Extensible triple-bracket delimiter with a new symbol

Question

\DeclarePairedDelimiter allows one to define extensible delimiters (for example using the \big option). An example is provided below with double brackets. I need a similar delimiter with triple brackets. As I was unable to find one, I built it from the double bracket symbol found in stmaryd. Unfortunately, I cannot use it with \DeclarePairedDelimiter :( So, my question is: How to define a macro for an extensible triple-bracket delimiter?

\documentclass{article}

\usepackage{mathtools,stmaryrd}

\DeclarePairedDelimiter{\dbr}{\llbracket}{\rrbracket}

\newcommand{\tbr}[1]{\llbracket\mkern-5mu\llbracket #1 \rrbracket\mkern-5mu\rrbracket}


\begin{document}

Double brackets:
\[
  \dbr{x} \quad \dbr[\big]{T^T}
\]

Triple brackets:
\[
  \tbr{x} \quad \tbr{T^T}
\]

\end{document}

basically you can't really do it unless you have a font with a triple bracket, but there isn't such a character in Unicode. You could use \Bigl\llbracket\!\Bigl[ or some such — David Carlisle, Mar 21, 2018 at 21:58
A solution could be to build the desired pair of triple brackets by means of a virtual font. — GuM, Mar 22, 2018 at 1:17
You can typeset such delimiters with the nath package, they are input as \triple[ and \triple], respectively; note, however, that this package also introduces a different way of writing math formulae in the source, making it superfuous, among other thigs, to use explicit \left and \right specifiers. — GuM, Mar 22, 2018 at 17:08

GuM · Accepted Answer · 2018-03-30 18:11:40Z

Encouraged by David Carlisle, I eventually resolved to post this answer. I had begun to write a comprehensive one that explained how the solution works, but I soon realized that it would have largely exceeded the 30000 character limit—indeed, only the code amounts to a total of more than 26000 bytes! Maybe I’ll post the explanations as a separate answer, for now please refer to:

How to create a virtual font?;
this answer to How can I create a new extensible symbol?;
my answer to the question Design of new brackets;
my answer to the question Arbitrary \left \right delimiters.

Solution based on virtual fonts; it provides you with two new extensible symbols named \lBbrack and \rBbrack, that you can use in exactly the same way (with \bigl & Co., \left, \right, \genfrac, \DeclarePairedDelimiter, …) as any other delimiter. So, for instance, along the lines of

\DeclarePairedDelimiter{\Bra}{[}{]}

you could similarly say

\DeclarePairedDelimiter{\WonderBra}{\lBbrack}{\rBbrack}

Instructions for testing the solution:

Create a new, empty directory and move to it.

Save the following code into tripledelimiters10.vpl:

