Upper-Intermediate Unit 10
Upper-Intermediate · Grammar Reference
Unit 10 — Modal Auxiliary Verbs II
must/can't/may/might/could have done · should/could/might have done · needn't have
10.1  Modal auxiliary verbs 2 — probability in the past

All modal auxiliary verbs can be used with the perfect infinitive. They express varying degrees of certainty. Will have done is the most certain, and might/could have done is the least certain.

Modal + have + PPCertaintyExample
will have beenMost certain'I met a girl at your party. Tall. Attractive.' 'That'll have been Sonya.'
must have beenLogical deductionIt must have been a good party. Everyone stayed till dawn.
can't haveLogically impossibleThe music can't have still been at dawn. Nobody danced.
may have gotPossibleHe may have got lost.
might have decidedPossibleHe might have decided not to come.
could have hadLess definiteHe could have had an accident.

Would have thought is common to express an assumption or supposition.

I'd have thought they'd be here by now. Where are they?
Other uses of modal verbs in the past
should have done
could have done
might have done
needn't have

Needn't have expresses an action that was done, but wasn't necessary. It was a waste of time.

I needn't have got up so early. The train was delayed.