Here is a minimal non-working example:
\documentclass{article} \begin{document} \let\@var\@empty \newcommand{\append}[1]{ \xdef\@var{\@var #1} } \append{1} \append{2} \append{3} \@var \end{document} I was expecting \@var to contain the string 1 2 3, but instead I get the following error:
! TeX capacity exceeded, sorry [input stack size=5000]. \@var->\@var How can I achieve what I was expecting to achieve?
You're missing \makeatletter...\makeatother pairs -- those are necessary due to \@ as macro (starter) name.
If the 'string' macro should not be indicated as internal (\@.... are internally 'hidden) choose another name, like \mystringvar, this will remove the issue with \makeatletter...\makeatother
\documentclass{article} \begin{document} \makeatletter \let\@var\@empty \newcommand{\append}[1]{\xdef\@var{\@var #1} } % Another variant with kernel \g@addto@macro \newcommand{\appendother}[1]{\g@addto@macro{\@var}{#1}} \makeatother \newcommand{\foo}{789} \append{1} \append{2} \append{3} \appendother{456\foo} \makeatletter \@var \makeatother \end{document} 
\append and \appendother, writing \appendother{\textbf{3}} gives the expected result, but \append{\textbf{3}} throws the error ! Argument of \reserved@a has an extra }. ? \xdef can't be applied to a protected macro like \textbf Christian has shown what you could do instead but to explain the error
@ is not a letter in the main document so
\let\@var\@empty does
\let\@=v then typesets ar\@empty producing the paragraph text arvempty (which you don't see as later errors prevent a pdf being made.
Then
\newcommand{\append}[1]{ \xdef\@var{\@var #1} } defines \append to typeset a space (why?) and then redefine \@ then typeset another space.
\append{1} is therefore a space (ignored as we are in vertical mode) then
\xdef\@var{\@var 1} this is defining the macro \@ to be followed by the tokens var to be the expansion of \@var 1 now at this point \@ is non-expandable as it is \let to v so now \@ has to be followed by var and expands to \@var 1
Then another ignored space is output and
\append{2} this outputs another space then
\xdef\@var{\@var 2} which again is redefining \@ to be a macro that must be followed by var but the definition is obtained by expanding \@var 1 but as noted above the expansion of \@var is at this point \@var 1 so the first expansion produces
\@var 1 2 Then \@ expands again producing
\@var 1 1 2 and so on until you run out of input stack. (because the 1's are all being pushed ahead of you)
\makeatletterrequired): did you run exactly this file?1 2 3but123. If you want to have the space in between you have to use\@var\ #1\space.