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    (SETCHAR O 101)
    )
  )
(CHARACTER O 102
  (CHARWD R 1.750006)
  (CHARDP R 0.600006)
  (VARCHAR
    (REP O 102)
    )
  (MAP
    (SETCHAR O 102)
    (MOVELEFT R 0.4375015)
    (SETCHAR O 102)
    (MOVELEFT R 0.4375015)
    (SETCHAR O 102)
    )
  )
(CHARACTER O 103
  (CHARWD R 1.750006)
  (CHARDP R 0.600006)
  (VARCHAR
    (REP O 103)
    )
  (MAP
    (SETCHAR O 103)
    (MOVELEFT R 0.4375015)
    (SETCHAR O 103)
    (MOVELEFT R 0.4375015)
    (SETCHAR O 103)
    )
  )
(CHARACTER O 104
  (CHARWD R 1.222226)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 34)
  (MAP
    (SETCHAR O 104)
    (MOVELEFT R 0.3055565)
    (SETCHAR O 104)
    (MOVELEFT R 0.3055565)
    (SETCHAR O 104)
    )
  )
(CHARACTER O 105
  (CHARWD R 1.222226)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 35)
  (MAP
    (SETCHAR O 105)
    (MOVELEFT R 0.3055565)
    (SETCHAR O 105)
    (MOVELEFT R 0.3055565)
    (SETCHAR O 105)
    )
  )
(CHARACTER O 120
  (CHARWD R 0.77778)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 0)
  (MAP
    (SELECTFONT D 2)
    (SETCHAR O 50)
    (MOVELEFT R 0.194445)
    (SETCHAR O 50)
    (MOVELEFT R 0.194445)
    (SETCHAR O 50)
    )
  )
(CHARACTER O 121
  (CHARWD R 0.77778)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 1)
  (MAP
    (SELECTFONT D 2)
    (SETCHAR O 51)
    (MOVELEFT R 0.194445)
    (SETCHAR O 51)
    (MOVELEFT R 0.194445)
    (SETCHAR O 51)
    )
  )
(CHARACTER O 122
  (CHARWD R 0.555558)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 2)
  (MAP
    (SELECTFONT D 2)
    (SETCHAR O 133)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 133)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 133)
    )
  )
(CHARACTER O 123
  (CHARWD R 0.555558)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 3)
  (MAP
    (SELECTFONT D 2)
    (SETCHAR O 135)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 135)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 135)
    )
  )
(CHARACTER O 124
  (CHARWD R 0.888892)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 4)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 142)
    (MOVELEFT R 0.222223)
    (SETCHAR O 142)
    (MOVELEFT R 0.222223)
    (SETCHAR O 142)
    )
  )
(CHARACTER O 125
  (CHARWD R 0.888892)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 5)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 143)
    (MOVELEFT R 0.222223)
    (SETCHAR O 143)
    (MOVELEFT R 0.222223)
    (SETCHAR O 143)
    )
  )
(CHARACTER O 126
  (CHARWD R 0.888892)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 6)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 144)
    (MOVELEFT R 0.222223)
    (SETCHAR O 144)
    (MOVELEFT R 0.222223)
    (SETCHAR O 144)
    )
  )
(CHARACTER O 127
  (CHARWD R 0.888892)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 7)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 145)
    (MOVELEFT R 0.222223)
    (SETCHAR O 145)
    (MOVELEFT R 0.222223)
    (SETCHAR O 145)
    )
  )
(CHARACTER O 130
  (CHARWD R 1.000004)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 10)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 146)
    (MOVELEFT R 0.250001)
    (SETCHAR O 146)
    (MOVELEFT R 0.250001)
    (SETCHAR O 146)
    )
  )
(CHARACTER O 131
  (CHARWD R 1.000004)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 11)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 147)
    (MOVELEFT R 0.250001)
    (SETCHAR O 147)
    (MOVELEFT R 0.250001)
    (SETCHAR O 147)
    )
  )
(CHARACTER O 132
  (CHARWD R 0.77778)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 12)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 150)
    (MOVELEFT R 0.194445)
    (SETCHAR O 150)
    (MOVELEFT R 0.194445)
    (SETCHAR O 150)
    )
  )
(CHARACTER O 133
  (CHARWD R 0.77778)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 13)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 151)
    (MOVELEFT R 0.194445)
    (SETCHAR O 151)
    (MOVELEFT R 0.194445)
    (SETCHAR O 151)
    )
  )
(CHARACTER O 134
  (CHARWD R 0.555558)
  (CHARHT R 0.75)
  (CHARDP R 0.25)
  (NEXTLARGER O 14)
  (MAP
    (SELECTFONT D 1)
    (SETCHAR O 152)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 152)
    (MOVELEFT R 0.1388895)
    (SETCHAR O 152)
    )
  )
(CHARACTER O 150
  (CHARWD R 0.944448)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 24)
  (MAP
    (SETCHAR O 150)
    (MOVELEFT R 0.236112)
    (SETCHAR O 150)
    (MOVELEFT R 0.236112)
    (SETCHAR O 150)
    )
  )
(CHARACTER O 151
  (CHARWD R 0.944448)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 25)
  (MAP
    (SETCHAR O 151)
    (MOVELEFT R 0.236112)
    (SETCHAR O 151)
    (MOVELEFT R 0.236112)
    (SETCHAR O 151)
    )
  )
(CHARACTER O 152
  (CHARWD R 1.055562)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 26)
  (MAP
    (SETCHAR O 152)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 152)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 152)
    )
  )
(CHARACTER O 153
  (CHARWD R 1.055562)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 27)
  (MAP
    (SETCHAR O 153)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 153)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 153)
    )
  )
(CHARACTER O 154
  (CHARWD R 1.055562)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 30)
  (MAP
    (SETCHAR O 154)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 154)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 154)
    )
  )
(CHARACTER O 155
  (CHARWD R 1.055562)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 31)
  (MAP
    (SETCHAR O 155)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 155)
    (MOVELEFT R 0.2638905)
    (SETCHAR O 155)
    )
  )
(CHARACTER O 156
  (CHARWD R 1.333338)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 32)
  (MAP
    (SETCHAR O 156)
    (MOVELEFT R 0.3333345)
    (SETCHAR O 156)
    (MOVELEFT R 0.3333345)
    (SETCHAR O 156)
    )
  )
(CHARACTER O 157
  (CHARWD R 1.333338)
  (CHARHT R 0.039999)
  (CHARDP R 1.760019)
  (NEXTLARGER O 33)
  (MAP
    (SETCHAR O 157)
    (MOVELEFT R 0.3333345)
    (SETCHAR O 157)
    (MOVELEFT R 0.3333345)
    (SETCHAR O 157)
    )
  )

