How does \input adds a space?

Question

Consider the following :

A\input{foo1}C

A\input{foo2}C

A\input{foo3}C

A\input{foo3}
C

with foo1.tex containing "B", foo2.tex containing "B%" and foo3.tex containing "B\n%".

In the first case, we obtain "AB C", in the second "ABC" and in the third "AB C" and in the fourth "AB C" (with double space).

Up to here we can think that A\input{foo}C is equivalent to A<insert foo>\n C.

But,

\begin{equation}
\input{bar}
\end{equation}

with bar.tex containing "a=b" will not produce the expected error (two \n makes an empty line inside the equation).

Question

So my question is : what \input{foo} is equivalent to ? Is there a conditional addition of \n when the file does not finish by % or something ?

I'm not asking how to get rid of the extra space, but, on the contrary, how to conserve this extra space when replacing \input{foo} by the content of foo.bar.

Non equivalence with an extra newline

Let foo.tex containing only "A"

\input{foo}B

will produce the same as "A\nB" but

\input{foo} B

will produce a larger space between A and B wich is not equivalent to "A\n B".

Answer 1

I guess that with \n you are meaning a “new line”.

Since file systems can do different things to files, TeX always adds an implicit end-of-line character at the end of input files. Here I'll talk about the primitive \input.

So your foo1.tex file can be seen to contain B<newline>, foo2.tex contains B%<newline> and foo3.tex has B<newline>%<newline>. The first two files have one record, the third one has two.

The <newline> is substituted by the \endlinechar, in our case ^^M of category code 5.

The action of a category code 5 character is to trigger insertion of a space token in the token input stream and to set TeX in state N. Normally, state N is what triggers insertion of a \par token if, after skipping blanks at the next line, only another ^^M is found.

When TeX starts reading an \input file, it is forced in state N, whatever the state was when \input was scanned. However, TeX resumes the state it was in before \input, when the file has been completely read in.

So you get the space (or the double space), because the last ^^M is not followed by ^^M in state N.

Exception (module 538 of tex.web): if the \input file is empty, it is considered to consist of a single empty line, which triggers \par.

It's the same with LaTeX, because \input eventually calls \@@input, which is the primitive \input.

Thus the behavior in the equation example is essentially the same as the behavior in the example

A\input foo1
C

that's equivalent to A\input{foo1}C in LaTeX syntax. No \par is inserted.