How to test if two macros have identical definition

Question

I want to test if two macro have identical definition. My naive attempt to use \detokenize does not seem to work in this simple case. However, I have used a similar approach before and it seems to have worked on a much more complicated case, but now that it fails with this simple test case I am a bit confused:

Since the \meaning of \iff and \MyIffWithDotsbNonStar is identical I would have expected them to match.

Related (but different):

• Test if two things typeset identical results

MWE

\documentclass{article}
\usepackage{mathtools}
\usepackage{xstring}
\usepackage{xcolor}
\usepackage{bm}% only for highlighting thre cross
\usepackage{amssymb}% only for checkmark symbol
\usepackage[paperwidth=10in]{geometry}% for better display of output
\newcommand{\MyIffWithDotsbNonStar}{\DOTSB;\Longleftrightarrow ;}
\newcommand{\MyIffWithoutDotsbNonStar}{;\Longleftrightarrow ;}
\newcommand{\MyIffWithDotsbStar}{\DOTSB;\Longleftrightarrow ;}
\newcommand{\MyIffWithoutDotsbStar}{;\Longleftrightarrow ;}
\newcommand{\OK}{\textcolor{blue}{\checkmark}}
\newcommand{\NotOK}{\textcolor{red}{\pmb{$\times$}}}
\newcommand{\MacrosHaveSameDefintiion}[4]{%
    % #1 = macros 1
    % #2 = macros 2
    % #3 = code to execute if macros are identical
    % #4 = code to execute if macros differ
    Macros \texttt{\string#1} and \texttt{\string#2} are
    \IfStrEq{\detokenize{#1}}{\detokenize{#2}}{#3}{#4}%
}%
\begin{document}
\par \verb|\iff|: \texttt{\meaning\iff}
\par \verb|\MyIffWithDotsbNonStar|: \texttt{\meaning\MyIffWithDotsbNonStar}
\medskip
\par\MacrosHaveSameDefintiion{\iff}{\iff}{identical}{different}  \OK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithDotsbNonStar}{identical}{different} \NotOK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithoutDotsbNonStar}{identical}{different} \OK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithDotsbStar}{identical}{different} \OK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithoutDotsbStar}{identical}{different} \OK
\end{document}

Answer 1

The conditional \ifx does exactly what you want. If you do

\ifx\macroA\macroB

where both \macroA and \macroB are macros (either defined by \def, \gdef, \edef, \xdef or \let to one defined that way), then \ifx returns true if all the following conditions are satisfied:

1. both macros have the same status with respect to \long (and \outer, but dealing with LaTeX we can leave this aside)

2. both macros have the same parameter text

3. both macros have the same replacement text

This should be the first choice, as it's a TeX primitive. The tests

\ifx\iff\iff
\ifx\iff\MyIffWithDotsbNonStar

both return true. However,

\ifx\iff\MyIffWithDotsbStar

will return false, because \iff is \long and \MyIffWithDotsbStar isn't.

Your test fails because you're not expanding the macros, so you're comparing the token lists produced by

\detokenize{\iff}

and

\detokenize{\MyIffWithDotsbNonStar}

which are clearly different. If you add \expandafter, the test should return true.

\documentclass{article}
\usepackage{mathtools}
\usepackage{xstring}
\usepackage{xcolor}
\usepackage{bm}% only for highlighting thre cross
\usepackage{amssymb}% only for checkmark symbol
\usepackage[paperwidth=10in]{geometry}% for better display of output

\newcommand{\MyIffWithDotsbNonStar}{\DOTSB\;\Longleftrightarrow \;}
\newcommand{\MyIffWithoutDotsbNonStar}{\;\Longleftrightarrow \;}

\newcommand*{\MyIffWithDotsbStar}{\DOTSB\;\Longleftrightarrow \;}
\newcommand*{\MyIffWithoutDotsbStar}{\;\Longleftrightarrow \;}

\newcommand*{\OK}{\textcolor{blue}{\checkmark}}
\newcommand*{\NotOK}{\textcolor{red}{\pmb{$\times$}}}

\newcommand{\MacrosHaveSameDefintiion}[4]{%
    % #1 = macros 1
    % #2 = macros 2
    % #3 = code to execute if macros are identical
    % #4 = code to execute if macros differ
    Macros \texttt{\string#1} and \texttt{\string#2} are
    \IfStrEq{\detokenize\expandafter{#1}}{\detokenize\expandafter{#2}}{#3}{#4}%
}%

\begin{document}
\par \verb|\iff|: \texttt{\meaning\iff}
\par \verb|\MyIffWithDotsbNonStar|: \texttt{\meaning\MyIffWithDotsbNonStar}
\medskip

\par\MacrosHaveSameDefintiion{\iff}{\iff}{identical}{different}  \OK

\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithDotsbNonStar}{identical}{different} \NotOK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithoutDotsbNonStar}{identical}{different} \OK

\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithDotsbStar}{identical}{different} \OK
\par\MacrosHaveSameDefintiion{\iff}{\MyIffWithoutDotsbStar}{identical}{different} \OK

\end{document}

But it seems killing a fly with a sledgehammer. And the test gives false positives: tests 2 and 4 give “identical” when they shouldn't.