[texhax] Some puzzling TeX

Donald Arseneau asnd at triumf.ca
Tue Feb 22 13:24:54 CET 2011

"Uwe Lueck" <uwe.lueck at web.de> writes:

> >On Sun, Feb 20, 2011 at 8:13 AM, Uwe Lueck  wrote:

> >> I am unable to get a catcode of \relax or \bgroup by \showthe\catcode.

This betrays a subtle misunderstanding.  There is no catcode of
\relax; only character tokens have category codes.  \bgroup is 
let equal to a character token so it does indeed have a category 
code (1).

However \catcode does not tell the category of a character token!
It only reports contents of the look-up table TeX uses to interpret
raw characters as they are input (or as they are re-scanned, in eTeX).
This has to be so since the argument for \catcode is a number, not
a token! 

Therefore the concept of "get a catcode of" some token, any token, 
by \showthe\catcode is without hope.

TeX provides no way to report the category code for a token except
by a deeply nested series of \ifcat comparisons.

> >> Only with \ifcat, I can see that \relax and \bgroup are different,
> >> while, e.g., after \let\BGROUP{\et\EGROUP}, \bgroup and \BGROUP
> >> are the same according to \ifcat.


> >> My conclusion at the moment is that one might better say that
> >> with \ifcat, control sequences behave "as if they had catcode 16 or ..."
> >> Especially, it seems to me that instead of "catcode 16" one could
> >> as well speak of "catcode -1" or anything else that is not among
> >> 0, ..., 15.

I think "TeX considers it to have", as in the TeXbook, gets the meaning 
across.  Yes, any other out-of-band or impossible value would have served 
as well.

> > Whew...  so, it looks like this myth of "control sequences have
> > catcode 16" can finally be put to rest.  The catcode of a control
> > sequence is, in fact, 0.  But since there's no way to ever get a naked
> > escape token (catcode 0) into the input stream, the fact that it has
> > the same catcode is irrelevant.

Interesting.  I wonder why DEK says 16 then.  Laziness? Simplicity
(avoid explaining why 0 is safe)? Forgetfulness?

Donald Arseneau                          asnd at triumf.ca

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