How to capture a macro's ultimate expansion as a string?

Question

I have a macro \a. I'd like to define a macro \b, whose replacement text, T, will satisfy the following requirements:

The catcode of every token of T is in the range 10-12.
Ignoring catcodes, T is token-by-token equal to \a's ultimate expansion.

For instance,

\def\z{12pt}%
\def\a{\noindent\fontsize{10pt}{\z}\selectfont}%
\def\b{???}%
\b

should typeset:

\noindent\fontsize{10pt}{12pt}\selectfont

If this is not possible, it will be OK, too, if \b expands everything recursively, until there's nothing more to expand.

Finally, the following example, too, will be good enough:

\def\a{\noindent\fontsize{10pt}{\a}\selectfont}%
\def\b{???}%
\b

should typeset:

\noindent\fontsize{10pt}{\a}\selectfont

"Ultimate expansion" -- at the time of definition (edef)? Or use (which is impossible)? — ShreevatsaR, Aug 05 '17 at 09:15
How does macro \b know that it should expand \z but not \fontsize and \selectfont? — Heiko Oberdiek, Aug 05 '17 at 09:21
@HeikoOberdiek: If this is unreasonable to ask, than consider the second example I gave after that. It will be OK too if \b expands everything recursively until it can't anymore. — Evan Aad, Aug 05 '17 at 09:22

Heiko Oberdiek · Accepted Answer · 2017-08-05T09:38:11.960

8

Without expansion of \a and with \meaning:

\documentclass{article}
\begin{document}
\def\z{12pt}%
\def\a{\noindent\fontsize{10pt}{\z}\selectfont}%
\makeatletter
\edef\b{\expandafter\strip@prefix\meaning\a}
\makeatother
\texttt{\b}
\end{document}

The spaces after command names are inserted by TeX.

Variant with e-TeX's \detokenize:

\edef\b{\detokenize\expandafter{\a}}

In both cases, the tokens in the definition text of \b have category code 12 (other) and the space has category code 10 (space).

If the contents of \a is more or less known, then the macros that should not be expanded can be prevented from expansion by redefining them to the meaning of \relax:

\documentclass{article}
\begin{document}
\def\z{12pt}%
\def\a{\noindent\fontsize{10pt}{\z}\selectfont}%

\begingroup
  \let\fontsize\relax
  \let\selectfont\relax
  \edef\x{\a}
  \xdef\b{\detokenize\expandafter{\x}}
\endgroup
\texttt{\b}
\end{document}

A full expansion of \a only works for some macros with more or less useful result:

\documentclass{article}
\begin{document}
\def\z{12pt}%
\def\a{\noindent\fontsize{10pt}{\z}\selectfont}%

\edef\tmp{\a}
\edef\b{\detokenize\expandafter{\tmp}}
\endgroup
\texttt{\b}
\end{document}

Adding package microtype, for example, will get a macro \a that breaks in a hard expansion by \edef:

! Argument of \MT@res@a has an extra }.
<inserted text>
                \par
l.7 \edef\tmp{\a}

LaTeX's protection mechanism can be used by the softer \protected@edef. Then, commands defined by \DeclareRobustCommands and commands with optional arguments are not expanded too much:

\documentclass{article}
\usepackage{microtype}
\begin{document}
\def\z{12pt}%
\def\a{\noindent\fontsize{10pt}{\z}\selectfont}%

\makeatletter
\protected@edef\tmp{\a}
\makeatother
\edef\b{\detokenize\expandafter{\tmp}}
\texttt{\b}
\end{document}

edited Aug 05 '17 at 09:38

answered Aug 05 '17 at 09:24

Heiko Oberdiek

271,626

Thank you. Is there also a version in which \a is expanded recursively until there's nothing left to expand? – Evan Aad Aug 05 '17 at 09:28
1

@EvanAad First \edef\a{\a} and then \edef\b{...} from above. – Henri Menke Aug 05 '17 at 09:29
The \strip@prefix is not very reliable, see the discussion in Is there a reliable way to get the number of arguments of a command?. – Henri Menke Aug 05 '17 at 09:31
By the way, will this also work when \a's expansion is ill formed? I don't even know how to write it, but something along the lines of \a\def{\macro{}, where the replacement string has just an opening brace. – Evan Aad Aug 05 '17 at 09:31
I meant \def\a{\macro{}. – Evan Aad Aug 05 '17 at 09:37
@EvanAad And how do you want to define such a macro? \def\a{\macro{} will for sure raise an error. – Henri Menke Aug 05 '17 at 09:38
@HenriMenke: As I said, I don't know exactly how to express this in TeX, but hopefully my meaning is clear: \a's replacement text is an incomplete TeX expression. Like when you define a new environment: the beginning and end of the environment. – Evan Aad Aug 05 '17 at 09:40
@EvanAad For unbalanced lists of tokens there is https://github.com/blefloch/latex-gtl – Henri Menke Aug 05 '17 at 09:41
1

@HenriMenke \def\a{\def\foobar{...}} with \foobar previously undefined will break in an \edef, because \def is not executed and \foobar is undefined. – Heiko Oberdiek Aug 05 '17 at 09:42

How to capture a macro's ultimate expansion as a string?

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