modal + perfect

Question

What would be the right way to express the thing:

She can't have left yet because of the rain.

or

She's not been able to leave yet because of the rain.

Answer 1

Either is okay but it's better to construct the first sentence this way:

She couldn't have left yet because of the rain.

In the sentence, she can walk and leave regardless if it is raining or not, but because she doesn't want the rain to drench her, she did not leave yet. Hence, the usage of could.

reference: https://english.stackexchange.com/questions/1/when-do-i-use-can-or-could

ShreevatsaR's answer:

". . .For instance:

We could go (if we like / but we won't / etc.), but

We can go (= We are capable of going / It is possible for us to go). . ."

Answer 2

The basic meaning of those two sentences is the same.  There is a difference in implication. 
 

She can't have left yet because of the rain. 
She couldn't have left yet because of the rain. 

I would expect to hear one of these if the speaker does not have direct knowledge of her actions or intent.  The speaker doesn't know whether she tried to leave or intended to leave, only that she didn't have the ability to leave. 

The difference between these two is mode.  "Can't" is indicative and present tense, but "couldn't" is subjunctive or past tense. 

 

She hasn't been able to leave yet because of the rain. 
She's not been able to leave yet because of the rain. 

I would expect to hear one of these if the speaker does have direct knowledge of her actions or intent.  She did try to leave or did intend to leave, and the speaker observed her being prevented. 

The difference between these two is the placement of the contraction.  "She's" contracts an auxiliary, but "hasn't" contracts an adverb. 
 

The alternatives in each pair represent formations that I imagine are more likely in different dialects.  To my American ear, the first of each pair sounds more American -- but that's an unsubstantiated and subjective judgment.