Normalization Generics (NFx, NFKx, NFxy)

[Zach Lym]

Okay, so points for pedantry ... but do you have any input on adding
normalization generics to Unicode pseudocode?

Or would you like to split this discussion out into a new topic?

On Tue, Dec 15, 2020 at 11:21 AM Richard Wordingham via Unicode
<unicode at unicode.org> wrote:
>
> On Sun, 13 Dec 2020 20:08:08 -0800
> Zach Lym via Unicode <unicode at unicode.org> wrote:
>
> > > What does that quoted statement mean?  I'm having a hard job working
> > > out what the meaning of full case folding is.  I'm not having any
> > > doubts about the meaning of toCasefold(NFD(X)), so there is no issue
> > > for 'canonical caseless matching'.
> >
> > The "case folding is closed under canonical normalization" or the
> > other part?
>
> That part.
>
> > Closed as in closure:
> > https://en.wikipedia.org/wiki/Closure_(mathematics)
>
> That only tells me what it means for a _set_ to be closed under an
> operation.  What does it mean for a _function_ (or similar) to be
> closed under an operation?
>
> If I must use the definition for a set, then I can only conclude that
> for one operation to be closed under another operation, the result
> should be independent of the order in which they are applied.
>
> But for X = <U+1FB3 GREEK SMALL LETTER ALPHA WITH YPOGEGRAMMENI, U+0342
> COMBINING GREEK PERISPOMENI>:
>
> NFD(toCasefold(X)) = <U+03B1 GREEK SMALL LETTER ALPHA, U+03B9 GREEK
> SMALL LETTER IOTA, U+0342>
>
> toCasefold(NFD(X)) = <U+03B1, U+0342, U+03B9>
>
> NFC(toCasefold(X)) = <U+03B1, U+1FD6 GREEK SMALL LETTER IOTA WITH
> PERISPOMENI>
>
> toCasefold(NFC(X)) = <U+1FB6 GREEK SMALL LETTER ALPHA WITH PERISPOMENI,
> U+03B9>
>
> So either "case folding is closed under canonical normalization" means
> something else, or it is simply not true.
>
> > Refer to page 240 of the standard, Chaper 5 "Implementation
> > Guidelines" Section 18 "Case Mappings":
> >
> > http://www.unicode.org/versions/latest/ch05.pdf
>
> Why?
>
> The trick is not to be deflecting by the opening paragraph in TUS
> Section 3.13, but to read on to find R4.
>
> Richard.