Issue with Expansions of Nested Macros

Question

I am trying to incorporate membership checking macros by marmot and Phelype Oleinik (thanks to both of them for their neat solutions) into an argument of another macro:

\singleBox{\convertNumPhelypeOleinik{1}{1}{0}{2}{1.46}}{200}{24}{13} % this fails
\singleBox{\convertNumMarmot{1}{1}{0}{2}{1.46}}{200}{24}{13} % this fails too

which results in the following error message:

Undefined control sequence. ...ypeOleinik{1}{1}{0}{2}{1.46}}{200}{24}{13}
Undefined control sequence. ...tNumMarmot{1}{1}{0}{2}{1.46}}{200}{24}{13}

The following is an MWE that demonstrates this issue. Could someone kindly help me with this?

\documentclass[tikz, border=0mm]{standalone}
\usepackage{tikz,xfp,expl3}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solution by marmot https://tex.stackexchange.com/users/121799/marmot
% https://tex.stackexchange.com/a/501776/23594
\newif\ifmember
\makeatletter% for \@for see e.g. https://tex.stackexchange.com/a/100684/121799
%from https://tex.stackexchange.com/a/498576/121799
\newcommand{\MemberQ}[2]{\global\memberfalse%
    \@for\next:=#1\do{\ifnum\next=#2\global\membertrue\fi}}
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solution by Phelype Oleinik https://tex.stackexchange.com/users/134574/phelype-oleinik
% https://tex.stackexchange.com/a/501777/23594
\ExplSyntaxOn
\prg_new_conditional:Npnn \afp_int_ismember:nn #1#2 { p, T, F, TF }
{ \__afp_ismember_loop:nw {#1} #2 , \q_recursion_tail , \q_recursion_stop }
\cs_new:Npn \__afp_ismember_loop:nw #1#2,
{
    \quark_if_recursion_tail_stop_do:nn {#2}
    { \prg_return_false: }
    \int_compare:nNnTF {#1} = {#2}
    { \use_i_delimit_by_q_recursion_stop:nw { \prg_return_true: } }
    { \__afp_ismember_loop:nw {#1} }
}
\ExplSyntaxOff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\singleBox}[4]{%
    \fill(\fpeval{#1}mm,\fpeval{#2}mm) rectangle
    (\fpeval{#1} mm + \fpeval{#3} mm,\fpeval{#2} mm - \fpeval{#4} mm);
}

\newcommand{\convertNum}[5]{%
    \fpeval{#1<6 ? #3 + 9 + (#4 + #5)*(#1-1) + (#2-1) : 0}
}

\newcommand{\convertNumPhelypeOleinik}[5] %
{
    \ExplSyntaxOn
    \fpeval{ \afp_int_ismember_p:nn {1} {1,2,3,4,5} ? #3 + 9 + (#4 + #5)*(#1-1) + (#2-1) : 0 }
    \ExplSyntaxOff
}

\newcommand{\convertNumMarmot}[5] % 
{
    \MemberQ{1,2,3,4,5,6}{#1}
    \ifmember \fpeval{#3 + 9 + (#4 + #5)*(#1-1) + (#2-1)} \fi
}


\begin{document}

    % Testing membeship using Phelype Oleinik's method
    \ExplSyntaxOn
    \fpeval{ \afp_int_ismember_p:nn {1} {1,2,3,4,5} ? 123 : 321 }\par
    \ExplSyntaxOff

    % Testing membeship using marmot's method
    \MemberQ{1,2,3,4}{2}
    \ifmember 2 is in list \fi

    \MemberQ{1,2,3,4}{5}
    \ifmember 5 is in list\else%
    5 is not in the list\fi

    \begin{tikzpicture}
        \draw[draw=black] (0mm,0mm) rectangle (300 mm, 400 mm);
        \singleBox{100}{200}{24}{13} % This works just fine
        \singleBox{\convertNum{1}{1}{0}{2}{1.46}}{200}{24}{13} % This work just fine

        \singleBox{\convertNumPhelypeOleinik{1}{1}{0}{2}{1.46}}{200}{24}{13} % this fails
        \singleBox{\convertNumMarmot{1}{1}{0}{2}{1.46}}{200}{24}{13} % this fails too
    \end{tikzpicture}

\end{document}

Answer 1

The macro proposed by our resident marmot is nice, but cannot be used in \fpeval as it relies to non expandable actions (\memberfalse and \membertrue).

The tags \ExplSyntaxOn and \ExplSyntaxOff are similar to \makeatletter and \makeatother: they have to surround the code where the expl3 syntax is used, not be inside the code.

