Is it possible to run a command stored as text in a variable?

Question

I have some complicated expressions with loads of nested commands which are difficult to work with. To solve this I wrote a parser using pgfparser which creates the expressions for me. I can then copy the output back in to LaTeX and it outputs what I need.

I was wondering if I could automate this. I can store the text (a sequence of commands) in a variable but then I can't find a way to run the commands in the variable

The parser itself is not of much interest but as a mwe this is a simplified version of what I have:

\documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{pgf}
\usepgfmodule{parser}

\pgfparserdef{mweparser}{initial}{\meaning [}{\textbackslash overline\{}
\pgfparserdef{mweparser}{initial}{\meaning ]}{\}}
\pgfparserdef{mweparser}{initial}{\meaning A}{A}
\pgfparserdef{mweparser}{initial}{subscript character _}{\_\{\pgfparserswitch{subscript}}
\pgfparserdef{mweparser}{subscript}{\meaning +}{\textbackslash hat\{\pgfparserswitch{edgename}}
\pgfparserdef{mweparser}{subscript}{\meaning -}{\textbackslash check\{\pgfparserswitch{edgename}}
\pgfparserdef{mweparser}{edgename}{\meaning a}{a\}\pgfparserswitch{subscript}}
\pgfparserdef{mweparser}{edgename}{\meaning b}{b\}\pgfparserswitch{subscript}}
\pgfparserdef{mweparser}{subscript}{subscript character _}{\}\pgfparserswitch{initial}}
\pgfparserdef{mweparser}{all}{the character ;}{\pgfparserswitch{final}}

\begin{document}
    \pgfparserparse{mweparser}[A_+a-b-a_[A_+a+b-a_]];%
\end{document}

This will output:

\overline{A_{\hat{a}\check{b}\check{a}}\overline{A_{\hat{a}\hat{b}\check{a}}}}

Which is what I would like to run (in math mode). I can store this text in a variable but can't see how I can run it.

I am new to this stuff so I apologise if I have done anything wrong.

Answer 1

I don't really know how the PGF parser works, but what you get with your code is a string which is not what you want: \textbackslash is not a backslash but a command to print one.

Here's an implementation with l3regex, the regular expression parser of LaTeX3; the wanted result has been added for checking against what the macros do.

\documentclass[border=3,varwidth]{standalone}
\usepackage[T1]{fontenc}
\usepackage{xparse,l3regex}

\ExplSyntaxOn
\NewDocumentCommand{\term}{m}
 {
  \dquick_term:n { #1 }
 }

\tl_new:N \l__dquick_input_tl

\cs_new_protected:Npn \dquick_term:n #1
 {
  \tl_set:Nn \l__dquick_input_tl { #1 }
  %% subscripts (works so long you don't have nested subscripts)
  \regex_replace_all:nnN { \_(.*?)\_ } { \cD\_\cB\{\1\cE\} } \l__dquick_input_tl
  %% [ becomes \overline\bgroup (nesting is allowed)
  \regex_replace_all:nnN { \[ } { \c{overline}\c{bgroup} } \l__dquick_input_tl
  %% ] becomes \egroup
  \regex_replace_all:nnN { \] } { \c{egroup} } \l__dquick_input_tl
  %% +<char> becomes \hat{<char>}
  \regex_replace_all:nnN { \+(.) } { \c{hat}\cB\{\1\cE\} } \l__dquick_input_tl
  %% -<char> becomes \check{<char>}
  \regex_replace_all:nnN { \-(.) } { \c{check}\cB\{\1\cE\} } \l__dquick_input_tl
  $\tl_use:N \l__dquick_input_tl$
 }
\ExplSyntaxOff

\begin{document}
\term{[G_+a-b-c_[H_+a+a-c_]]}

$\overline{G_{\hat{a}\check{b}\check{c}}\overline{H_{\hat{a}\hat{a}\check{c}}}}$
\end{document}

---

A slightly different version that allows specifying delimiter characters (they must be different) for nested macro, here shown with \overline.

\documentclass[border=3,varwidth]{standalone}
\usepackage[T1]{fontenc}
\usepackage{xparse,l3regex}

\ExplSyntaxOn
\NewDocumentCommand{\term}{m}
 {
  \dquick_term:n { #1 }
 }

\tl_new:N \l__dquick_input_tl

\cs_new_protected:Npn \dquick_term:n #1
 {
  \tl_set:Nn \l__dquick_input_tl { #1 }
  %% subscripts (works so long you don't have nested subscripts)
  \regex_replace_all:nnN { \_(.*?)\_ } { \cD\_\cB\{\1\cE\} } \l__dquick_input_tl
  %% brackets can be nested, this requires a slower routine
  \dquick_replace_nested:nnn { \[ } { \] } { overline }
  %% +<char> becomes \hat{<char>}
  \regex_replace_all:nnN { \+(.) } { \c{hat}\cB\{\1\cE\} } \l__dquick_input_tl
  %% -<char> becomes \check{<char>}
  \regex_replace_all:nnN { \-(.) } { \c{check}\cB\{\1\cE\} } \l__dquick_input_tl
  \tl_use:N \l__dquick_input_tl
 }

\cs_new_protected:Npn \dquick_replace_nested:nnn #1 #2 #3
 {% #1 is the left delimiter
  % #2 is the right delimiter
  % #3 is the macro name for replacement
  \regex_match:nVT { #1 ( [^#1#2]*? ) #2 } \l__dquick_input_tl
   {
    \regex_replace_all:nnN { #1 ( [^#1#2]*? ) #2 } { \c{#3}\cB\{\1\cE\} } \l__dquick_input_tl
    \dquick_replace_nested:nnn { #1 } { #2 } { #3 }
   }
 }
\cs_generate_variant:Nn \regex_match:nnT { nV }

\ExplSyntaxOff

\begin{document}
$\term{[G_+a-b-c_[H_+a+a-c_]]}$

$\overline{G_{\hat{a}\check{b}\check{c}}\overline{H_{\hat{a}\hat{a}\check{c}}}}$
\end{document}