\tl_gput_right:Nn gets ! TeX capacity exceeded, sorry [input stack size=5000]

Question

The following file gets ! TeX capacity exceeded, sorry [input stack size=5000]. If I remove the call to \tl_gput_right:Nn then it compiles successfully.

\documentclass{article}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{xparse} % loads expl3
%See interface3.pdf

\ExplSyntaxOn

\NewDocumentCommand{\uqual}{mm}
 {
   \int_compare:nTF { \tl_count:n { #1 } > 1 }
     {
       Extended \ parm \ #1 \
       \bool_gset_true:N \g_tmpa_bool
       \tl_gclear:N \g_tmpa_tl
       \tl_map_inline:nn{#1}
       {
         mapping \ ##1 \
         \if_bool:N \g_tmpa_bool
           {
             first \ item \ ##1 \
             \bool_gset_false:N \g_tmpa_bool
              \tl_gset_eq:NN \g_tmpa_tl ##1
           } \else: {
             next \ item \ ##1
             \tl_gput_right:Nn \g_tmpa_tl {xx ##1}
           } \fi:
       }
       test \ tokenlist=\g_tmpa_tl \
       \expandafter
         \left ( {\forall}_{ \g_tmpa_tl} \right ) #2
     }
     {
        single \ parm \ #1 \
       \expandafter
         \left ( {\forall}_{#1} \right ) #2
     }
 }

\ExplSyntaxOff

\begin{document}

$\uqual{{X}}{P(X.Y)}$

$\uqual{{X}{Y}}{P(X,Y)}$

\end{document}

Answer 1

There is an error where you do \tl_gset_eq:NN \g_tmpa_tl ##1, because ##1 will generally not start with a control sequence variable and, even if it does, the result is not what you'd like to be.

Remember that N denotes an argument that should consist of a single token; in particular, \tl_gset_eq:NN makes the token list variable given as first argument globally equal to the token list variable given as second argument (no coercion, in case you're asking).

A braced argument is denoted in the function name with n. What you really want is

\tl_gset:Nn \g_tmpa_tl { ##1 }

(globally set \g_tmpa_tl to the given argument).

However, there are other parts to tidy up. For instance, you're using global settings and variables where you don't need to. Also,

\if_bool:N <boolean>
  <true text>
\else:
  <false text>
\fi:

is not the recommended coding; in any case, the true and false texts should not be braced (which is probably your reason for using global assignments); it's better to do

\bool_if:NTF <boolean>
 {
  <true text>
 }
 {
  <false text>
 }

The problem with _ is easily solved; since in expl3 syntax it is part of macro names, when you want to denote a math subscript, use \c_math_subscript_token.

However, there are easier ways to accomplish your task (which I guess is listing the variables in the first argument separated by commas):

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse} % loads expl3

\ExplSyntaxOn

\seq_new:N \l_shmuel_uqual_seq

\NewDocumentCommand{\uqual}{mm}
 {
  \seq_set_split:Nnn \l_shmuel_uqual_seq { } { #1 }
  ( \forall \c_math_subscript_token { \seq_use:Nn \l_shmuel_uqual_seq { , } } ) #2
 }

\ExplSyntaxOff

\begin{document}

$\uqual{X}{P(X.Y)}$

$\uqual{XY}{P(X,Y)}$

\end{document}

This means: split the first argument “at nothing” (which is the same division as done by \tl_map_inline:nn) into a sequence; then deliver the sequence with items separated by commas.

If you want to stack the variables given in the first argument, then change the macros like below:

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse} % loads expl3

\ExplSyntaxOn

\seq_new:N \l_shmuel_uqual_seq

\NewDocumentCommand{\uqual}{mm}
 {
  \seq_set_split:Nnn \l_shmuel_uqual_seq { } { #1 }
  ( 
  \forall \c_math_subscript_token
   {
    \substack{  \seq_use:Nn \l_shmuel_uqual_seq { \\ } } 
   }
  ) #2
 }

\ExplSyntaxOff

\begin{document}

$\uqual{X}{P(X.Y)}$

$\uqual{XY}{P(X,Y)}$

\end{document}

Answer 2

\tl_gset_eq:NN 

expects two arguments of type N and not one of type N and one of type n.

What you want here is simply

\tl_gset:Nn \g_tmpa_tl {##1}

which works fine.

EDIT

The code works fine for me if I simply substitute the replacement above for the line I mentioned. This is not to say that other changes are not needed for the intended functionality (whatever that is) or that it might not be wise to do certain things differently, but it certainly does not fail to compile.

That is,

\documentclass{article}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{mathtools}
\usepackage{xparse} % loads expl3
%See interface3.pdf

\ExplSyntaxOn

\NewDocumentCommand{\uqual}{mm}
 {
   \int_compare:nTF { \tl_count:n { #1 } > 1 }
     {
       Extended \ parm \ #1 \
       \bool_gset_true:N \g_tmpa_bool
       \tl_gclear:N \g_tmpa_tl
       \tl_map_inline:nn{#1}
       {
         mapping \ ##1 \
         \if_bool:N \g_tmpa_bool
           {
             first \ item \ ##1 \
             \bool_gset_false:N \g_tmpa_bool
              \tl_gset:Nn \g_tmpa_tl {##1}
           } \else: {
             next \ item \ ##1
             \tl_gput_right:Nn \g_tmpa_tl {xx ##1}
           } \fi:
       }
       test \ tokenlist=\g_tmpa_tl \
       \expandafter
         \left ( {\forall}_{ \g_tmpa_tl} \right ) #2
     }
     {
        single \ parm \ #1 \
       \expandafter
         \left ( {\forall}_{#1} \right ) #2
     }
 }

\ExplSyntaxOff

\begin{document}

$\uqual{{X}}{P(X.Y)}$

$\uqual{{X}{Y}}{P(X,Y)}$

\end{document}

compiles without error. I don't know if the output is what you want, but it certainly produces a PDF.