Re: [I18nrp] Mappings for IDNA2008 ?

[Martin J. Dürst <[e-mail]>]

Hello Patrik, others,

On 2019/02/13 17:25, Patrik Fältström wrote:
> 
> 
>> On 13 Feb 2019, at 09:19, Asmus Freytag (c) <[e-mail]> wrote:
>>
>>> On 2/12/2019 11:46 PM, Patrik Fältström wrote:
>>>
>>>> On 13 Feb 2019, at 08:18, Martin J. Dürst <[e-mail]> wrote:
>>>>
>>>> If f(x) is the generic mapping, and f'(x) is the mapping of the
>>>> exceptions, then f(f'(x)), which applies f' *before* f, should do the job.
>>> This works in some cases and not in other cases.
>> Examples?
> 
> This is math. :-)
> 
> If f(x)=x’ and in the locale used f(x) should be x and not x’, you have dependencies between f(x) and f’(x) if you want f(f’(x)) to be x’ and f(f”(x)) to be x.

Well, I have to admit that I didn't explicitly talk about that case in 
my 'proof'. For functions in general (e.g. a function such as f(x) = 
(x+7) mod 15), you are right.

But f(x) (the general mapping function) is idempotent (i.e. f(x) = 
f(f(x)), which means that you can map as many times as you want, you 
always get the same result). This is also true for any locale-dependent 
mapping function. If it were not the case, human users would be very 
surprised: a maps to A, but then A maps to a: That wouldn't make any sense.

Also, and even more important, for the general mapping function, if x is 
allowed in IDNs, then f(x) = x. This may not be true for a 
locale-dependent mapping function (i.e. it would be possible for a 
German mapping function to map (Hungarian) ȁ to ä, although that's not 
needed because German keyboards won't produce ȁ in the first place).

So if f(x)=x', that would mean that x is not allowed in IDNs. That would 
mean that it is impossible that in a specific locale, the desired result 
of f(f'(x)) is x. It may be different from x', i.e. y, but we can easily 
get this by defining that f'(x) = y.

So applying the (in most if not all cases very small) locale-specific 
mapping before the general mapping always will work.

Regards,   Martin.