Assignment macro

Question

Out of curiosity I wanted to find the limits of TeX regarding macro definitions. Assume there should be an assignment command which assigns the value of an already defined macro to a yet undefined macro, so something like

\def\newVariable{\variable}

just with the syntax usually find in other languages, i.e. using the equal sign as an assignment operator.

I guess it's not possible to write

\newVariable = \variable

as this results in an 'Undefined control sequence' when \newVariable is read. Is it possible to hook into the execution of whatever detects the undefined control sequence and look ahead with @ifnextchars for an equal sign and an macro?

What were if we'd write

newVariable = \variable

Now this should at least run without error. When \variable is expanded, is there any chance to remove the text newVariable = from the output string again (do some sort of rewinding) and use it in \variable as an option similar to \variable{newVariable}? So I guess here I would look for something like \@iflastchars. I am all open for bizarre solutions with all TeX flavours like finding the string in the output routine or in the aux or even in the PDF file produced by the last run (or any of the other output files).

I guess the answer will be "this is not possible", but as there are a lot of smart people around liking a challenge, I thought I'd give it a try. Please note, that I am fully aware of the solution with the normal TeX syntax so this is a more a theoretical exercise.

Answer 1

If TeX doesn't know the meaning of a control sequence, it will complain with Undefined control sequence, unless you are assigning a meaning to the control sequence itself.

So, no, there is no way to say something like

\varB=\varA

where \varB has no previous meaning. Anyway, a syntax like this is allowed only for registers (that have previously been declared or are primitive). So, for instance,

\tolerance=\mycount

is a legitimate assignment to the primitive register \tolerance, but only when \mycount is a register of the same type (in this case an integer), be it primitive or defined by \countdef, for instance

\countdef\mycount=123

(Such an assignment, that makes \mycount equivalent to the primitive register \count123, is usually performed behind the scene by the macro \newcount.)

If one says

\varB=\varA

where \varA has a meaning and \varB hasn't there will be an error, as said before. If \varB has a meaning and it is not compatible with the assignment, there will be again an error. For instance,

\newcount\varA \varA=42
\newdimen\varB
\varB=\varA

will throw the error Illegal unit of measure (pt inserted), unless, by chance, the following tokens may be interpreted as a legal unit of measure.

Conversely,

\newdimen\varA \varA=42pt
\newcount\varB
\varB=\varA

is legal and \varB will hold the integer 2752512 (the equivalent of 42pt in scaled points: 2752512 = 42 * 65536). This is because dimensions are stored internally as integers, but it's a rather esoteric topic.

Notice that

\newcount\varA \varA=42
\newcount\varB
\varB=\varA

is very different from

\newcount\varA \varA=42
\let\varB=\varA

In the first case, changing the value stored in \varA will not change the one stored in \varB, while in the second case it will, because \varB has become an alias for \varA.

Hooking into the mechanism that discovers undefined control sequences is not possible at the user's level and requires rewriting "TeX the program".

Of course it's theoretically possible to modify the syntax rules of TeX by declaring all characters active after having created a suitable set of macros; so, for instance, each letter might store itself somewhere waiting for some operator to come along telling what to do with the saved tokens. Say

newvariable = myvar ;

where the semicolon acts as "end of instruction". The active = would be defined as "look at what comes until the semicolon, determine its type and perform the assignment to the variable whose name results from the tokens in the storage bin". There are papers by Jonathan Fine on TUGboat describing this sort of plays, see for instance "Active TeX and the DOT Input Syntax" (TUGboat, v. 20, n.3, p. 248–254). Nothing is really impossible, the problem is: is it worth the labor? Of course one must define a "programming environment" and a "typesetting environment", since, after all, TeX's job is primarily typesetting documents.

Answer 2

No, it is not possible to make TeX do some action on finding an undefined sequence, other than invoking an error. TeX core reads the input sequence lineary, so no command can really influence what was read before. Moreover, the chracter = needs to be used in other contexts as well so it cannot easily be made active.

As I point out in the comments, there are cases where = means assignment:

• \let definition: \let\newmacro=\oldmacro
• Lengths assignment: \topskip = 10pt
• Counter assignment: \c@section = 5