Modal auxiliaries and the perfect tenses in English

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Modal auxiliaries and the perfect tenses

The Modal Auxiliary + Have + Past Participle type construction (Modal Auxiliary + Perfect) allows us to speak retrospectively about a completed action in the past:
It must have been hot last summer. I imagine that it was probably hot last summer.
He could not have murdered her, since he was in Chicago. It's impossible that he murdered her, because he was in Chicago.
They may have crossed the border by now. They might have already crossed the border by now.
You might have missed a very good opportunity. It's possible that you have missed a very good opportunity.
She needn't have cleaned the entire house. It wasn't necessary for her to have cleaned the entire house.

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