Is the structure “can have verb-ed” possible?

I have seen and heard sentences like these:

He could have gone too far.

John can’t have eaten all the cake.

But I don’t seem to encounter this structure:

She can have done the work.

I tried Googling it and found some examples, but I’m still unsure if it’s acceptable.

I understand that "may have verb-ed" and "might have verb-ed" are frequently used in English. So if, in contrast, "can have verb-ed" is never used or is considered awkward, what’s the reason for this?

Answer

An excellent question, which merits more investigation than might be possible here. The short answer is that in contexts like this can’t is not the negative of can, but the negative of must when used for deduction, as in She can’t have done the work and John can’t have eaten all the cake. The main uses of can in its positive form are to express possibility and ability, but not deduction.

Attribution
Source : Link , Question Author : KSS , Answer Author : Barrie England

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