Include empty delimiter in `\DeclarePairedDelimiter`

Question

I want to define a restriction operator \restrict{f}{X} which is capable of resizing in the style of mathtools's \DeclarePairedDelimiter options. For example:

• \restrict*{f}{X} should resize automatically
• \restrict[\Big]{f}{X} should provide a large vertical bar regardless of what f is
• &c.

The MWE I currently have throws an error:

\documentclass{article}
\usepackage{mathtools}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\DeclarePairedDelimiterXPP{\restrict}[2]{}{}\rvert
        {\IfNoValueTF{#2}{}{_{#2}}}
        {#1}
\begin{document}
\begin{equation}
        \restrict{f}{X}
        = \restrict*{\frac{f}{1}}{X}
\end{equation}
\end{document}

When running this, I get an appropriate output, but the error:

Missing delimiter (. inserted).

This makes sense, since the left delimiter I provided was the empty token {}. However, if I replace it with {.}, then for the nonstarred \restrict, a period is introduced in the typesetting which I do not wish for.

Is there a way to communicate to \DeclarePairedDelimiter that I want an empty delimiter, or must I go the route of error-surpressing?

Answer 1

Don't use \DeclarePairedDelimiter.

\documentclass{article}
\usepackage{mathtools}
\usepackage{mleftright}
\NewDocumentCommand{\restrict}{sO{}mm}{%
  \IfBooleanTF{#1}{% star
    \mleft.\kern-\nulldelimiterspace
    #3
    \mright|%
  }{% no star
    #3#2|%
  }%
  % the subscript
  _{#4}%
}
\begin{document}
\begin{equation}
  \restrict{f}{X} = \restrict*{\frac{f}{1}}{X} = \restrict[\Big]{f}{X}
\end{equation}
\end{document}