Purpose of DOTSB in definition of \iff

Question

What exactly is the purpose of the \DTOSB in the definition of \iff? There is a mention in Is there a left-handed equivalent of \implies? that the \DOTSB makes \iff "dots aware". But, when I try to use \dots on either side I don't see any difference.

Egreg commented that you need \newcommand* in order for DOTSB to have an effect. But, it seems that the definition with using the star option in \newcommand* differs from the definition of \iff. Its the

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

the produces the same meaning as \iff.

References:

• How do magic \dots work in amsmath?
• Is there a left-handed equivalent of \implies?
• How can I make amsmath's \dots look ahead after macro expansion?

MWE:

\documentclass{article}
\usepackage{mathtools}
\usepackage{xcolor}
\usepackage[paperwidth=10in]{geometry}% for better display of output
\newcommand{\MyIffWithDotsbNonStar}{\DOTSB;\Longleftrightarrow ;}
\newcommand{\MyIffWithoutDotsbNonStar}{;\Longleftrightarrow ;}
\newcommand{\MyIffWithDotsbStar}{\DOTSB;\Longleftrightarrow ;}
\newcommand{\MyIffWithoutDotsbStar}{;\Longleftrightarrow ;}
\begin{document}
\par \verb|\iff|: \texttt{\meaning\iff}
\par \verb|\MyIffWithDotsbNonStar|: \texttt{\meaning\MyIffWithDotsbNonStar}
\par \verb|\MyIffWithDotsbStar|: \texttt{\meaning\MyIffWithDotsbStar}
\medskip
\par $a \iff b$ using \verb|\iff|
\par $a \MyIffWithDotsbNonStar b$ using \verb|\MyIffWithDotsbNonStar|
\par $a \MyIffWithoutDotsbNonStar b$ using \verb|\MyIffWithoutDotsbNonStar|
\par $a \MyIffWithDotsbStar b$ using \verb|\MyIffWithDotsbStar|
\par $a \MyIffWithoutDotsbStar b$ using \verb|\MyIffWithoutDotsbStar|
\medskip
\par $a \dots \iff \dots b$ using \verb|\dots \iff \dots|
\par $a \dots \MyIffWithDotsbNonStar \dots b$ using \verb|\dots \MyIffWithDotsbNonStar \dots|
\par $a \dots \MyIffWithoutDotsbNonStar \dots b$ using \verb|\dots \MyIffWithoutDotsbNonStar \dots|
\par $a \dots \MyIffWithDotsbStar \dots b$ using \verb|\dots \MyIffWithDotsbStar \dots| \textcolor{red}{\bfseries DIFFERS}
\par $a \dots \MyIffWithoutDotsbStar \dots b$ using \verb|\dots \MyIffWithoutDotsbStar \dots|
\end{document}

Answer 1

If you use amsmath 2.15 then you can use \newcommand or \newcommand* as \long is ignored when checking the \meaning. This means that \dots now works as intended with \iff and gives centred dots.