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:
(b) undergo inversion in questions:
(c) form question tags:
I. Modal auxiliaries:
(a) appear only in combination with, and always to the left of, another verbal element:
(b) always appear to the left of negation, and negative and other preverbal adverbs:
(c) appear only in finite clauses (since they do not have infinitival forms):
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:
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:
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:
(b) cannot appear in infinitival clauses:
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
This shows that do is not base-generated under Vį and moved to INFL, but that it is base-generated under INFL.