Latex3: Passing empty token list to another command and detecting it as empty token list

Question

I am sorting some tokens in a token list using the nice features of latex3 (see below command \nom). These tokens can be sometimes empty, and when they are empty they would trigger different conditions within another command, below called \amc. The problem is that when receiving the arguments in \amc they are not detected as empty. Thus, the condition is never triggered.

I have already tried with passing within \clist_if_empty:NTF \l__wdsgn_notation_subscript_clist {**HERE**} { \clist_use:Nn \l__wdsgn_notation_subscript_clist {,} }

1. An empty field {}
2. An empty constant \c_empty_tl, and
3. No value token \c_novalue_tl (current implementation below)

and

1. \tl_if_empty:nTF,
2. \tl_if_blank:nTF, and
3. \tl_if_eq:nnTF (current implementation below)

without success.

Here you find the minimal working example:

\documentclass{article}

\usepackage{amssymb, amsmath}
\usepackage{xparse}

\ExplSyntaxOn

\keys_define:nn { notation/nom }
 {
  A .tl_set:N = \l_wdsgn_notation_A_tl,
  B .tl_set:N = \l_wdsgn_notation_B_tl,
  C .tl_set:N = \l_wdsgn_notation_C_tl, 
  A .initial:n = {},
  B .initial:n = {},
  C .initial:n = {}, 
}

\NewDocumentCommand{\nom}{ m O{} }
 {
  \group_begin:
  \wdsgn_notation_nom:nn { #1 } { #2 }
  \group_end:
 }

\clist_new:N \l__wdsgn_notation_subscript_clist

\cs_new:Nn \wdsgn_notation_nom:nn
 {
  \keys_set:nn { notation/nom } { #2 }
% Gerneration of subscript list 
\clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_A_tl
\clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_B_tl
\amc{#1}
{
  \clist_if_empty:NTF \l__wdsgn_notation_subscript_clist {\c_novalue_tl} { \clist_use:Nn \l__wdsgn_notation_subscript_clist {,} }
}
{ % here we exploit the fact that \clist_use:Nn disregards empty items
 \clist_if_empty:NTF \l_wdsgn_notation_C_tl { \c_novalue_tl  } { \l_wdsgn_notation_C_tl }
}
}

\NewDocumentCommand \amc { m m m }
{
    (#1) -- 
    \tl_if_eq:nnTF {#2} {\c_novalue_tl} {empty} {not empty} -- 
    \tl_if_eq:nnTF {#3} {\c_novalue_tl} {empty} {not empty}
}

\ExplSyntaxOff

\begin{document}

\begin{align}
\nom{K}[A=A, B=B] \\
\nom{K}[A=A] \\
\nom{K}[B=B] \\
\nom{K}[C=guid]
\end{align}

\end{document}

As you can see empty is never printed when either #1 or #2 are empty.

Output:

Thanks in advance for the help.

Answer 1

If you use \tl_if_eq:nnTF {#1} { \c_novalue_tl } you're comparing these tokens exactly, so only a #1 that contains exactly \c_novalue_tl is true (so \tmp:n { \c_novalue_tl } with \tmp:n containing this check).

Your usage of \amc does not expand the arguments, so #2 will be

\clist_if_empty:NTF \l__wdsgn_notation_subscript_clist {\c_novalue_tl} { \clist_use:Nn \l__wdsgn_notation_subscript_clist {,} }

which is never \c_novalue_tl if you don't expand it with the correct number of expansion steps.

The following fixes this by expanding the first argument to \amc fully (\clist_use:Nn will prevent that the value is expanded too often), and for the second uses the value of your token list directly.

\documentclass{article}

\usepackage{amssymb, amsmath}
\usepackage{xparse}

\ExplSyntaxOn

\keys_define:nn { notation/nom }
 {
  A .tl_set:N = \l_wdsgn_notation_A_tl,
  B .tl_set:N = \l_wdsgn_notation_B_tl,
  C .tl_set:N = \l_wdsgn_notation_C_tl,
  A .initial:n = {},
  B .initial:n = {},
  C .initial:n = {},
}

\NewDocumentCommand{\nom}{ m O{} }
 {
  \group_begin:
  \wdsgn_notation_nom:nn { #1 } { #2 }
  \group_end:
 }

\clist_new:N \l__wdsgn_notation_subscript_clist

\exp_args_generate:n { neV }
\cs_new:Nn \wdsgn_notation_nom:nn
  {
    \keys_set:nn { notation/nom } { #2 }
    % Gerneration of subscript list
    \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_A_tl
    \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_B_tl
    \exp_args:NneV \amc{#1}
      {
        \clist_if_empty:NF \l__wdsgn_notation_subscript_clist { \clist_use:Nn \l__wdsgn_notation_subscript_clist {,} }
      }
      % here we exploit the fact that \clist_use:Nn disregards empty items
      \l_wdsgn_notation_C_tl
  }

\NewDocumentCommand \amc { m m m }
  {
    (#1) --
    \tl_if_empty:nTF {#2} {empty} {not empty} --
    \tl_if_empty:nTF {#3} {empty} {not empty}
  }

\ExplSyntaxOff

\begin{document}

\begin{align}
\nom{K}[A=A, B=B] \\
\nom{K}[A=A] \\
\nom{K}[B=B] \\
\nom{K}[C=guid]
\end{align}

\end{document}

Answer 2

\c_novalue_tl is a very specific token list that cannot be used to test for emptiness.

You should expand the arguments before passing them to \amc (that I made an internal command, for this purpose).

\documentclass{article}

\usepackage{amssymb, amsmath}

\ExplSyntaxOn

\keys_define:nn { notation/nom }
 {
  A .tl_set:N = \l_wdsgn_notation_A_tl,
  B .tl_set:N = \l_wdsgn_notation_B_tl,
  C .tl_set:N = \l_wdsgn_notation_C_tl, 
  A .initial:n = {},
  B .initial:n = {},
  C .initial:n = {}, 
}

\NewDocumentCommand{\nom}{ m O{} }
 {
  \group_begin:
  \wdsgn_notation_nom:nn { #1 } { #2 }
  \group_end:
 }

\clist_new:N \l__wdsgn_notation_subscript_clist

\cs_new_protected:Nn \wdsgn_notation_nom:nn
 {
  \keys_set:nn { notation/nom } { #2 }
  % Gerneration of subscript list 
  \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_A_tl
  \clist_put_right:NV \l__wdsgn_notation_subscript_clist \l_wdsgn_notation_B_tl
  \wdsgn_notation_amc:nee {#1}
   {
    \clist_if_empty:NTF \l__wdsgn_notation_subscript_clist
     {empty}
     { \clist_use:Nn \l__wdsgn_notation_subscript_clist {,} }
   }
   {
    \tl_if_empty:NTF \l_wdsgn_notation_C_tl { empty } { \l_wdsgn_notation_C_tl }
   }
 }

\cs_new:Nn \wdsgn_notation_amc:nnn
 {
    (#1) -- (#2) -- (#3)
 }
\cs_generate_variant:Nn \wdsgn_notation_amc:nnn { nee }

\ExplSyntaxOff

\begin{document}

\nom{K}[A=A, B=B]

\nom{K}[A=A]

\nom{K}[B=B]

\nom{K}[C=guid]

\end{document}