[Tex/LaTex] Are all commands with an optional argument fragile

Question

Here is a discussion of fragile command in LaTeX. And it says that any commands that have an optional argument are fragile, for instance \footnote[2]{myfoottext} and \footnot{myotherfoottext}. I have tried the example below which the commmand \b has an optional parameter but it works without \protect.

\documentclass{article}
\def\b[#1]#2{.#2.\bf #1}
\begin{document}
\tableofcontents
\section{\protect\b[one]two}    %works
\section{\b[one]two}    %also works
\end{document}

Here is the code in the .toc file:

\contentsline {section}{\numberline {1}\b [one]two}{1}% 
\contentsline {section}{\numberline {2}.t.\bf onewo}{1}%

However, it shows the effect of the command \protect .

Answer 1

The command you defined does not take an optional argument, it takes a delimited argument. If you do:

\def\b[#1]#2{.#2.\bf #1}
\b[one]two

it will work fine, however if you remove the [one] TeX will throw an error:

\def\b[#1]#2{.#2.\bf #1}
\b two

! Use of \b doesn't match its definition.
l.5 \b t
        wo
?

because when you define a command with \def\b[#1]#2{.#2.\bf #1}, TeX expects that when you use \b, the input matches exactly the parameter text (i.e., [#1]#2), which means that the next token must be [, and when it is not that error is raised. See here for a brief description of that.

When using just \def none of the arguments are optional! However, let's say you define:

\newcommand\b[2][--empty--]{.#2.\bf #1}

then the command will have 2 arguments, the first of which is optional, and if not given the default value is --empty--. When you use \b, the defined command does not actually take any argument, but it checks if the next character is a [. If it is, the command proceeds to use an "inner" \b (let's call it \b@opt), which is defined as you did, with \def\b@opt[#1]#2{.#2.\bf #1}. However if you use \b without the following [, then a \b@noopt is used, which is defined as \def\b@noopt{\b@opt[--empty--]}. So after all you end up using \b@opt, but the underlying definition provides the optional argument if you don't give it one.

You can manually define that with:

\makeatletter
\def\b{%
  \@ifnextchar[%
    {\b@opt}{\b@noopt}%
}
\def\b@noopt{\b@opt[--empty--]}
\def\b@opt[#1]#2{.#2.\bf #1}
\makeatother

---

Now, what makes the optional argument thing “fragile”?

A command is fragile when it can't work properly in an expansion-only context, which is usually when being written to a temporary file, like in section headings as you showed, captions, and the like, but also inside an \edef or, more recently, in \expanded.

It's said that commands with optional arguments are fragile because the mechanism that checks if an optional argument is there (precisely, the \@ifnextchar macro above) usually is fragile. It is possible, under some restrictions, to check for an optional argument expandably, like in xparse's \NewExpandableDocumentCommand, but usually that's not the case.

Taking the command defined above as example, if you do \edef\test{\b[one]{two}} (or \write or \expanded) TeX starts expanding from left to right, so the first thing it sees is \b, which is expanded to

\@ifnextchar[{\b@opt}{\b@noopt}

Next the \@ifnextchar test is expanded to:

\let\reserved@d=[%
\def\reserved@a{\b@opt}%
\def\reserved@b{\b@noopt}%
\futurelet\@let@token\@ifnch

Here the problem appears. \let, \def, and \futurelet aren't expandable, so TeX leaves them as they are, and proceeds expanding the rest. All other macros there will be expanded by TeX, but by doing so the \let and \def will not define \reserved@d and such, but their expansion, and this will make the code not work as intended.

Of course this is just an example, but the basic principle of fragility is that a command that contains non-expandable tokens is being used in an expansion-only context.

---

How to make a command robust?

Until a couple decades ago the only way to make a command robust was to prevent its expansion with \noexpand\command, which makes TeX temporarily treat \command as unexpandable and skip it in an expansion-only context. The downside of this is that as soon as the expansion was carried out the \noexpand would disappear and the command would be fragile again.

To circumvent this LaTeX defines \protect and the accompanying macros \protected@edef and \protected@write, which define \protect as \def\protect{\noexpand\protect\noexpand}. Then, in an expansion-only context \protect\command will expand to \noexpand\protect\noexpand\command. TeX will throw both \noexpands away, temporarily making \protect\command both unexpandable. If you happened to use the command again, it would continue being robust if you used the \protected@... macros instead of the normal ones.

Commands with optional arguments defined with LaTeX2ε's \newcommand and the like have a different look (but the same machinery underneath). If you define \newcommand\b[2][--empty--]{.#2.\bf #1}, then \b will actually be \protected@testopt \b \\b {--empty--} (that \\b is the command \\b, with two backslashes, not \\ then b). \protected@testopt will use the \protect machinery to test whether it can be safely expanded. If it cannot it will leave \protect\b, otherwise it will proceed to use \\b, which contains the actual definition of the command.

All this became easier when ε-TeX introduced the \protected primitive, which allows you to make a macro engine-protected. This means that instead of tricking TeX to \noexpand your macro, you will define the macro as robust with:

\protected\def\b{%
  \@ifnextchar[%
    {\b@opt}{\b@noopt}%
}

and then TeX itself will know that \b is not supposed to be expanded inside an \edef or \write or \expanded, without additional machinery.

LaTeX2ε doesn't use \protected to define robust macros because of backwards compatibility. LaTeX2ε predates ε-TeX, so the protection mechanism was established much earlier. LaTeX3, for example, dropped the 2ε protection mechanism and uses only \protected to define robust macros.

---

As a side note, I'd change that definition of yours to:

\newcommand\mybold[2][--empty--]{.#2.\textbf{#1}}

and use as:

\mybold[one]{two}

I changed the command to \mybold, as one-letter command names are not generally a good idea. I also changed \bf (which is deprecated for decades now) to \textbf and put the second argument in braces, so that the second argument is two, not just t.