We were checking some exercises and I wanted to know what’s the correct modal to use:
Gemma is away in Australia all summer. You ___ (can / see) her yesterday!
The answer is can’t have seen, which is I selected. However, some of my classmates were saying that couldn’t have seen is also an option. Is this valid too?
Yes, both are valid, with only very slightly differences in meaning (for most purposes they are all but identical). In fact, I would find couldn’t have seen more appropriate, especially since the event in question clearly occurred yesterday.
This is an example of a conditional perfect tense (e.g. would have been) with a modal verb (can/could) replacing the standard would.
Interestingly, the structure “could have [past participle]” appears to be fairly rare when discussing these kinds of modal constructions. For example, this British Council page and this SpeakSpeak page both discuss the could have formation but not the can have formation (at least, not in its positive sense; can’t have is discussed). Wikipedia mentions that can have been is a “rarer alternative” to could have been, but that section is listed without source, so take from that what you will.
Beyond the grammar, couldn’t in this context appears to be more common in my experience, and is evidenced in this Ngram.