What is the definition of \abc in this case?

Question

When I compile the following code I get the error:

"use of \abc doesn't match its definition"

What is the definition of \abc?

\documentclass{article}
\begin{document}
\def\foo#1{\def\abc#1{test}}
\foo{gh}
\abc x y z
\end{document}

Answer 1

\def\abc gh{test}

defines \abc to be a macro that must be followed by gh and expands to test, use as

\abc gh x y z

Answer 2

Add \show\foo and \show\abc. Then run LaTeX in interactive mode:

\documentclass{article}
\begin{document}
\def\foo#1{\def\abc#1{test}}
\foo{gh}
\show\foo
\show\abc
\abc x y z
\end{document}

TeX will stop like for an error and show

> \foo=macro:
#1->\def \abc #1{test}.
l.8 \show\foo

Hit return to see the next message

> \abc=macro:
gh->test.
l.9 \show\abc

Hit return again to get

! Use of \abc doesn't match its definition.
l.11 \abc x
            y z

^{If you can't run in interactive mode, say \meaning\foo instead and look at the generated output.}

The format for \show when the token to be shown is a macro is

<parameter text>-><replacement text>.

(note the final period that's not part of the replacement text).

The parameter text in the case of \foo is #1, which means that TeX will look for an argument with the usual rules. Notice that the parameter text denotes something that TeX must find. For instance, if you call {\foo}, TeX will complain because it cannot find an argument: a closing brace is not a suitable token to be taken as argument.

In the case of \abc what's shown as parameter text is gh, which means that after \abc TeX must find gh. If not, an error will be raised.

But you don't really need \show: just follow the expansion. The call

\foo{gh}

will result in TeX replacing \foo with its replacement text after looking for the arguments:

\def\abc gh{test}

Not \def\abcgh as you might expect. In the replacement text of \foo, \abc is a single token and TeX only processes tokens. So you get, with • for dividing tokens,

\def•\abc•g•h•{•t•e•s•t•}

The parameter text is anything that follows the macro to be defined up to the first {. It can contain # for denoting required arguments like in the case of \foo, but it needn't.