Modal Verbs & Auxiliary Verbs

must have + past participle

She must have left already / He must have been tired — logical deduction

can't have + past participle

She can't have forgotten — she never forgets / He can't have seen that

might / may have + past participle

He might have missed the train / They may have already eaten

should have + past participle

I should have called her / You shouldn't have said that — past regret

could have + past participle

I could have gone but I didn't / She could have won easily

would have + past participle

I would have helped if I had known / She would have come if invited

be able to — replaces "can"

She wasn't able to come / I haven't been able to sleep — can has no infinitive

be supposed to

You're supposed to be here at 9 / She was supposed to call me

had better — strong advice

You had better leave now / We'd better hurry — stronger than "should"

used to / would — past habits

I used to run every morning / She would cook every Sunday — past routines