tex.md

TeX Tidbits

Expansion

\expandafter

The following is a high-level (possibly not entirely accurate) model of how TeX \expandafter works.

An important realization in learning TeX expansion is the difference between expansion and execution/actions (an expansion is merely a transformation of an input sequence of TeX tokens into an output sequence of tokens). This point is covered in Part 5 of the excellent article series on \expandafter on Overleaf: How does \expandafter work: A detailed macro case study.

1. Initial expression

   \ea1\ea2\ea3\a\ea4\b\c

2. \ea1 expanded

   1. \ea2 saved

   2. \ea3 expanded

      1. \a saved

      2. \ea4 expanded

         • \b saved

         • \c expanded

3. Expression after previous expansion:

   \ea2\a\b<expansion of \c>
   

4. \ea2 expanded

   a. \a saved

   b. \b expanded

5. Expression after previous expansion:

   \a<expansion of \b><expansion of \c>
   

6. \a expanded

7. Expression after previous expansion:

   <expansion of \a><expansion of \b><expansion of \c>
   

TeXbook Exercise 20.16

Prompt

Given arbitrary \b, \c, \d (macros without arguments), for example

\def\b{\c\c}
\def\c{*}
\def\d{\b\c}

define \a so that its replacement text consists of \b fully expanded, \c not expanded, and \d expanded exactly once. That is, with the above definitions thereplacement text of \a should be

**\c\b\c

You may not use \the or \noexpand in the solution.

Solutions

Many solutions are documented in 1 Expansion in Around The Bend, but they are all significantly longer than the following:

\edef\next#1#2{\def#1{\b#2}}
\expandafter\next\expandafter\a\expandafter{\expandafter\c\d}

After the above, \meaning\a prints out

macro:->**\c \b \c

as intended. The way it works is that the first \expandafter triggers an expansion which results in the expansion of \d as

\next\a{\c\b\c}

thus accomplishing the expansion of \d exactly once.