Unconfounding the is

Identify is in the following sentences.
Is it a main verb, a modal verb, an auxiliary verb or a linking verb?

1. Bill is drinking far too much for a person of his size.
2. Mary is extraordinarily happy.
3. Smole is walking her dog.
4. Mis_nomer is fed-up with grammar.

is drinking/ is walking
AUXILIARY VERBS. is is an auxiliary verb when it helps to change the tense of the main verb.

is happy/ is fed-up
LINKING VERBS. is is a linking verb when it is a being verb.