Type the following at the shell prompt:
```
vptovf tripledelimiters10.vpl
```
This will generate two files called tripledelimiters10.tfm and tripledelimiters10.vf, always in the same directory.

Save the following code into tridelim.sty:

\NeedsTeXFormat{LaTeX2e}\relax % LaTeX2e is required!
\ProvidesPackage{tridelim}
                [2018/03/25 v0.01 (development)]

\DeclareFontFamily{U}{tridelim}{\hyphenchar\font \m@ne}
\DeclareFontShape{U}{tridelim}{m}{n}{<->tripledelimiters10}{}

\DeclareSymbolFont{triplesymbols}{U}{tridelim}{m}{n}
\DeclareMathDelimiter{\lPparen}{\mathopen}
  {triplesymbols}{"50}{triplesymbols}{"50}
\DeclareMathDelimiter{\rPparen}{\mathclose}
  {triplesymbols}{"51}{triplesymbols}{"51}
\DeclareMathDelimiter{\lBbrack}{\mathopen}
  {triplesymbols}{"52}{triplesymbols}{"52}
\DeclareMathDelimiter{\rBbrack}{\mathclose}
  {triplesymbols}{"53}{triplesymbols}{"53}
\DeclareMathDelimiter{\lFfloor}{\mathopen}
  {triplesymbols}{"54}{triplesymbols}{"54}
\DeclareMathDelimiter{\rFfloor}{\mathclose}
  {triplesymbols}{"55}{triplesymbols}{"55}
\DeclareMathDelimiter{\lCceil}{\mathopen}
  {triplesymbols}{"56}{triplesymbols}{"56}
\DeclareMathDelimiter{\rCceil}{\mathclose}
  {triplesymbols}{"57}{triplesymbols}{"57}
\DeclareMathDelimiter{\lBbrace}{\mathopen}
  {triplesymbols}{"58}{triplesymbols}{"58}
\DeclareMathDelimiter{\rBbrace}{\mathclose}
  {triplesymbols}{"59}{triplesymbols}{"59}
\DeclareMathDelimiter{\lAangle}{\mathopen}
  {triplesymbols}{"5A}{triplesymbols}{"5A}
\DeclareMathDelimiter{\rAangle}{\mathclose}
  {triplesymbols}{"5B}{triplesymbols}{"5B}
\DeclareMathDelimiter{\Vvert}{\mathord}
  {triplesymbols}{"5C}{triplesymbols}{"5C}
\DeclareMathDelimiter{\lVvert}{\mathopen}
  {triplesymbols}{"5C}{triplesymbols}{"5C}
\DeclareMathDelimiter{\rVvert}{\mathclose}
  {triplesymbols}{"5C}{triplesymbols}{"5C}
\DeclareMathDelimiter{\Aarrowvert}{\mathord}
  {triplesymbols}{"3C}{triplesymbols}{"3C}
\DeclareMathDelimiter{\Bbracevert}{\mathord}
  {triplesymbols}{"3E}{triplesymbols}{"3E}
\DeclareMathDelimiter{\lGgroup}{\mathopen}
  {triplesymbols}{"3A}{triplesymbols}{"3A}
\DeclareMathDelimiter{\rGgroup}{\mathclose}
  {triplesymbols}{"3B}{triplesymbols}{"3B}

