General use of modal verbs of deduction
We can use certain modal auxiliary verbs to make deductions, i.e. to make guesses based on known facts.
We can make deductions about the present :
'She's not here. She must be in the kitchen.'
We can also make deductions about the past :
'How do you think the burglar got in?'
'He must have climbed through the window.'
We use different modal axiliary verbs depending on how strong our guess is :
He must be in the kitchen. - Very sure - 99%
He can't be in the garden. - Very sure - we think it's impossible - 99%
He may / might / could be in his bedroom. We think it's possible - 50%
to make guesses about the past, we use the same modals and add the auxiliary verb have. This is followed by the past participle of the main verb :
He must have climbed through the window. - Very sure - 99%
He cant't have climbed through the window. - Very sure - we think it's impossible - 99%
He may / might / could have climbed through the window. We think it's possible - 50%
When using past forms, the have that follows the modal auxiliary verb is usually contracted to 've in rapid speech.
He can't've been here long.
She must've been in a hurry.
These contracted forms are often written in dialogue; in novels, for example.
In rapid speech these are often further contracted to :
He can'ta been here long.
She musta been in a hurry.
This kind of contraction is rarely written.