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# A time-traveling edge case in TeX

### July 8, 2021

Suppose you have the following raw TeX (not LaTeX) file first.tex:

\def\month{\relax The month is May.}
\input second.tex \month


This defines a custom macro, inputs a second file, and then prints the output of the custom macro. Suppose that second.tex contains:

June has begun.
\def\month{\relax The month is now June.}


What’s the output of pdftex first.tex? It’s what you’d expect:

June has begun. The month is now June.


The custom macro \month is first defined, then the second file is processed during which the macro is redefined, so when \month is expanded it has the second definition.

But what if we change first.tex by removing the space after \month?

\def\month{\relax The month is May.}
\input second.tex\month
%                ^ space removed


Seems like an innocuous change. Let’s run pdftex first.tex:

June has begun. The month is May.


The result is different! And we’ve travelled back in time!

This example illustrates a funny little edge case in TeX processing. Here’s what’s happening. When processing the \input command, TeX scans the following characters to obtain the name of the file to input. It keeps scanning until it encounters either a space or a command like \relax that cannot be expanded. If it encounters an expandable command like a macro, however, it needs to expand the command. This is to support cases where the filename is stored in a macro:

\def\filename{a_file.tex}
\input\filename


In this case the \input command needs to expand \filename to obtain a_file.tex.

In the original version of first.tex above, the processing stops when the space after the string second.tex is encountered. In the edited version of first.tex, the input scanning continues until \month because there is no space to stop it. Because \month is expandable, TeX expands the command in case the replacement text contains more characters for the file name. After this expansion the line looks like this:

\input second.tex\relax The month is now May.
%                ^ processing continues here


The next command is \relax which is not expandable, so the input command takes second.tex as the filename and carries on. However expansion is irreversible! So when processing returns to first.tex, it is the previously expanded text of \month that is used.