Dynamic LaTeX command substitution

Question

The last solution in the following post is great and we can add other shortcuts.

One thing I don't understand is that I can't add a shortcut with a _ :

Exemple : \mathbb{R}_+ doesn't transform correctly as a shortcut ... the + is normal size instead of being correct.

Any idea why ?

Post: Seeking Enhancements and Solutions for Dynamic LaTeX Command Substitution

I don't understand expl3 so I don't know what the problem is (it work with ^ and not with _ for some reason) and if it is possible to improve the code to work with underscore too or if I have to do it manualy in the text.

The code is :

\documentclass{article}
\usepackage{amsmath}
\usepackage{xparse}
\ExplSyntaxOn
\seq_new:N \l_math_subs_seq
\msg_new:nnn {math} {symbol-exists} {symbol~#1~already~exists}
\int_new:N \g_math_struct_counter
\int_gset:Nn \g_math_struct_counter {1}
\cs_new_protected:Npn \mathstruct_new:N #1
{
  \tl_set:Nx #1 {l_mathstruct_internal_\int_use:N \g_math_struct_counter _prop}
  \prop_new:c {#1}
  \int_gincr:N \g_math_struct_counter
\prop_new:c {l_mathstruct_internal_\int_use:N \g_math_struct_counter prop}
  \prop_put:cnn {#1} {value} {}
  \prop_put:cnn {#1} {exist} {\c_false_bool}
  \prop_put:cnn {#1} {mapping} {}
  \prop_put:cnx {#1} {children} {l_mathstruct_internal\int_use:N \g_math_struct_counter _prop}
  \int_gincr:N \g_math_struct_counter
}
\mathstruct_new:N \l_math_prefix_tree_root
\tl_new:N \l_math_children_prop_tl
\tl_new:N \l_math_tmpa_tl
\tl_new:N \l_math_tmpb_tl
\tl_new:N \l_math_tmpc_tl
\cs_new_protected:Npn \math__recursive_add_sub:nnnn #1#2#3#4
 {
\str_if_empty:nTF {#2} 
  {
    \prop_get:cnN {#1} {exist} \l_math_tmpa_tl
    \exp_args:NV \bool_if:nTF {\l_math_tmpa_tl}
    {
      % if symbol alreasy exists, send a warning
      \msg_warning:nnn {math} {symbol-exists} {#4}
    }
    {
      % need to set this symbol as "exists" and set the mapping
      \prop_put:cnn {#1} {exist} {\c_true_bool}
      \prop_put:cnn {#1} {mapping} {#3}
    }
  }
  {
    \prop_get:cnN {#1} {children} \l_math_children_prop_tl
    \str_set:Nx \l_math_tmpa_tl {\str_head:n {#2}}
    % see if it is one of its children
    \prop_if_in:cVTF {\l_math_children_prop_tl} \l_math_tmpa_tl
    {
      % if the node exists, continue recursively
      \tl_set:Nx \l_math_tmpc_tl {\str_tail:n {#2}}
      \prop_get:cVN {\l_math_children_prop_tl} \l_math_tmpa_tl \l_math_tmpb_tl
      \math__recursive_add_sub:Vxnn \l_math_tmpb_tl {\str_tail:n {#2}} {#3} {#4}
    }
    {
      % otherwise, need to create new node
      \mathstruct_new:N \l_math_tmpb_tl
      \prop_put:cnV {\l_math_tmpb_tl} {value} \l_math_tmpa_tl
      \prop_put:cVV {\l_math_children_prop_tl} \l_math_tmpa_tl \l_math_tmpb_tl
      % apply recursively
      \math__recursive_add_sub:Vxnn \l_math_tmpb_tl {\str_tail:n {#2}} {#3} {#4}
    }
}
 }
\cs_generate_variant:Nn \math__recursive_add_sub:nnnn {Vxnn,VVVV}
\tl_new:N \l_math_add_tmpa_tl
\tl_new:N \l_math_add_tmpb_tl
 \cs_new_protected:Npn \math_add_sub:nn #1 #2
 {
   \tl_set_rescan:Nnn \l_math_add_tmpa_tl {\cctab_select:N\c_code_cctab} {#1}
   \tl_set_rescan:Nnn \l_math_add_tmpb_tl {\cctab_select:N\c_code_cctab} {#2}
\math__recursive_add_sub:VVVV \l_math_prefix_tree_root \l_math_add_tmpa_tl \l_math_add_tmpb_tl \l_math_add_tmpa_tl
 }
% post order traversal 
 \cs_new_protected:Npn \math__sub_recursive_generate:nn #1#2
 {
  \group_begin:
    % check children first
    \prop_get:cnN {#1} {children} \l_math_children_prop_tl
    \prop_map_inline:cn {\l_math_children_prop_tl}
    {
      \math__sub_recursive_generate:nn {##2} {#2##1}
    }
% check current node
\prop_get:cnN {#1} {exist} \l_math_tmpa_tl
\bool_if:nT {\l_math_tmpa_tl}
{
  \prop_get:cnN {#1} {mapping} \l_math_tmpb_tl
  \tl_set_rescan:Nnn \l_math_tmpc_tl { \cctab_select:N \c_document_cctab } {#2}
  \seq_gput_right:Nx \l_math_subs_seq { {\exp_not:V \l_math_tmpc_tl}  {\exp_not:V \l_math_tmpb_tl} }
}

