I need some doubled versions of the standard parentheses, namely parentheses, braces, brackets and angles. They should be scalable and the output should look roughly like this:
\documentclass[border=3mm, varwidth]{standalone}
\usepackage{mathtools}
\begin{document}
$\left\lbrack\!\left\lbrack a\right\rbrack\!\right\rbrack$
$\left\lbrack\!\!\left\lbrack \frac12\right\rbrack\!\!\right\rbrack$
$\left\lbrack\!\!\left\lbrack \dfrac{1}{2}\right\rbrack\!\!\right\rbrack$
$\left\lbrace\!\!\left\lbrace a\right\rbrace\!\!\right\rbrace$
$\left\lbrace\!\!\left\lbrace \frac12\right\rbrace\!\!\right\rbrace$
$\left\lbrace\!\!\!\left\lbrace \dfrac{1}{2}\right\rbrace\!\!\!\right\rbrace$
\end{document}
For example, the package stmaryrd provides the commands \llbracket resp. \rrbracket for doubled brackets. However I have some compatability issues with this package and also, the other delimiters are missing. Finally, I would like to be able to turn my symbols into Delimiters using the mathtools functionality. How can I achieve all this?
Edit: Bernard found a package providing doubled brackets and doubled angles (thanks for this!) but I am still interested in the other symbols.

mathabxprovides\ldbracket(alias\semantic)and\rdbracket(\rsemantic).MnSymbolhas\lsem,\rsem,\llangle,rrangle. – Bernard Jan 28 '18 at 14:30stmaryrdpackage might help. Also, this is related: https://tex.stackexchange.com/questions/100966/defining-scalable-white-curly-brackets-and-and – Steven B. Segletes Jan 29 '18 at 11:04unimath-symbolsat http://mirrors.dotsrc.org/ctan/macros/latex/contrib/unicode-math/unimath-symbols.pdf for the coverage. – Andrew Swann Jan 29 '18 at 11:11unimath-symbolsbasically works. However the commands\lBraceand\rBracedon't work and neither does the scaling of e.g.\lAngleand\rAngleusing\bigor\left. Any Ideas what I am doing wrong? – Jan 29 '18 at 11:38\setmathfont{xits}instead of\setmathfont{xits math}. Otherwise please edit your question to show the code you have tried. – Andrew Swann Jan 29 '18 at 12:04[]and()•{}(pdflatex only, no Unicode) •<>. Unrelated, but there's also||– user202729 Dec 17 '21 at 05:42