1. Jim has to find his lost wallet.
Is "has" the main verb or auxiliary?
2. I used to be a student.
What about "used"? If "used" is the auxiliary verb, what is the main verb -- to be?
Neither "has (to)" nor "used (to)" is an auxiliary verb if "auxiliary verb" is defined as a verb with the following behavioral properties:
1)
Used in Forming Negation: We add the auxiliary "do." We say "Jim doesn't have to find his lost wallet" and "I didn't use(d) to be a student," not "
Jim hasn't to find his lost wallet" or "
I use(d)n't to be a student." The latter constructions are, however, found here and there in historical usage.
2)
Used in Question Formation: We add the auxiliary "do." We say "Doesn't Jim have to find his lost wallet" and "Did you use(d) to be a student," not "
Has Jim to find his lost wallet" or "
Used you to be a student?" The latter constructions, or at least the one with "used," used to be used by some speakers.
3)
Used in Clausal Emphasis: We add the auxiliary "do." We say "Jim DOES have to find his lost wallet" and "I DID use(d) to be a student," not "Jim HAS to find his lost wallet" or "I USED to be a student." Though the latter sentences are fine, they do not constitute emphasis at the level of the clause.
4)
Licenses Verb Phrase Ellipsis: We need "to." We say "Jim doesn't want to look for his wallet, but he has to" and "I don't go to school now, but I used to," not
*"[strike]
Jim doesn't want to look for his wallet, but he has[/strike]" or
*"[strike]
I don't go to school now, but I used.[/strike]"