THE PERFECT INFINITIVE
to have + past participle: to have worked, to have spoken
В – Use with auxiliary verbs
1/ With was/were to express an unfulfilled plan or arrangement (see 114):
The house was to have been ready today, (but it isn’t)
2/ With should, would, might and could to form the perfect conditional
If 1 had seen her I should have invited her.
3/ With should or ought to express unfulfilled obligation; or, in the negative, a wrong or foolish action
He should have helped her. (but he didn’t)
I shouldn’t/oughtn’t to have lied to him. (but I did)
4/ With should/would like to express an unfulfilled wish:
He would like to have seen it. (but it wasn’t possible) or
He would have liked to see it.
i.e. we can put either verb into the perfect infinitive without changing the meaning.
5/ With could to express past unused ability or past possibility:
/ could have made a lot of money, (but I didn’t)
He could/might have phoned her. (Perhaps he (has) phoned.)
6/ With might/could to indicate that the speaker feels upset or indignant at the non-performance of an action:
He might/could have told me! =
I am annoyed that he didn 't tell me.
7/ With may/might in speculations about past actions:
He may/might have left =
It is possible that he (has) left.
You might/could have been killed!
8/ With can’t/couldn’t to express negative deduction:
He can 't/couldn 't have moved the piano himself.
We knew he couldn’t have paid for it, because he had no money.
9/ With must to express affirmative deduction
He must have come this way; here are his footprints.
10/ With needn’t to express an unnecessary past action: You needn 't have hurried. Now we are too early. You needn’t have cooked it. We could have eaten it raw.
С – With certain other verbs
1/ With appear, happen, pretend, seem
Note the difference between present and perfect infinitives here: Present infinitive:
He seems to be a great athlete = It seems that he is . . .
He seemed to be a great athlete = It seemed that he was . . . Perfect infinitive:
He seems to have been . . . = It seems that he was . . .
He seemed to have been . . . = It seemed that he had been . . . i.e. the action of the perfect infinitive is an earlier action; it happens before the time of the main verb. Other examples:
/ happened to have driven that kind of car before =
It happened that I had driven that kind of car before.
He pretended to have read the book =
He pretended that he had read it.
2/ With the following verbs in the passive voice: acknowledge, believe, consider, find, know, report, say, suppose, think, understand:
He is understood to have left the country.
3/ The perfect infinitive is possible but less usual with claim, expect, hope, promise:
He expects/hopes to have finished by June =
He expects/hopes that he will have finished by June.
THE PERFECT INFINITIVE
Thank you for your contributions but I should point out that these and the other forums are primarily intended for people wanting to ask questions on vocab, grammar and idiom rather than for posting exercises.
The source of the exercises seems to be “A Practical English Grammar” (Thomson & Martinet).