In the same way that we use modal verbs to say how certain we are about things in the present we can also use them to speculate about the past.
Have + past participle (‘have done’, ‘have been’ have stolen’ etc.) is called the perfect infinitive. When we use modal verbs to talk about the present they are followed by an infinitive without ‘to’. When we use modal verbs to talk about the past they are followed by a perfect infinitive.
We use must + perfect infinitive when we feel sure about something in the past.
- You must have been delighted when you heard you’d won the lottery.
- The thieves must have come in through the window. Look – it’s still open.
- Oh no! Where’s my car? Someone must have stolen it!
We use might, may or could with the perfect infinitive to say that we think something was possible but we aren’t sure.
- The thieves might have escaped by car but we can’t be sure.
- He should be here by now. He may have been delayed by a traffic jam or something.
- I can’t find my purse. I could have left it in the supermarket but I just don’t know.
We use can’t + perfect infinitive when we feel sure something didn’t happen in the past.
- I thought I saw John in town this morning but it can’t have been him – he’s in Greece this week.
- I can’t have left it in the supermarket – I had it on the bus on the way home.
- You can’t have read the instructions properly. They’re perfectly clear