A better coding:

\documentclass[border=0mm]{standalone}
\usepackage{tikz,xfp,xparse}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Solution by Phelype Oleinik https://tex.stackexchange.com/users/134574/phelype-oleinik
% https://tex.stackexchange.com/a/501777/23594
\ExplSyntaxOn
\prg_new_conditional:Npnn \afp_int_ismember:nn #1#2 { p, T, F, TF }
  {
    \__afp_ismember_loop:nw {#1} #2 , \q_recursion_tail , \q_recursion_stop
  }
\cs_new:Npn \__afp_ismember_loop:nw #1#2,
  {
    \quark_if_recursion_tail_stop_do:nn {#2}
    { \prg_return_false: }
    \int_compare:nNnTF {#1} = {#2}
    { \use_i_delimit_by_q_recursion_stop:nw { \prg_return_true: } }
    { \__afp_ismember_loop:nw {#1} }
  }
\NewExpandableDocumentCommand{\convertNum}{mmmmm}
  {
    \fp_eval:n
      {
         \afp_int_ismember_p:nn {1} {1,2,3,4,5} ? #3 + 9 + (#4 + #5)*(#1-1) + (#2-1) : 0
      }
  }
\ExplSyntaxOff
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\singleBox}[4]{%
    \fill(\fpeval{#1}mm,\fpeval{#2}mm) rectangle
    (\fpeval{#1} mm + \fpeval{#3} mm,\fpeval{#2} mm - \fpeval{#4} mm)
}

\begin{document}

    \begin{tikzpicture}
        \draw[draw=black] (0mm,0mm) rectangle (300 mm, 400 mm);
        \singleBox{100}{200}{24}{13};
        \singleBox{\convertNum{1}{1}{0}{2}{1.46}}{200}{24}{13};
    \end{tikzpicture}

\end{document}

Answer 2

It is true that my macro is "not expandable" BUT I would never ever use \fpeval in coordinates of a tikzpicture. This is because TikZ has a very powerful parser, so you can just pass expressions to TikZ and it parses them automatically, so you can just ignore all this "hey, my stuff is expandable" discussion altogether. In particular, it is rather straightforward to declare a function memberQ that can be parsed like any other function. The resulting code is IMHO much more elegant than a wild mix of \fpeval and ordinary TikZ parsings.

\documentclass[tikz, border=0mm]{standalone}
\makeatletter
\pgfmathdeclarefunction{memberQ}{2}{%
  \begingroup%
    \edef\pgfutil@tmpb{0}%
    \edef\pgfutil@tmpa{#2}%
    \expandafter\pgfmath@member@i\pgfutil@firstofone#1\pgfmath@token@stop
    \edef\pgfmathresult{\pgfutil@tmpb}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup}
\def\pgfmath@member@i#1{%
    \ifx\pgfmath@token@stop#1%
    \else
      \ifnum#1=\pgfutil@tmpa\relax%
      \gdef\pgfutil@tmpb{1}%
      %\typeout{#1=\pgfutil@tmpa}
      \fi%
      \expandafter\pgfmath@member@i
    \fi}    
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\singleBox}[4]{%
    \fill({(#1)*1mm},{(#2)*1mm}) rectangle
    ({(#1+#3)*1mm},{(#2-#4)*1mm});
}

\begin{document}
    \begin{tikzpicture}
        \draw[draw=black] (0mm,0mm) rectangle (300 mm, 400 mm);
        \singleBox{100}{200}{24}{13} % This works just fine

        \pgfmathparse{memberQ({1,2,3,4,5,6,7,8,9,10,11},3)}
        \typeout{\pgfmathresult}
        \singleBox{ifthenelse(memberQ({1,2,3,5},3),200,300)}{200}{24}{13} % This works just fine
    \end{tikzpicture}
\end{document}

ADDENDUM: a memberQ function that seems to work for arbitrary lists.

\documentclass[tikz, border=0mm]{standalone}
\makeatletter
\pgfmathdeclarefunction{memberQ}{2}{%
  \begingroup%
    \edef\pgfutil@tmpb{0}%
    \edef\pgfutil@tmpa{#2}%
    \expandafter\pgfmath@member@i\pgfutil@firstofone#1\pgfmath@token@stop
    \edef\pgfmathresult{\pgfutil@tmpb}%
    \pgfmath@smuggleone\pgfmathresult%
  \endgroup}
\def\pgfmath@member@i#1{%
    \ifx\pgfmath@token@stop#1%
    \else
      \edef\pgfutil@tmpc{#1}%
      \ifx\pgfutil@tmpc\pgfutil@tmpa\relax%
      \gdef\pgfutil@tmpb{1}%
      %\typeout{#1=\pgfutil@tmpa}%
      \fi%
      \expandafter\pgfmath@member@i
    \fi}    
\makeatother
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}
 \pgfmathparse{memberQ({3,4,5},3)}\pgfmathresult

 \pgfmathparse{memberQ({3,4,5},1)}\pgfmathresult

 \pgfmathparse{memberQ({"a","b","c"},1)}\pgfmathresult

 \pgfmathparse{memberQ({"a","b","c"},"a")}\pgfmathresult
\end{document}