\ifcsname x\endcsname when it isn't apparent that \x was made \relax

Question

A few days ago I tried to point out to Will Robertson one of the pitfalls of eTeX’s \ifcsname and \ifdefined but he didn’t seem to get the message. Please am I right in saying that the following beckons us to be cautious when using\ifcsname and \ifdefined, since they return 'true' when a command is made \relax? Tests like etoolbox's \ifdef and \ifcsdef should be preferred when the aim is to test if a command is equivalent to \undefined.

With the hope of later doing, e.g., \expandafter<cmd>\x, I defined

\edef\x{\unexpanded\expandafter{\csname test@\romannumeral\currentgrouplevel\endcsname}}

After some intervening code, I then did

\ifcsname test@\romannumeral\currentgrouplevel\endcsname
  \def\y{Yes}
\else
  \def\y{No}
\fi
\show\y

On the face of it, there was no apparent relation between defining \x and the later test. I first wondered where test@\romannumeral\currentgrouplevel was defined. It took me some time to locate the problem.

Answer 1

It's not misleading because it follows the precisely laid out rules.

1. When \csname is expanded, TeX looks for the matching \endcsname with expansion; then TeX forms a control sequence token from the character tokens (irrespective of category code) it has found or issues an error if some non character token is discovered.

2. After the formation of the token, TeX looks up in its memory to find if that token has a meaning. If it hasn't, that token is made equivalent to \relax with a local assignment.

3. \edef expands the tokens it finds between the braces that delimit the replacement text before storing the resulting <balanced text> as the replacement text.

Thus your \edef\x{\csname totallyundefined\endcsname} is equivalent to

\let\totallyundefined\relax
\def\x{\totallyundefined}

On the contrary, the \ifdefined and \ifcsname tests (by precise choice of e-TeX's developers) never perform the assignment to \relax of an undefined token.

The \relax assignment is performed in many other cases as a precaution against premature expansions. Two cases mentioned in the TeXbook are

\chardef\cs=10\cs
\font\cs=name\cs

where \cs is temporarily made equivalent to \relax in order to stop expansion when the assignment is performed. In such cases it's really temporary, as \cs will immediately be assigned a new meaning; in the case of \csname it isn't. Where's the problem? If \cs had a previous definition, without the temporary assignment to \relax, TeX would expand \cs searching for a number in the first case or the end of the file name in the second. Even worse, if \cs was undefined, an error would be raised, because TeX hasn't yet assigned to \cs the new meaning. Of course, using such a syntax is discouraged.

It may be unfortunate that e-TeX uses \ifcsname...\endcsname with the same rules of \csname...\endcsname for the formation of the token to be examined, but with the fundamental difference that the equivalence to \relax is not performed, but that's what it is.

---

In the case you're presenting, that is

\edef\x{\unexpanded\expandafter{\csname test@\romannumeral\currentgrouplevel\endcsname}}

you might do it indirectly:

\edef\x{\noexpand\csname @test\romannumeral\currentgrouplevel\endcsname}

so that the \csname won't be executed. Of course \x would need two expansions steps:

\expandafter\expandafter\expandafter\cs\x

Answer 2

Both \ifcsname and \ifdefined test if the control sequence is defined at all, this includes control sequences which are equal to \relax. Earlier tests use \expandafter\ifx\csname abc\endcsname\relax which uses the feature of \csname to define undefined control sequences automatically to be equal to relax. You are right that mixing these two ways to test is dangerous, because any \ifx\csname test or other \csname on the same name will change the outcome of the other two tests on the same control sequence, because it is now defined equal to \relax. Both \ifcsname and \ifdefined intensionally do not define the control sequence to \relax and should actually be preferred over \ifx\csname, but you might only want them to use with control sequences your package etc. defines itself where no other code tested it using a different test.

BTW: You can use grouping like: \begingroup\expandafter\ifx\csname abc\endcsname\relax\endgroup ..\else\endgroup .. \fi, to keep the \csname definition local, but the LaTeX core macro \@ifundefined doesn't do that.

Answer 3

Not sure if the second part of the question will be migrated but here is an explanation in any case.

The expansion of \ifnum...\fi is empty if the test is false, \relax otherwise, thus the meaning of

   `\edef\x{\ifnum0=0\fi}`

is

   `macro:->\relax`

Try this test for fun:

    {\def\relax{0}\xdef\foo{\ifnum0=0\fi}}

This puts \relax in \foo. Although tricky, this token is not the same token as the one that follows the \def, since otherwise 0\fi would expand to 0\relax\fi then 00\fi, then 00\relax\fi without end (and without overflow).

This behaviour is not an oddity, but a mind boggling fact!