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How come you always read about the verb to do being used to replace an afforementioned verb?

They go to school, don't they?

Does she work there? No she doesn't

But you never hear of other modals, which also perform this function, doing this?

They can go to school, can't they?

Can you go to School? No, I can't.

Also, if there is no auxiliary in a sentence, do we use 'do' invairably in the question tag?

Everybody likes her, don’t they
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Where do you read about auxiliary do without reading about the other auxiliaries in this function?

Without the auxiliary in the main clause, we almost always use 'do', I guess. There are exceptions (?): Let's go, shall we?
Here is one such example:

Any reasons why you think they have neglected to mention the others function as such?

Primary helping verbs (3 verbs)

These are the verbs be, do, and have. Note that we can use these three verbs as helping verbs or as main verbs. On this page we talk about them as helping verbs. We use them in the following cases:

  • be

    • to make continuous tenses (He is watching TV.)
    • to make the passive (Small fish are eaten by big fish.)

    • have

      • to make perfect tenses (I have finished my homework.)
      do

      • to make negatives (I do not like you.)
      • to ask questions (Do you want some coffee?)
      • to show emphasis (I do want you to pass your exam.)
      • to stand for a main verb in some constructions (He speaks faster than she does.)
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Any reasons why you think they have neglected to mention the others
function as such?--Ah, because the topic of the section is be/have/do, that is all.
Further down the page they discuss modals without mentioning this, though... (I just didn't want to fill the whole post)

Have you a source that does detail this?

Thanks
Quirk, et al mention the similarity in a note to section 12.60, where other auxiliaries can be, with do, considered 'stranded operators':

1. Sam kicked the ball harder than Dennis did.
2. Sam kicked the ball harder than Dennis can.

But I guess that most grammars want to separate them, since their realization is different:

3. Sam kicked the ball harder than Dennis did [kicked the ball].-- NOT [did kick the ball].

4. Sam kicked the ball harder than Dennis can [kick the ball].

So they consider 'do' under substitution and the others under ellipsis.
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Mister MicawberSo they consider 'do' under substitution and the others under ellipsis

[Y] Thanks, MM. I thought that may have been the case. I also found the term 'pro-verb' discussed on Wiki, which doesn't seem to differentiate between 'do' and other pro-verbs like 'can'...

http://en.wikipedia.org/wiki/Pro-verb