Modal perfect

We can use the modal perfect to talk about the past.
modal perfect = modal + have + past participle
e.g. You should have seen what Emma wore to the party.

possibility Simon may/might/could have been al the party. I can't really remember. (= It's possible he was at the party.)

certainty Francis must have been 11 when he moved to france. (= I'm sure he was 11.)
Francis can't/couldn't have been 10 when he moved to france. (= I'm sure he wasn't 10.)

hypothetical I could/would have passed the exam if I'd studied harder.
situatons (= I didn't pass because I didn't study hard enoungh.)
note: here could = would have benn able to

opinion You ought to/should have called me. (= You didn't call me but I wish you had called me.)
He oughtn't to/shouldn't have spoken to her like that. (= he did speak to her like that but I think what he did was wrong.)

Note: modal perfect continuous = modal + have + been + -ing form
e.g. We must have been dancing for hours.

We use the modal perfect continuous:
- For actions in progresss or interrupted when another action happens
e.g. He can't have been driving carefully when he crashed the car.

- To emphasise that an action continued for a long time
e.g. Jan must have been talking on the phone for al least 3 hours!

Minaya Aguilar.