This is formed with the infinitive of 'have' and the past participle
Eg. to have written, to have seen, etc.
Table 53.1 Uses of perfect infinitives with should, would, might and could
English
To form the perfect conditional
If I had seen that snake, I would have killed it.
To express unfulfilled obligation
He should have helped me (but he didn’t).
He should have bought that book (but he didn’t).
To express past unused ability
I could have lifted that stone (but I didn’t).
In speculations about past actions
They may / might have finished the work.
Who could have taken the money?
To express negative deductions
She can’t / couldn’t have married him.
With ‘must’ to express an affirmative deduction
He must have passed the exam; he is a good student.