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Constituent structure (advanced)

I. Constituent tests show that:
(a) Modal auxiliaries and periphrastic do are not part of the VP whose head is the main verb.
(b) Auxiliary have and be are not part of the VP whose head is the main verb, or of the projection containing the modal auxiliaries or periphrastic do:

VP-deletion:

Modal auxiliaries:

John should write the report but Sally will.

* John should write the report but Sally.

do:

John should write the report but Sally does.

* John should write the report but Sally.

have and be:

John should have written the report but Sally will have.

John should have written the report but Sally will.

VP-fronting:

Modal auxiliaries:

John should write the report and write the report he will.

* John should write the report and will write the report he.

do:

John should write the report and write the report he did.

* John should write the report and did write the report he.

have and be:

John should have written the report and written the report he will have.

John should have written the report and have written the report he will.

THUS:
(a) Modal auxiliaries and periphrastic do (which both appear only in finite clauses) are base-generated in a position, namely INFL, which is a different one from that of:

(i) main verbs

(ii) auxiliary have and be

(b) Auxiliary have and be are base-generated in a V position outside of the VP whose head is the main verb.
BUT:
The parallels in syntactic behaviour between modal auxiliaries/periphrastic do and auxiliary have and be can be captured syntactically (see below).

II. Modal auxiliaries, auxiliary have and be, and periphrastic do are heads, and thus, according to X-Bar theory:
(a) must project to the level of the phrase.
(b) may (and in fact must) have complements:

each requires a VP-complement, whose head is not inflected for tense/agreement:

* she can swam/swims

* she has/is swam/swims

* she does swam/swims

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