The perfect infinitive has the following structure: (to) have + past participle.
Examples are: to have missed, to have written, to have worked, to have left etc.
Perfect infinitives can have the same kind of meaning as perfect or past tenses.
- I am glad to have found a new job. (= I am glad that I have found a new job.)
- She was sorry to have missed the concert. (= She was sorry that she had missed the concert.)
- You seem to have annoyed him. (= It seems that you have annoyed him.)
- The perfect infinitive is often used after the modal auxiliary verbs could, would, might, ought, should and needn’t to talk about unreal situations.
- You should have asked my permission before going out. (The person didn’t.)
- She should have discussed the matter with him. (She didn’t discuss the matter with him.)
- I would have gone to university, if I had passed my exam. (I didn’t pass my exam.)
- You shouldn’t have provoked him. (You provoked him.)
- We needn’t have waited for his approval. (We waited for his approval.)
The structure modal auxiliary + perfect infinitive is not always used to talk about unreal past situations. It can also be used to express certainty.
- She should have arrived by now.
- They will have reached the station by now.