Re: String complements

>    >    For a simplified example, revert("abc") would produce "zyx" .
This is doable and really valuable.
>
>      In what sense is “zyx” the complement of “abc”? Over what set of
codepoints and in what collation?
>
>      I am very skeptical that such a function is well defined across all
collations and will always produce a single, correct result in all cases.
>
>      Can you provide a detailed description of how this would work?

Yes, as Michael Kay already explained, this is doable if either: the
"biggest" symbol in the collation is not used (which btw happens in some
collations, for example the biggest symbol in the English(American)
collation is 0xFE) - or add an additional symbol that is "bigger" than any
other symbol in the collation.

Let us, just for convenience, refer to this special symbol as '$' (this is
just a convention on how to refer to this special symbol, not the actual
dollar character).

Then, if S1, S2, ..., Sn are all n symbols in the collation ordered by
their value in the collation,  perform this mapping:

"" :             '$' ,
S1 : Sn || '$' ,
S2 : Sn-1 ||  '$' ,
.  .  .  .  .  .  .
Sk : Sn-k+1 || '$',
.  .  .  .  .  .  .

Sn : S1 || '$'

And certainly, adding a new symbol to a collation is actually creating a
new collation, and this would maybe be the most straight-forward way of
inverting strings.

We may not even create any new collation, we could just have a *convention*
that a collation named "Inverted" || {Real-Collation-Name} produces the
negated comparison results of the ones produced by the
{Real-Collation-Name} collation. Or, as I mentioned before, this is the
same as "decorating a collation".

This is one more way to get rid of the $orders parameter in our current
functions.

Thanks,
Dimitre

On Thu, Mar 14, 2024 at 3:24 AM Norm Tovey-Walsh <norm@saxonica.com> wrote:

> Dimitre Novatchev <dnovatchev@gmail.com> writes:
> >    This function can easily handle strings - produce a "string
> complement" in the value space for a particular collation.
> >
> >    For a simplified example, revert("abc") would produce "zyx" . This is
> doable and really valuable.
>
> In what sense is “zyx” the complement of “abc”? Over what set of
> codepoints and in what collation?
>
> I am very skeptical that such a function is well defined across all
> collations and will always produce a single, correct result in all cases.
>
> Can you provide a detailed description of how this would work?
>
>                                         Be seeing you,
>                                           norm
>
> --
> Norm Tovey-Walsh
> Saxonica
>