Is there a better term for "perfect infinitive", "perfect participle" or "perfect gerund"?

Solution 1:

That's interesting. I hadn't been aware of "perfect infinitive" or "perfect gerund" monikers. But thanks to your clear examples, I can see that there is no way these could be named in parallel with the former three, because the "tense" of have does not change. It seems as if "have" or "having" have no tense at all (or rather, that they can adapt to any tense)

Having learned English, she [speaks/spoke/has been speaking/could then speak] it well.

She [seems/seemed/had seemed] to have learned English when she was little.

So we could not apply tense terms to the latter three.

Clearly "participle" and "gerund" are apt. "Infinitive" seems to make sense, if only because the verb form includes "to".

So what are we left with? Just whether they are all "perfect", right? Well, do they denote that something has completed? Yes, they do.

So, despite the confusion of having so many similar names, I don't see how we could improve on these last three. They are logically named, although not "consistent" (parallel/symmetrical) in the way you seem to want them to be.

We could make the names longer, but what would we add? Shorter? That would be even more confusing! I'm afraid your stuck with these.