Formula in Latex: How to use special symbols in Latex?

Question

I want to write following formula in Latex:

The problem is the "i" underneath "x". It is not a regular fraction. It means that value "x" will be replaced with "i". How can I write this one in Latex? Additionally, the underlines are longer than the regular one which is used by typing "_". How can I modify the lenght of the underline?

    \documentclass[12pt, a4paper]{article}
    \usepackage[T1]{fontenc}                
    \usepackage[utf8]{inputenc}             
    \usepackage[english,ngerman]{babel} 
    \usepackage{amsmath,amsfonts,amssymb,amstext} 

    \begin{document}
    $\langle x\,\,\underline{\,\,\,}\rangle_{k}\,\,\langle \underline{\,\,}\,\,x \mapsto i\,\,\underline{\,\,\,}\rangle_{state}$
    \end{document}

Hopefully, you can help me.

Edit:

Thanks for your help! I have copied your extension and pasted it into my align environment.

\begin{align}
\centerline{Computational rules}
\[
p[\tabbedShortunderstack{
\udash{l_1}&,&\udash{l_2}&,&\dots&,&\udash{l_n}\\
r_1        & & r_2       & &     & & r_n
}]
\]
\centerline{Structural rules}
\[
p[\tabbedShortunderstack{
\uddash{l_1}&,&\uddash{l_2}&,&\dots&,&\uddash{l_n}\\
r_1         & & r_2        & &     & & r_n
}]
\]
\end{align}

If I try to run it, process stops with following error:

Bad math environment delimiter. \end{align}

What does that mean?

Answer 1

Here's one idea. In the MWE, you can adjust the .7em specification to change the size of both the underscore and the \mygap.

\documentclass{article}
\usepackage{tabstackengine,amssymb}
\stackMath
\newcommand\udash[2][\hrulefill]{\stackunder{#2}{\makebox[.7em]{#1}}}
\newcommand\mygap{\udash[]{}}
\begin{document}
\[
\langle\tabbedShortunderstack{
  \udash{x}&\mygap&\udash{}\\ i&&}\rangle_k 
  \langle\udash{}\mygap x \mapsto i\mygap\udash{}\rangle_{\mathrm{state}}
\]
\end{document}

SUPPLEMENT

Seeing the OP's deleted answer, I have extended the result to include line dashing. Also, here, \udash and \uddash will extend to the width of the argument (plus a little buffer), but with a minimum width of .7em.

\documentclass{article}
\usepackage{tabstackengine,amssymb}
\stackMath
\newlength\replength
\newcommand\ruleht{0pt}% ELEVATION OF RULE
\newcommand\repfrac{.6}% SOLID FRACTION OF DASH LINE [0->1] (USE 1 FOR SOLID)
\replength=.2em\relax% PERIOD OF DASHED RULE
\newcommand\rulewidth{.4pt}% THICKNESS OF RULE
\newcommand\drulefill{\leavevmode\dashfill\hfil%
  \kern\dimexpr\repfrac\replength-\replength\relax}
\newcommand\dashfill[1][\repfrac]{\cleaders\hbox to \replength{%
  \smash{\rule[\ruleht]{\repfrac\replength}{\rulewidth}}}\hfill}

\newcommand\udash[2][\hrulefill]{%
  \setbox0=\hbox{\stackon{\kern.7em}{\,#2\,}}%
  \stackunder{#2}{\makebox[\wd0]{#1}}}
\newcommand\uddash[1]{\udash[\drulefill]{#1}}
\newcommand\mygap{\hspace{.7em}}
\begin{document}
\[
\langle\tabbedShortunderstack{
  \udash{x}&\mygap&\udash{}\\ i&&}\rangle_k 
  \langle\udash{}\mygap x \mapsto i\mygap\udash{}\rangle_{\mathrm{state}}
\]
\centerline{Computational rules}
\[
 p[\tabbedShortunderstack{
   \udash{l_1}&,&\udash{l_2}&,&\dots&,&\udash{l_n}\\
   r_1        & & r_2       & &     & & r_n
 }]
\]
\centerline{Structural rules}
\[
 p[\tabbedShortunderstack{
   \uddash{l_1}&,&\uddash{l_2}&,&\dots&,&\uddash{l_n}\\
   r_1         & & r_2        & &     & & r_n
 }]
\]
\end{document}