Save the following code into test.tex:

% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly 
                                 % declare the paper format.

\usepackage[T1]{fontenc}         % Not always necessary, but recommended.
\usepackage[utf8]{inputenc}      % Not always necessary, but recommended.
% End of standard header.  What follows pertains to the problem at hand.

\usepackage{mathtools}
\usepackage{tridelim}

\DeclarePairedDelimiter{\tripleparen}{\lPparen}{\rPparen}
\DeclarePairedDelimiter{\triplebrack}{\lBbrack}{\rBbrack}
\DeclarePairedDelimiter{\triplefloor}{\lFfloor}{\rFfloor}
\DeclarePairedDelimiter{\tripleceil} {\lCceil} {\rCceil}
\DeclarePairedDelimiter{\triplebrace}{\lBbrace}{\rBbrace}
\DeclarePairedDelimiter{\tripleangle}{\lAangle}{\rAangle}
\DeclarePairedDelimiter{\triplevert} {\lVvert} {\rVvert}
\DeclarePairedDelimiter{\triplegroup}{\lGgroup}{\rGgroup}
\DeclarePairedDelimiter{\triplearrowvert}{\Aarrowvert}{\Aarrowvert}
\DeclarePairedDelimiter{\triplebracevert}{\Bbracevert}{\Bbracevert}

\DeclarePairedDelimiterX\triplebracket[3]{\lAangle}{\rAangle}
  {#1\,\delimsize\Vvert\,\mathopen{}#2\,\delimsize\Vvert\,\mathopen{}#3}

\newcommand*{\testfraction}{\frac{a}{b}}
\newcommand*{\testbigfraction}{%
  \frac{\,\frac{d^{n}}{dt^{n}}\,}{n!}%
}
\newcommand*{\testmatrix}{%
  \begin{matrix}%
    1&0&0&0\\%
    0&1&0&0\\%
    0&0&1&0\\%
    0&0&0&1%
  \end{matrix}%
}

\begin{document}

We begin with a simple formula: \( P\lPparen x\rPparen \).
Is it OK in sub-\slash superscripts too?  Let’s check:
\( Z^{P\lPparen x\rPparen} \), and \( 2^{Z_{P\lPparen x\rPparen}} \).
It works, but is suboptimal: indeed, compare it closely with
\( Z^{P(x)} \) and \( 2^{Z_{P(x)}} \).

