In a sentence like the following:
What a wonderful thing to have happen on your birthday!
what is the grammatical form of to have happen? I know the sentence is grammatical, but I can't identify how. It isn't a perfect infinitive, as in the following:
What a wonderful place to have visited on your birthday!
because to have happened would be incorrect in the original sentence. I thought it might just be the infinitive of a phrasal verb have happen, as one can in fact say something like:
I have happened to visit her in Atlanta quite recently.
But on reflection, the latter construction just appears to be the present perfect of happen. So I discarded that idea.
I searched online, but 'have happen' grammar and 'have happen' definition didn't yield anything useful.