From: Kenneth Whistler (kenw@sybase.com)
Date: Wed Jan 19 2005 - 20:07:10 CST
> One might give a purely mathematical definition of a Unicode character,
> freed from any computer representation, as a pair (k, s), where k is an
> integer, and s is string, or finite list, of elements from the set S := {A,
> ..., Z, ' '} (i.e., an element in the free monoid on the set S). Then, UTF-8
> defines a function f: (k, s) |-> (b, s), where b is a finite sequence of
> bytes (math definition omitted), where k in [0, 0x10FFFF]. The
> transformation I spoke about is a function g: k |-> b, where k in [0,
> 2^32-1] such that f(k, s(k)) = (g(k), s(k)) when k in [0, 0x10FFFF].
Which is just mathematical gobbledygook for saying you want
to define an extension of UTF-8 which does the same mapping
of code point to byte sequence for any code point in the
Unicode scalar value range (which is [0, 0xDFFF] U [0xE000, 0x10FFFF],
by the way, *not* [0, 0x10FFFF]), and which also gives you
a mapping of integers to byte sequence for the entire range
[0, 0xFFFFFFFF].
And which is just as objectionable stated in mathematics as stated
in terms understood by character encoders.
By the way, I believe your formulation to be bogus, because s(k)
is not defined here in any meaningful way for a character encoding
when k is not an element of the defined code space.
In other words, you *could* claim you have a pair (k, s) where
k = 0x10101010 and s = "HANS ABERG", but that would not be
a "Unicode character" in any sense acceptable to the standardizers
or the implementers.
Also, your set S is incorrectly defined.
--Ken
>
> Hans Aberg
>
>
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