Here are the normal sizes, in display:
\begin{align*}
  & x \tripleparen{y} z &
  & x \triplebrack{y} z &
  & x \triplefloor{y} z &
  & x \tripleceil {y} z &
  & x \triplebrace{y} z
  \\
  & x \tripleangle{y} z &
  & x \triplevert {y} z &
  & y \triplearrowvert*{x} z & % needs "\left" and "\right"
  & y \triplebracevert*{x} z   % needs "\left" and "\right"
\end{align*}

Here are the \verb|\big| sizes, in display:
\begin{align*}
  & x \tripleparen[\big]{y} z &
  & x \triplebrack[\big]{y} z &
  & x \triplefloor[\big]{y} z &
  & x \tripleceil [\big]{y} z &
  & x \triplebrace[\big]{y} z
  \\
  & x \tripleangle[\big]{y} z &
  & x \triplevert [\big]{y} z &
  & x \triplearrowvert[\big]{y} z &
  & x \triplebracevert[\big]{y} z
\end{align*}

Here are the \verb|\Big| sizes, in display:
\begin{align*}
  & x \tripleparen[\Big]{\testfraction} z &
  & x \triplebrack[\Big]{\testfraction} z &
  & x \triplefloor[\Big]{\testfraction} z &
  & x \tripleceil [\Big]{\testfraction} z &
  & x \triplebrace[\Big]{\testfraction} z
  \\
  & x \tripleangle[\Big]{\testfraction} z &
  & x \triplegroup[\Big]{\testfraction} z & % not available at smaller sizes
  & x \triplevert [\Big]{\testfraction} z &
  & x \triplearrowvert[\Big]{\testfraction} z &
  & x \triplebracevert[\Big]{\testfraction} z
\end{align*}

Here are the \verb|\bigg| sizes, in display:
\begin{align*}
  & x \tripleparen[\bigg]{\testfraction} z &
  & x \triplebrack[\bigg]{\testfraction} z &
  & x \triplefloor[\bigg]{\testfraction} z &
  & x \tripleceil [\bigg]{\testfraction} z &
  & x \triplebrace[\bigg]{\testfraction} z
  \\
  & x \tripleangle[\bigg]{\testfraction} z &
  & x \triplegroup[\bigg]{\testfraction} z &
  & x \triplevert [\bigg]{\testfraction} z &
  & x \triplearrowvert[\bigg]{\testfraction} z &
  & x \triplebracevert[\bigg]{\testfraction} z
\end{align*}

Here are the \verb|\Bigg| sizes, in display:
\begin{align*}
  & x \tripleparen[\Bigg]{\testbigfraction} z &
  & x \triplebrack[\Bigg]{\testbigfraction} z &
  & x \triplefloor[\Bigg]{\testbigfraction} z &
  & x \tripleceil [\Bigg]{\testbigfraction} z
  \\
  & x \triplebrace[\Bigg]{\testbigfraction} z &
  & x \tripleangle[\Bigg]{\testbigfraction} z &
  & x \triplegroup[\Bigg]{\testbigfraction} z 
  \\
  & x \triplevert [\Bigg]{\testbigfraction} z &
  & x \triplearrowvert[\Bigg]{\testbigfraction} z &
  & x \triplebracevert[\Bigg]{\testbigfraction} z
\end{align*}

And finally, the glorious auto-sizing delimiters, always in display:
\begin{align*}
  & x \tripleparen*{\testmatrix} z &
  & x \triplebrack*{\testmatrix} z &
  & x \triplefloor*{\testmatrix} z
  \\
  & x \tripleceil* {\testmatrix} z &
  & x \triplebrace*{\testmatrix} z &
  & x \triplegroup*{\testmatrix} z
  \\
  & x \triplevert* {\testmatrix} z &
  & x \triplearrowvert*{\testmatrix} z &
  & x \triplebracevert*{\testmatrix} z
\end{align*}

For the following example, cf.~p.~26 of the manual of the \textsf{mathtools}
package:
\( \triplebracket[\big]{B}{\sum_{k} f_k}{C} \).

\end{document}

Compiling test.tex should produce the following output:

Interested in the details?

