Extensible triple-bracket delimiter with a new symbol

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:

  1. Create a new, empty directory and move to it.
  2. Save the following code into tripledelimiters10.vpl:
    (FAMILY TRIPLEDELIMITERS)
    (CODINGSCHEME FONTSPECIFIC)
    (DESIGNSIZE R 10.0)
    (COMMENT DESIGNSIZE IS IN POINTS)
    (COMMENT OTHER SIZES ARE MULTIPLES OF DESIGNSIZE)
    (MAPFONT D 0 (FONTNAME cmex10))
    (MAPFONT D 1 (FONTNAME cmsy10))
    (MAPFONT D 2 (FONTNAME cmr10))
    (FONTDIMEN
      (SLANT R 0.0)
      (SPACE R 0.0)
      (STRETCH R 0.0)
      (SHRINK R 0.0)
      (XHEIGHT R 0.430555)
      (QUAD R 1.000003)
      (EXTRASPACE R 0.0)
      )
    (CHARACTER O 0
      (CHARWD R 0.916672)
      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 20)
      (MAP
        (SETCHAR O 0)
        (MOVELEFT R 0.229168)
        (SETCHAR O 0)
        (MOVELEFT R 0.229168)
        (SETCHAR O 0)
        )
      )
    (CHARACTER O 1
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      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 21)
      (MAP
        (SETCHAR O 1)
        (MOVELEFT R 0.229168)
        (SETCHAR O 1)
        (MOVELEFT R 0.229168)
        (SETCHAR O 1)
        )
      )
    (CHARACTER O 2
      (CHARWD R 0.833338)
      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 150)
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        (SETCHAR O 2)
        (MOVELEFT R 0.2083345)
        (SETCHAR O 2)
        (MOVELEFT R 0.2083345)
        (SETCHAR O 2)
        )
      )
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      (CHARWD R 0.833338)
      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 151)
      (MAP
        (SETCHAR O 3)
        (MOVELEFT R 0.2083345)
        (SETCHAR O 3)
        (MOVELEFT R 0.2083345)
        (SETCHAR O 3)
        )
      )
    (CHARACTER O 4
      (CHARWD R 0.944448)
      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 152)
      (MAP
        (SETCHAR O 4)
        (MOVELEFT R 0.236112)
        (SETCHAR O 4)
        (MOVELEFT R 0.236112)
        (SETCHAR O 4)
        )
      )
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      (CHARWD R 0.944448)
      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
      (NEXTLARGER O 153)
      (MAP
        (SETCHAR O 5)
        (MOVELEFT R 0.236112)
        (SETCHAR O 5)
        (MOVELEFT R 0.236112)
        (SETCHAR O 5)
        )
      )
    (CHARACTER O 6
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      (CHARHT R 0.039999)
      (CHARDP R 1.160013)
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      (MAP
        (SETCHAR O 6)
        (MOVELEFT R 0.236112)
        (SETCHAR O 6)
        (MOVELEFT R 0.236112)
        (SETCHAR O 6)
        )
      )
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      (MAP
        (SETCHAR O 7)
        (MOVELEFT R 0.236112)
        (SETCHAR O 7)
        (MOVELEFT R 0.236112)
        (SETCHAR O 7)
        )
      )
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        (SETCHAR O 10)
        (MOVELEFT R 0.291668)
        (SETCHAR O 10)
        (MOVELEFT R 0.291668)
        (SETCHAR O 10)
        )
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        (MOVELEFT R 0.291668)
        (SETCHAR O 11)
        (MOVELEFT R 0.291668)
        (SETCHAR O 11)
        )
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        (MOVELEFT R 0.236112)
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        (SETCHAR O 25)
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        (SETCHAR O 27)
        (MOVELEFT R 0.291668)
        (SETCHAR O 27)
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        (SETCHAR O 30)
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        (SETCHAR O 31)
        (MOVELEFT R 0.291668)
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        )
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        (SETCHAR O 40)
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        (SETCHAR O 40)
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        (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)
        )
      )
    
  3. 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.

  4. 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}

  5. 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}

  6. Compiling test.tex should produce the following output: Output of the test
Interested in the details?


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