Why is there no \mudimendef primitive?

Question

The TeXbook defines in chapter 24 (page 270 in my edition) the notion of <dimen>, <skip>, <mudimen> and <muskip>, the first two being used in horizontal and vertical mode, while the other ones are used in math mode.

However this parallel between math mode and other modes is broken by registers: only \dimendef, \skipdef and \muskipdef exist, and not \mudimendef. Similarly, \dimen 0, \skip 0 and \muskip 0 exist, but not \mudimen 0.

The only primitive that manipulates mudimens seems to be \mkern. Why are <mudimens> so special?

EDIT: extra question. I'm asking this because I try to be able to grab the argument of any primitive. To grab a <dimen>, for instance, one can use \newdimen\MyDimen and \afterassignment\DoSomethingWithMyDimen \MyDimen=. Given that TeX does not have <mudimen> parameters, I cannot use the same trick for that. I cannot use a muskip either, because it may mistakenly grab a stretch or shrink part which \mkern would stop at. It may be that I can use a \count register in some cases, but not all: how could I distinguish between cases like \mkern 1mu and \mkern \MyMuskip (with automatic coercion)?

Answer 1

Well, the answer is that there's no \mudimen register. :) So there can't be a \mudimendef command. Why Knuth didn't provide this kind of register, I don't know; but probably because \mkern and \mskip are not used so much that different registers for them are needed.

The chances to find \mkern 3mu plus in a document are, I believe, infinitesimal, but you can always test for plus after the specification, in case of \mkern.

There's no coercion either: \mkern 3pt is illegal, just like \mkern 33. In e-TeX there are \mutoglue and \gluetomu to do calculations (with \glueexpr) or comparisons (with \ifdim), but they simply transform 1mu into 1pt or vice versa. And code such as \ifdim\mutoglue\mymuskip>\mydimen is nonsensical, although legal.

For \mkern you could use \afterassignment\DoSomethingForMKern\tempmuskip=, but this, as you observe, will gobble a plus or minus part that might be hidden in a macro, but would stop the argument to \mkern, while the original token list would already be lost. Alas, I don't think it's really possible to do more than this.