Popping a stack item in a file stream

Question

Using the answer from Push/Pop or save a length/dimension?, I have implemented a simple stack with a push and a pop function.

I would like to use the pop function in conjunction with newfile's addtostream so that I can export the latest item on the stack onto a file.

I am however unable to figure out how to make this work. The stack functions work fine in the text, but when inside addtostream everythings goes to hell...

Here is a MWE:

\documentclass{article}

\usepackage{etoolbox}
\usepackage{newfile}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Stack functions
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% push #1 onto #2
\newcommand{\push}[2]{%
   \begingroup\toks0={{#1}}
   \edef\XXX{\endgroup\global#2={\the\toks0 \the#2}}\XXX
}
% pop from #1
\newcommand{\pop}[1]{%
   \begingroup\edef\XXX{\endgroup\noexpand\splitList\the#1(tail)#1}\XXX
}
\def\splitList#1#2(tail)#3{%
   \ifx#1\empty Can't pop an empty stack.\else#1\global#3={#2}\fi
}
% creation of #1
\newcommand{\newstack}[1]{
  \newtoks#1
  #1={\empty}
}


\begin{document}

\section*{Testing the stack function}

  \newstack{\stackb}
  \push{{HHHH}}{\stackb}%
  \push{{XXXX}}{\stackb}%
  \push{{WWWW}}{\stackb}%
  if this: \pop{\stackb} shows "WWW", then it worked.

\section*{Testing the stack function popping to a file}

  \newoutputstream{AStream}
  \openoutputfile{criss.dta}{AStream}
  \newcommand{\bibi}{A simple macro can be sent to a file}

  \addtostream{AStream}{\bibi}
  %\addtostream{AStream}{\pop{\stackb}} % This one not working...
  \closeoutputstream{AStream}

\end{document}

Thanks for the help.