be inferred  
for mf as one can pass [`Off | `On] where [< `Off | `On] is waited  
(as [`tag1 | `tag2 ... | `tagn] is shorthand for [< tag1 | `tag2 ...  
| `tagn > tag1 | `tag2 ... | `tagn]).




I apologize for my questions if they are trivial but I must confess  
that I am having a hard time understanding the subtleties of  
polymorphic variants.


Xavier Clerc