Active apostrophe character in math mode

Question

For some reason, I need a package providing an active apostrophe. For the sake of simplicity, let's say that every apostrophe shall be replaced by ABC in text mode. In math mode, the default behaviour shall remain.

The apostrophe character is defined as “math-active” in latex.ltx, lines 4548 to 4563:

\def\active@math@prime{^\bgroup\prim@s}
{\catcode`\'=\active \global\let'\active@math@prime}
\def\prim@s{%
  \prime\futurelet\@let@token\pr@m@s}
\def\pr@m@s{%
  \ifx'\@let@token
    \expandafter\pr@@@s
  \else
    \ifx^\@let@token
      \expandafter\expandafter\expandafter\pr@@@t
    \else
      \egroup
    \fi
  \fi}
\def\pr@@@s#1{\prim@s}
\def\pr@@@t#1#2{#2\egroup}

This code makes sure that a sequence of apostrophe characters is converted into a sequence of prime symbols in math mode.

To fulfil my needs, I have devised the following code:

\begin{filecontents}{mypackage.sty}
\RequirePackage{xparse}
\ProvidesExplPackage {mypackage} {2019-09-20} {1.0} {My package}
\cs_new:Npn \mypackage_apostrophe:
  {
    \mode_if_math:TF
      {
        \active@math@prime % latex.ltx, line 4548
      }
      {
        ABC % dummy text for testing
      }
  }
\char_set_active_eq:NN ' \mypackage_apostrophe:
\NewDocumentCommand \Activate { }
  {
    \char_set_catcode_active:N '
  }
\NewDocumentCommand \Deactivate { }
  {
    \char_set_catcode_other:N '
  }
\end{filecontents}
\documentclass{article}
\usepackage{mypackage}
\begin{document}
a'b $f'(x)$ $f''(x)$

\Activate
a'b $f'(x)$ $f''(x)$

\Deactivate
a'b $f'(x)$ $f''(x)$
\end{document}

This code produces an error message if the apostrophe character is active and a second derivation $f''(x)$ is needed:

! Double superscript. \active@math@prime ->^
                      \bgroup \prim@s
l.30 a'b $f'(x)$ $f''
                   (x)$

How can I avoid this error message (keeping ' as active)?

Answer 1

The lines

\catcode`\'=\active 
\def\svprime{\active@math@prime}
\def'{\ifmmode\expandafter\svprime\else\expandafter\ABC\fi}
\def\ABC{ABC}

almost had it working. But then I finally realized that since \pr@m@s employs a test for the repeated ', I had to make ' active before defining \pr@m@s, or else it would always fail the \ifx test for the repeated '.

Commented out are other parts associated with the \prime definition in latex.ltx.

\documentclass{article}
\makeatletter
\catcode`\'=\active 
%\def\active@math@prime{^\bgroup\prim@s}
%{\catcode`\'=\active \global\let'\active@math@prime}
%\def\prim@s{%
%  \prime\futurelet\@let@token\pr@m@s}
\def\pr@m@s{%
  \ifx'\@let@token
    \expandafter\pr@@@s
  \else
    \ifx^\@let@token
      \expandafter\expandafter\expandafter\pr@@@t
    \else
      \egroup
    \fi
  \fi}
%\def\pr@@@s#1{\prim@s}
%\def\pr@@@t#1#2{#2\egroup}
\def'{\ifmmode\expandafter\active@math@prime\else\expandafter\ABC\fi}
\def\ABC{ABC}
\makeatother
\begin{document}
Text mode: x'x
\begin{equation}
a = v'(t) = x''(t)
\end{equation}
\end{document}

Answer 2

The macro \pr@m@s still looks for a category code 12 apostrophe. Patching it is easy.

\documentclass{article}
\usepackage{regexpatch}

\makeatletter
\regexpatchcmd{\pr@m@s}{'}{\cA'}{}{} % \pr@m@s should look for an active '
% now define the active '
\catcode`'=\active
\protected\def'{\ifmmode\expandafter\active@math@prime\else ABC\fi}
\makeatother

\begin{document}

' in text mode

$f'+f''$

\end{document}

In a real world it would probably be

\protected\def'{%
  \ifmmode
    \expandafter\active@math@prime
  \else
    \expandafter\wehro@active@text@prime
  \fi
}

where \wehro@active@text@prime is the macro you want to use in text mode.