Note that the LaTeX code does not compile (I am using pdflatex); e.g., ( and ) should read \( and \). — user94293, Mar 30, 2018 at 0:10
All your new symbols are beautiful. There seem however to have some very small spacing issues in the triple bracket symbols. — user94293, Mar 30, 2018 at 0:12
I would suggest that your turn this into a package to put on CTAN. This is very useful work. — user94293, Mar 30, 2018 at 0:13
@user94293: You are right, the code, as copied-and-pasted from this page, didn’t compile. As I said, I was having problems with the 30000 character limit, so, in order to save some thousands keystrokes, I used <PRE> tags for the code excerpts instead of the four space indentation; unfortunately, inside <PRE> tags several backslashes were misinerpreted as starts of escape sequences, and disappeared from the visible code. I hope I’ve now correctly “escaped from the escapes”: indeed, I tried to copy-and-paste the code from this page back to my editor, and it did compile. Be forgiving… :-| — GuM, Mar 30, 2018 at 1:51

EuklidAlexandria · Accepted Answer · 2018-08-16 13:08:32Z

You can use \DeclarePairedDelimiterX{\tbr}[1]{\llbracket}{\rrbracket}{\mkern-5mu\delimsize\llbracket \mathopen{}#1 \mathclose{} \delimsize\rrbracket\mkern-5mu}

You can find further information on page 26 in the mathtools manual. Basically \DeclarePairedDelimiterX{〈cmd〉}[〈num args〉]{〈left_delim〉}{〈right_delim〉}{〈body〉} allows you to additionally specify a macro surrounded by the outer brackets. \delimsize gives the sizes of the outer brackets. \mathopen{} and \mathclose{} fix problem with the spacing which may occur (see this answer and the footnote on page 26 in the mathtools manual).

EDIT: Here is what I have so far . There is a slight displacement with the smallest brackets and the starred version does not work. For better results I think one have to redefine \DeclarePairedDelimiter.

\documentclass{article}

\usepackage{mathtools,stmaryrd}

\usepackage{xcolor}


\DeclarePairedDelimiter{\dbr}{\llbracket}{\rrbracket}

\DeclarePairedDelimiterX{\tbr}[1]{\llbracket}{\rrbracket}{\nhphantom{$\delimsize\llbracket$}\delimsize\llbracket \mathopen{} #1 \mathclose{} \delimsize\rrbracket \nhphantom{$\delimsize\rrbracket$}}

\newcommand{\nhphantom}[1]{\sbox0{#1}\hspace{-0.751\wd0}}


\begin{document}

Double brackets:
\[
  \dbr{x} \quad \dbr[\big]{T^T}
\]

Triple brackets:
\[
  \tbr{x} \quad \tbr[\big]{T^T}
\]

\[
  {\llbracket}\nhphantom{$\llbracket$}{\textcolor{red}{\llbracket}} \quad
  {\big\llbracket}\nhphantom{$\big\llbracket$}{\textcolor{red}{\big\llbracket}} \quad
  {\Big\llbracket}\nhphantom{$\Big\llbracket$}{\textcolor{red}{\Big\llbracket}} \quad
  {\bigg\llbracket}\nhphantom{$\bigg\llbracket$}{\textcolor{red}{\bigg\llbracket}} \quad
  {\Bigg\llbracket}\nhphantom{$\Bigg\llbracket$}{\textcolor{red}{\Bigg\llbracket}}
\]


\end{document}

Result: result

With \big, it appears to be quadruple brackets rather than triple brackets. — user94293, Mar 22, 2018 at 2:38
@user94293 Sorry, I have not noticed before. I have edited the post now. Now it is right. — EuklidAlexandria, Mar 22, 2018 at 3:29
It is right with \big but not without (it appears as a double bracket) — user94293, Mar 22, 2018 at 3:40
\hspace{-0.751\dimexpr\the\wd0 \relax} is a long way to get the same as \hspace{-0.751\wd0}. — egreg, Apr 13, 2018 at 13:27

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