Classification and position (advanced)

Modals and auxiliary do are not classified as V, but as INFL elements.
Auxiliary have and be are classified as V (based on the evidence given below).

Position: Lexical verbs versus have/be and modal auxiliaries
In contrast to main verbs, modal auxiliaries, auxiliary have and be, and periphrastic do can:
(a) be negated directly:

Sarah doesnít/shouldnít drive too fast.
Sarah hasnít driven too fast.
Sarah isnít driving too fast.
cf.: * Sarah drivesn't too fast.

(b) undergo inversion in questions:

Should/Does Sarah drive too fast?
Has Sarah driven too fast?
Is Sarah driving too fast?
cf.: *Drove Sarah too fast?

(c) form question tags:

Sarah drives too fast, doesnít she?
Sarah should drive too fast, shoudn't she?
Sarah has driven too fast, hasnít she?
Sarah is driving too fast, isnít she?
cf. * Sarah drives too fast, drivesnít she?

I. Modal auxiliaries:
(a) appear only in combination with, and always to the left of, another verbal element:

Tom should write the report.
Tom should have written the report.

(b) always appear to the left of negation, and negative and other preverbal adverbs:

Sarah would not/never/sometimes drive too fast.

(c) appear only in finite clauses (since they do not have infinitival forms):

I would like him to be able to drive a car.
* I would like him to can drive a car.

II. Auxiliary have and be:
(a) appear to the right of modal auxiliaries
(b) appear to the right of negation when occurring with modal auxiliaries:

John should not have stolen the money.

The fact that they occur in combination with modals shows that they must be base-generated in a category other than INFL.
(c) appear to the left of negation when no modal verb is present:

John has not stolen the money.

The fact that they can occur to the left and to the right of the negator shows that they can move to INFL (when this position is not occupied by a modal).
(d) appear in finite and non-finite clauses.
The fact that they can appear in non-finite clauses shows that they are not base-generated under INFL (since INFL [-Tense] can only dominate the infinitive marker to).

III. Periphrastic do:
(a) cannot appear with modal auxiliaries or auxiliary have and be:

* didnít have stolen/* will didnít steal

(b) cannot appear in infinitival clauses:

* I told him to didnít steal the money.

The fact that do is in complementary distribution with the infinitive marker to suggests that it is base-generated under INFL.
(c) appears to the left of negation, like modal auxiliaries and unlike auxiliary have and be

He did not steal the money.
* He not did steal the money.

This shows that do is not base-generated under Vį and moved to INFL, but that it is base-generated under INFL.