\group_end:
 }
% traverse the tree to get the correct order
 \cs_new_protected:Npn \math_sub_generate:
 {
  \seq_gclear:N \l_math_subs_seq
  \exp_args:NV \math__sub_recursive_generate:nn \l_math_prefix_tree_root {}
 }
\cs_new_protected:Npn \math_ascii_sub:n #1
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \seq_map_inline:Nn \l_math_subs_seq
   {
    \tl_replace_all:Nnn \l_tmpa_tl ##1
   }
  \tl_use:N \l_tmpa_tl
 }
\cs_new_protected:Npn \math_grabinline:w #1 $
 {
  \math_ascii_sub:n { #1 } $
 }
\cs_new_protected:Npn \math_grabdisplay:w #1 ]
 {
  \math_ascii_sub:n { #1 } ]
 }
\cs_set_eq:NN \MathAddSub \math_add_sub:nn
\cs_set_eq:NN \MathGenSub \math_sub_generate:
% Enable substitutions for $...$ and [...]
\everymath { \math_grabinline:w }
\tl_put_right:Nn [ { \math_grabdisplay:w }
\ExplSyntaxOff
\begin{document}
\centering
\newcommand*{\test}[1]{%
  $#1$%
  [#1]%
}
\MathAddSub{ << }{ \ll  }
\MathAddSub{ <> }{ \neq }
\MathAddSub{ <= }{ \leq }
\MathAddSub{ >> }{ \gg  }
\MathAddSub{ >= }{ \geq }
\MathAddSub{ -+ }{ \mp }
\MathAddSub{ +- }{ \pm }
\MathAddSub{ == }{ \equiv }
\MathAddSub{ =. }{ \doteq }
\MathAddSub{ =( }{ \subseteq }
\MathAddSub{ =) }{ \supseteq }
\MathAddSub{ =[ }{ \sqsubseteq }
\MathAddSub{ =] }{ \sqsubseteq }
\MathAddSub{ <== }{ \Leftarrow }
\MathAddSub{ <=> }{ \Leftrightarrow }
\MathAddSub{ <-- }{ \leftarrow }
\MathAddSub{ <-> }{ \leftrightarrow }
\MathAddSub{ --> }{ \rightarrow }
\MathAddSub{ ==> }{ \Rightarrow }
\MathAddSub{ ... }{ \dots }
\MathAddSub{ int }{ \int }
\MathAddSub{ Re }{ \mathbb{R}^* } %---------- This works
\MathAddSub{ Rp }{ \mathbb{R}_+ } %---------- This doesn't works
\MathAddSub{ RR }{ \mathbb{R}}    %---------- This works
% generate the substitution table based on post-order traversal of the prefix tree
\MathGenSub
\ExplSyntaxOn
% show the substitution table
\seq_show:N \l_math_subs_seq
\ExplSyntaxOff
\test{RR \qquad Re \qquad Rp (doesn't work) while \qquad RR_+ (does)}
\test{a << b < c <= d >= e > f >> g}
\test{a <> b = c =. d == e}
\test{a <== b <-- c <-> d <=> e --> f ==> g}
\test{a +- b = -(-a -+ +b)}
\test{a, ..., z <> a + ...+ z}
\test{a =( b =) c =[ e =] f}
\test{int _a^b}
\test{@@@@@ @@@@ @@@}
\MathAddSub{ @@@ }{ \mbox{~}THREE\mbox{~} }
\MathAddSub{ @@@@ }{ \mbox{~}FOUR\mbox{~} }
\MathAddSub{ @@@@@ }{ \mbox{~}FIVE\mbox{~} }
% generate the substitution table again
\MathGenSub
\ExplSyntaxOn
% show the substitution table
\seq_show:N \l_math_subs_seq
\ExplSyntaxOff
\test{@@@@@ @@@@ @@@}
\end{document}