Dấu ngoặc nhọn đôi và dấu ngoặc vuông đôi trong LaTeX

Dấu ngoặc nhọn đôi

\documentclass{article}
\usepackage[utf8]{vietnam}
\usepackage{xparse}

\NewDocumentCommand{\dgal}{sO{}m}{%
  \IfBooleanTF{#1}
    {\dgalext{#3}}
    {\dgalx[#2]{#3}}%
}

\NewDocumentCommand{\dgalext}{m}{%
  \sbox0{%
    \mathsurround=0pt % just for safety
    $\left\{\vphantom{#1}\right.\kern-\nulldelimiterspace$%
  }%
  \sbox2{\{}%
  \ifdim\ht0=\ht2
    \{\kern-.625\wd2 \{#1\}\kern-.625\wd2 \}%
  \else
    \left\{\kern-.7\wd0\left\{#1\right\}\kern-.7\wd0\right\}%
  \fi
}

\NewDocumentCommand{\dgalx}{om}{%
  \sbox0{\mathsurround=0pt$#1\{$}%
  \sbox2{\{}%
  \ifdim\ht0=\ht2
    \{\kern-.625\wd2 \{#2\}\kern-.625\wd2 \}%
  \else
    \mathopen{#1\{\kern-.7\wd0 #1\{}
    #2
    \mathclose{#1\}\kern-.7\wd0 #1\}}
  \fi
}


\begin{document}

\def\test#1{#1|xxx}

Hàng thứ nhất:

$\dgal*{\test{}}$
$\dgal*{\test{\big}}$
$\dgal*{\test{\Big}}$
$\dgal*{\test{\bigg}}$
$\dgal*{\test{\Bigg}}$

Hàng thứ hai:

$\dgal{xxx}$
$\dgal[\big]{xxx}$
$\dgal[\Big]{xxx}$
$\dgal[\bigg]{xxx}$
$\dgal[\Bigg]{xxx}$

\end{document}

Dấu ngoặc vuông đôi

\documentclass{article}
\usepackage[utf8]{vietnam}
\usepackage{stmaryrd}

\begin{document}

Ký hiệu:  $ \llbracket{v}\rrbracket $

\end{document}