[Tex/LaTex] \nothing, \varnothing and \emptyset

tex-core

This is probably a question about TeX's history.

Why there is no command \nothing? If there's no \nothing, why \varnothing is called \varnothing instead of \nothing?

If I try to compile a document with \nothing, I get the error "! Undefined control sequence."

The command \varnothing is defined by the amssymb package, and \emptyset is defined by TeX itself, but neither defines \nothing. Is \nothing defined by something?

I contacted the author of cjw-latex, Colin J. Wynne. He does not remember why he wrote that line, since it was more than 20 years ago. But he said that

my best working hypothesis is that an earlier version of AMS-(La)TeX
did, indeed, use the sequence \nothing as an alias or substitute for
\emptyset. AMS-(La)TeX did, indeed, come up with their own names for
a few things, and quite a few custom symbols. Given that I preferred
the \varnothing, I can assume most other folks did, too, and they
eventually dropped their \nothing, but left \varnothing because that
was the control sequence most people were using.

Currently I'm hoping something can be discovered by perusing ftp://ftp.tug.org/historic/ Unfortunately, the oldest version of AMS-TeX they have is from 1993, so we can't test Colin's theory. They also have a LaTeX from 1983, which defines \emptyset but does not define \nothing.

Since this turned out to be such a hard question, I'm putting a bounty on it.

Best Answer

not a definitive answer, but perhaps a reasonable hypothesis ...

\varnothing is shorter than \varemptyset. mathematicians aren't generally great typists.

although \varempty is even shorter, \empty, while not a primitive, has quite a different meaning, and a "var" of that would only be confusing.

"the joy of tex", while it mentions both, has nothing useful to say on the matter (sorry, must be on auto-pun this morning), and in fact doesn't even point out that they have the same meaning.

the control sequence \nothing does show up in cjwmath.sty, where it is equated to \varnothing, and there is a further alias, \leer, for \nothing. i didn't find this name anywhere else in any package on tex live.

so the reason, to me, is lost in the mists of time.

i suppose i could ask mike spivak.

i have consulted the documentation for the composition system used at ams prior to tex. the name given to the slashed circle is "null set", for which a "short name", empty, was assigned for use by input keyboarders. (the system was highly encoded, and the canonical code was *yo; keyboarders were free to use whichever form they preferred, i.e., more easily remembered.) so the term "nothing" was not in use at ams in any relation to this symbol prior to the creation of the ams symbol fonts.

what would be in those fonts was defined by a committee; i've sent an inquiry to one of the few surviving members of the committee in the hope that he remembers.

i did ask mike spivak, and he doesn't remember, except that he's pretty sure he wasn't responsible.

i have found the definitive release notice of the original ams extra symbol fonts in the july 1985 issue of tugboat. these were the msxm and msym fonts, and initially (and erroneously) referred to as "euler", a lapse corrected in an update later that year. the name \varnothing is used, however without any commentary on choice of names. (and, unfortunately, the page in the scan of the update that would show this symbol is missing; but i've confirmed its presence in the paper copy on my bookshelf. i'll try to get the posted copy on the tugboat web site corrected.)

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[Tex/LaTex] \jobname, character codes and \detokenize

Three questions there, but I think you'll be let off!

'Balanced text' means that the argument has to have balanced grouping characters, usually { and } pairs. This is because \detokenize requires an argument starting with a token with category code 1 (begin-group), in the same way as a token register. Indeed, you can do very similar things with a token register and with \detokenize:

\newtoks\mytoks
\def\test{stuff}
\mytoks\expandafter{\test}% \mytoks holds 'stuff' as letters
\detokenize\expandafter{\test}% Ouputs 'stuff' as 'other' tokens

On the category codes in \jobname, there are a number of places where you get a 'string' from TeX where everything except spaces has category code 12. You see the same with \the\<somedimen> and \meaning (more on the later in a moment). You'd have to ask DEK for the full story, but my understanding is that this 'string' approach is used so that no tokens are accidentally added to a control sequence name. There are places where if they were 'letters' then trouble might arise.

Finally, on the approach before e-TeX. As I said, \jobname is not the only place where you see 'string' output. In particular, \meaning does the same. So if you do

\def\testa{<whatever>}
\edef\testa{\meaning\testa}
\edef\testb{\jobname}
\edef\testb{\meaning\testb}
\ifx\testa\testb
...

the test will be true if the two names agree as lists of characters. There are variations on this method, see for example LaTeX's \strip@prefix, which can be used to make a 'string' without any prefix:

\makeatletter
\def\testa{<whatever>}
\edef\testa{\expandafter\strip@prefix\meaning\testa}% Now a 'string'

(As pointed out by Martin Scharrer, LaTeX's \@onelevel@sanitize is the same as the above: \@onelevel@sanitize\testa would be equivalent to the last line above. To show what is going on it's clearer to see the \meaning but in use you'd pick \@onelevel@sanitize.)

[Tex/LaTex] Why isn’t everything expandable

While a definitive answer can only come from the Stanford team involved in development of TeX, and from Professor Knuth in particular, I think we can see some possible reasons.

First, Knuth designed TeX primarily to solve a particular problem (typesetting The Art of Computer Programming). He made TeX sufficiently powerful to solve the typesetting problems he faced, plus the more general case he decided to address. However, he also kept TeX (almost) as simple as necessary to achieve this. While expandable macros are useful, they are not required to solve many issues.

Secondly, there are cases where an expandable approach would be at least potentially ambiguous. Bruno's \edef\foo{\def\foo{abc}} is a good case. I'd say that here the expected result with an expandable \def is that \foo expands to nothing, but I'd also say this is not totally clear. There is the much more common case where you want something like

\begingroup
\edef\x{%
 \endgroup
 \def\noexpand\foo{\csname some-macro-to-fully-expand\endcsname}%
 }
 \x

which would be made more complex with expandable primitives.

The above example points to another grey area: what would happen about things like \begingroup and more importantly \relax. The fact that the later is a non-expandable no-op is often important in TeX programming. (Indeed, the fact that \numexpr, etc., gobble an optional trailing \relax is sometimes regarded as a bad thing.)

Finally, I suspect that ease of implementation is important. The approach of having separate expansion and execution steps makes the flow relatively easy to understand, and I also suspect to implement. An approach which mixes expansion and execution requires a more complex architecture. Here, we have to remember when Knuth was writing TeX, and the fact that programming ideas which we take for granted today were not necessarily applicable in the late 1970s. A fully-expandable approach would I suspect have made the code more complex and slower. The speed impact is one that was important when TeX was running on 'big' computers.

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