Why is \active defined as \char13 (and not 13)?

Question

In plain TeX, we have

\chardef\active=13
\catcode`\~=\active

I thought a catcode should be assigned a number between 0 and 15, but \active is \char13. So how does it work?

Would \catcode`\~=13 also work?

Answer 1

There are three issues here, two about performance and one about 'safety'. A \chardef'd token is parsed slightly faster than TeX looking for the end of a number, so \active is a little better in that regard than an explicit 13. Today this is not so much of an issue, but was in the past. Similarly, \active is a single token in terms of memory, whereas 13 is two tokens: there's a saving in using the former. Once again,, memory usage today isn't a big problem but was in the past.

Perhaps more important is the rule that TeX keeps looking for the end of a number when digits are given explicitly, whereas for a \chardef token this doesn't happen. So for example

\catcode`\a=134

gives an error but

\catcode`\a=\active4

isn't. In an explicit use that's not likely to be an issue but if we

\def\foo{\catcode`\a=\active}

then \foo 4 is OK, whereas for an explicit 13 we need a space or \relax (so yet another token).

(TeX is 'looking for a number' in this context so a \chardef or \mathchardef token is fine in place of an explicit run of digits. Making \active a macro expanding to 13 has the some of the same issues as an explicit value.)