The meaning of \@@

Question

A couple of times in the latex.ltx kernel, the macro \@@ is used. For instance in the definition of \@next (l.6222):

\def\@next#1#2#3#4{\ifx#2\@empty #4\else
   \expandafter\@xnext #2\@@#1#2#3\fi}

I don't see the macro defined anywhere. (Quick searches with e.g. \let, \def, \newcommand with and without star, etc. didn't yield anything meaningful.) I also don't see it in plain.tex. I kind of don't understand what \@next does because of this macro, and a canonical answer wasn't available on the site yet anyway.

So what does \@@ mean?

Answer 1

You can't understand the definition of \@next without looking also at the definition of \@xnext and at an example of usage; the complete code is

\def\@next#1#2#3#4{\ifx#2\@empty #4\else
   \expandafter\@xnext #2\@@#1#2#3\fi}
\def\@xnext \@elt #1#2\@@#3#4{\def#3{#1}\gdef#4{#2}}

and an example of usage is at line 5963

\@next\@marbox\@freelist{\global\count\@marbox\m@ne}%
   {\@floatpenalty\z@
    \@fltovf\def\@currbox{\@tempboxa}\def\@marbox{\@tempboxa}}%

The second argument to \@next should be a parameterless control sequence (due to the \ifx test and the following \expandafter). The macro \@freelist is such a macro, used in connection with the float queues, and it is updated when a float is started or floats are flushed with \clearpage. Its definition at startup is

\@elt\bx@A\@elt\bx@B\@elt\bx@C...\@elt \bx@R

that is, it lists the insertion classes pertaining to floats (here ... denote similar tokens).

If \@freelist contains nothing, the fourth argument is delivered; otherwise

\expandafter\@xnext\@freelist\@@\@marbox\@freelist{\global\count\@marbox\m@ne}\fi

remains on the input stream. So, assume \@freelist is not empty and, for the sake of simplicity, it is the same as at startup. The \expandafter makes TeX see

\@xnext\@elt\bx@A\@elt\bx@B\@elt\bx@C...\@elt \bx@R\@@\@marbox\@freelist{\global\count\@marbox\m@ne}\fi

Note that, in order for this to work, the first level expansion of the second argument to \@next must begin with \@elt. What's \@elt? It's just a token usually defined to be \relax, which is used to store ordered lists of tokens in the form \@elt<token1>\@elt<token2>... that allows for list manipulations.

Now the definition of \@xnext comes into play. It has a complex parameter text that can be described as follows:

1. \@elt is expected just after the command

2. #1 means an undelimited argument, so just one token or a braced group, because it's immediately followed by #2

3. #2\@@ means a delimited argument, that is, TeX will substitute #2 with everything up to (and excluding) the first \@@ token it finds;

4. #3 and #4 are undelimited arguments (the same as for #1 applies).

In the context of delimited arguments, the delimiter tokens need not be defined; TeX looks for the exact sequence of tokens and control sequences are considered equal only if their names are the same.

The delimiters are removed from the input stream as part of macro expansion. So in this particular case, \@elt is found and the search for the following arguments can start (\@elt will be removed); argument #1 is \bx@A; argument #2 is

\@elt\bx@B\@elt\bx@C...\@elt \bx@R

and arguments #3 and #4 are \@marbox and \@freelist respectively.

Expansion of \@xnext makes all that code be replaced by

\gdef\@marbox{\bx@A}\gdef{\@freelist}{\@elt\bx@B\@elt\bx@C...\@elt \bx@R}

The two definitions are performed, which in particular shows how \@marbox becomes equivalent to \bx@A (the first insertion class) and \@freelist is updated, essentially removing the first item. The dangling \fi remaining disappears by general TeX rule (the expansion of \fi is empty, provided it resulted from expansion of a previous conditional, which in this case was the \ifx we started with).

The token \@@ is used in a very similar way, that is, as a pure delimiter, in the auxiliary macros for the loop functions \@for and \@tfor.

Answer 2

Actually, just the next line defines a macro that uses \@@ as a delimiter:

\def\@next#1#2#3#4{\ifx#2\@empty #4\else
   \expandafter\@xnext #2\@@#1#2#3\fi}
\def\@xnext \@elt #1#2\@@#3#4{\def#3{#1}\gdef#4{#2}}

So it seems to be used as a delimiter (like \@nil or \relax in traditional LaTeX or quarks in expl3, \q_stop, etc.). I don't know it there's an additional idea behind \@@ (like there's when someone uses quarks or \relaxs, etc.).

Answer 3

If you get the documentation for the array environment (say texdoc array) then it refers to \@@serving as an argument delimiter — see, for example, page 9 of the documentation from TeX Live 2014 (and other distributions). The sources2e documentation (say texdoc sources2e) has \@@ in its index but does not explicitly mention its usage (at least anywhere I could see). Perhaps this is a standard TeX technique ?