|1. Perfect or Past Meaning|
Perfect infinitives such as to have done, to have flown, etc. can take similar meaning as perfect or past tenses.
I'm glad to have done my project early.
Fred hopes to have done th presentation himself.
She was relieved to have flown before the typhoon hit.
|2. Perfect Infinitive for unreal past|
When perfect infinitives are used after some verbs such as mean, be, would like, they refer to unreal past which is the opposite of what actually happened.
I meant to have invited you, but I lost your number.
She was to have been the main actress, but she refused the offer.
He would like to have met you in person but he got caught up with work.
|3. Perfect Infinitives after Modals|
When perfect infinitives follow modal verbs such as could, might, ought, should, would, needn't, they refer to unreal situations.
He could have fallen from the ledge.
You needn't have to drive all the way to the airport.
I would have bought that house had I enough money.
|In some cases, perfect infinitives after modals can also refer to situations that are uncertain.|
The dish could/should/ought to/may/will/must have cooked by now.