You are correct. And I am correct. But we are
not taking about even a little
bit of the same thing.

Once again I will try to be clear:
Knuth's work resulted in a computer program, TeX,
as an EXE file, say, tex.exe.

A user of TeX as a word processor types
in a file with three letter extension TEX,
say, my_math.tex. This file, my_math.tex,
actually is a computer program, that is,
has allocate-free storage, if-then-else,
file read-write, arithmetic, string manipulations,
etc. This computer program my_math.tex is
not Knuth's program tex.exe.

Yes, maybe not
all TeX users have their TeX input files,
say, my_math.tex, do file reading or writing,
but such file manipulations are just routine
usage of TeX that I do nearly always. And I
have some TeX macros I wrote that do
storage allocation-freeing. Maybe not all
TeX users do such things, but they are routine
usage of TeX, and I do them.

To be more clear on just why file my_math.tex
is a computer program, when Knuth's tex.exe
runs file my_math.tex (interpretively), the program
my_math.tex can read files. Then the output
my_math.dvi can vary depending on what was in
the file, say, my_math.dat that program my_math.tex read.

Well, there can be no file my_math.htm
that will read a file my_math.dat, that is,
read the file
and process it like my_math.tex can.

So, if only for this reason, as a result,
program my_math.tex can never be
translated to a file my_math.htm.
And program my_math.tex can't be
translated to my_math.pdf or my_math.ps
either.

But a file my_math.dvi, from my_math.tex and a particular my_math.dat, can be
translated to a file my_math.pdf or my_math.ps.

And in this thread I have been suggesting that
there could be a program that would
translate my_math.dvi to my_math.htm.

> TeX -> PDF can be done without an intermediate DVI stage using pdftex.

Although this is a small point,
for pdftex,
I am quite sure that internally a DVI file
is generated if only because that is
what Knuth's program tex.exe generates and
rewriting Knuth's TeX code, likely now in C,
say, tex.c,
would be both unnecessary and the
difficult approach. Just generating the
DVI file is the easy approach, even if
don't have the user aware of the intermediate
DVI file.

What PDFTEX does I do frequently by putting in the
extra step of going to DVI and then from DVI to PDF.
Fine.

I want the DVI file because I like the
DVI preview program I have and like it much more than
than using a PDF viewer. When I get something that looks
good with my DVI preview program, then usually I go
ahead and make the PDF file.

However, what I am doing getting a PDF file
and what you are talking about with pdftex are
not, in the sense I am discussing, a translation of TeX to PDF. Not at all.

> Any reasoning about TeX being able to do things that HTML can't is irrelevant.

True for what you are talking about. False for
my point that a file my_math.tex can't be
translated to a file my_math.htm.

Or, for a short explanation, you are saying that
a file my_math.dvi can be translated to
file types PS and PDF and maybe also HTM,
and I agree.
But I am also saying that a file
my_math.tex cannot ever be translated
to a file my_math.htm.

To be still more clear,
HTML is a mark-up language, and TeX looks like
it is also a mark-up language, so
one might try to translate TeX mark-up to
HTML mark-up. Well, such a translation is
just impossible, and will always be.