Passing stack data to tikz node names

Question

I'm trying to use a stack data structure (as discussed here: Push/Pop or save a length/dimension?) to store the various names of a set of tikzmark node names (as discussed in tikzmark manual) scatted throughout my text.

Separately the stack implementation (WE1) and \tikzmark (WE2) work perfectly, but their combined behaviours somehow clash with multiples errors.

I can't for the life of me figure out what's going wrong when I try passing the popped stack data elements as node names within a \tikzmark command (MWE below). Is this a problem arising from my LaTeX code not immediately evaluating the \pop commands (I've tried playing around with \expandafter and \edef to no success...)? I've also tried passing \pop{\latexstack} to a \newcommand{}, but I haven't managed to get that method to work either...

MWE [Incorrect combined behaviours...]

\documentclass{article}
\usepackage{blindtext, tikz}
    \newtoks\latexstack
    \latexstack={\empty}

    \def\push#1#2{
        \begingroup
        \toks0={{#1}}
        \edef\act{\endgroup\global#2={\the\toks0 \the#2}}\act
    }

    \def\pop#1{
        \begingroup
        \edef\act{\endgroup\noexpand\SplitOff\the#1(tail)#1}\act
    }

    \def\SplitOff#1#2(tail)#3{
        \ifx#1\empty
            \errhelp{Attempting to pop empty stack #3.}
            \errmessage{You can't pop an empty stack.}
        \else
            #1\global#3={#2}
        \fi
    }

    \newcommand\tikzmark[1]{\tikz[overlay,remember picture] \node(#1) {};}

\begin{document}
    \push{A1}{\latexstack}
    \push{B2}{\latexstack}

    \blindtext \tikzmark{\pop{\latexstack}}\\ 
    \blindtext \tikzmark{\pop{\latexstack}}\\ 

    \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
        \draw[red] (A) -- (B);
    \end{tikzpicture}
\end{document}

WE1 [Correct behaviour of stack data structure: A1, B2, C3, and D4 are pushed and sequentially popped from the data structure]

\documentclass{article}
    \newtoks\latexstack
    \latexstack={\empty}

    \def\push#1#2{
        \begingroup
        \toks0={{#1}}
        \edef\act{\endgroup\global#2={\the\toks0 \the#2}}\act
    }

    \def\pop#1{
        \begingroup
        \edef\act{\endgroup\noexpand\SplitOff\the#1(tail)#1}\act
    }

    \def\SplitOff#1#2(tail)#3{
        \ifx#1\empty
            \errhelp{Attempting to pop empty stack #3.}
            \errmessage{You can't pop an empty stack.}
        \else
            #1\global#3={#2}
        \fi
    }

\begin{document}
    \push{A1}{\latexstack}
    \push{B2}{\latexstack}
    \push{C3}{\latexstack}
    \push{D4}{\latexstack}

    \pop{\latexstack},\\ 
    \pop{\latexstack},\\ 
    \pop{\latexstack},\\ 
    \pop{\latexstack}.
\end{document}

WE2 [Correct behaviour of \tikzmark: Points A and B are marked, and connected together with a red line]

\documentclass{article}
\usepackage{blindtext, tikz}

    \newcommand\tikzmark[1]{\tikz[overlay,remember picture] \node(#1) {};}

\begin{document}
    \blindtext \tikzmark{A}\\
    \blindtext \tikzmark{B}

    \begin{tikzpicture}[remember picture,overlay,scale=0.5] 
        \draw[red] (A) -- (B);
    \end{tikzpicture}
\end{document}

Answer 1

I think the problem here is expansion. When TikZ creates nodes the node name is fully expanded using \edef.

Assuming the OPs original code then consider the following

\push{A1}{\latexstack}
\push{B2}{\latexstack}
\edef\nodename{\pop{\latexstack}}
\show\nodename

This illustrates the full expansion and will give (in the log file):

! Undefined control sequence.
\pop #1^^@- \begingroup \edef \act 
                                 {\endgroup \noexpand \SplitOff \the #1(tail...
l.36     \edef\nodename{\pop{\latexstack}
                                       }
! Undefined control sequence.
\pop ... \noexpand \SplitOff \the #1(tail)#1}\act 

l.36     \edef\nodename{\pop{\latexstack}
                                       }
> \nodename=macro:
-> \begingroup \edef {\endgroup \SplitOff {B2}{A1}\empty (tail)\latexstack }.
l.37     \show\nodename

Note the problem is not that \act is undefined. The errors will disappear if \let\act=\relax is placed somewhere in the preamble, but the contents of \nodename is still a whole bunch of LaTeX code, not the desired node name.

One solution is to have a \popto command which pops the value at the top of the stack into a macro which is then used as a node name (NB. I also reimplemented the \push macro):

\def\push#1#2{%
  \def\tmp{{#1}}%
  \expandafter\expandafter\expandafter%
    #2\expandafter\expandafter\expandafter{\expandafter\tmp\the#2}%
\ignorespaces}

\def\popto#1#2{%
  \expandafter\SplitOffTo\the#1\stop{#1}{#2}%  
}

\def\SplitOffTo#1#2\stop#3#4{%
  \def\tmp{#1}%
  \ifx\tmp\empty%
    \errhelp{Attempting to pop empty stack #3.}%
    \errmessage{You can't pop an empty stack.}%
  \else%
    \def#4{#1}\global#3={#2}%
  \fi%
}

This can be used like this:

\newtoks\latexstack
\latexstack={\empty}
\push{A1}{\latexstack}
\push{B2}{\latexstack}

\popto{\latexstack}{\nodename}
\tikzmark{\nodename}
\show\nodename
Some text \tikzmark{\nodename}

\popto{\latexstack}{\nodename}
\tikzmark{\nodename}
\show\nodename
Some more text \tikzmark{\nodename}

The log file will show (something like) this:

> \nodename=macro:
->B2.
l.31 \show\nodename

> \nodename=macro:
->A1.
l.34 \show\nodename

If all of that seems like a bit of a nuisance then the \popto stuff could be tied up in a \tikzmarkpop macro:

\documentclass[border=5]{standalone}
\usepackage{tikz}

\def\push#1#2{%
  \def\tmp{{#1}}% 
  \expandafter\expandafter\expandafter%
    #2\expandafter\expandafter\expandafter{\expandafter\tmp\the#2}%
\ignorespaces}

\def\popto#1#2{%
  \expandafter\SplitOffTo\the#1\stop{#1}{#2}%  
}

\def\SplitOffTo#1#2\stop#3#4{% 
  \def\tmp{#1}
  \ifx\tmp\empty% 
    \errhelp{Attempting to pop empty stack #3.}%
    \errmessage{You can't pop an empty stack.}%
  \else%
    \def#4{#1}\global#3={#2}%
  \fi}


\def\tikzmarkpop#1{%
\popto{#1}{\nodename}%
\tikz[remember picture, overlay]\coordinate(\nodename);} 

\newtoks\latexstack
\latexstack={\empty}

\begin{document}

\push{A1}{\latexstack}
\push{B2}{\latexstack}  

Some text\tikzmarkpop{\latexstack}
Some more text\tikzmarkpop{\latexstack}

\begin{tikzpicture}[remember picture, overlay] 
  \draw [red, <->] (A1) -- (B2);
\end{tikzpicture}
\end{document}