If we say that something must have been a fruit, it could be fruit, or it might have been fruit — only we do not know the kind — it is first of all our thought we manage. Auxiliary HAVE can work great with thought in real time.
Let us begin with a picture for the infinitive and head time.
38. I remember to exercise.
Let us think the exercise makes us physically fit and happy.
MAIN GRAMMATICAL TIME: THE PRESENT
38a. I am happy to exercise.
If we recall our exercise as something prior, ■ANTECEDENT, we might say:
MAIN GRAMMATICAL TIME: THE PRESENT
38b. I am happy to HAVE exercised.
Auxiliary HAVE generally gives an auxiliary time extent, and it can make antecedent reference to grammatical main time, too. Antecedent time may be, but it does not have to be a past time. It is always antecedent to the main time, and that can be the grammatical Present, Past, or Future.
MAIN GRAMMATICAL TIME: THE PAST
39. I was happy to have exercised
BUT
MAIN GRAMMATICAL TIME: THE FUTURE
40. I will be happy to have exercised.
To compare,
If we say we have learned something, we say we began learning some time before speaking about it, that is, the PRESENT.
If we will have learned, or we had learned something, respectively, we begin learning some time before a FUTURE or PAST time.
Let us return to our theory fruit. If we do not expect to find the stalk, our Modal frame for it will be closed. The theory time is over.
PROBABILITY
41. The handle MAY HAVE broken off.
41a. It MIGHT HAVE broken off.
41b. It COULD HAVE broken off.
Let us compare some more Modal syntax.
CERTAINTY
42. The handle MUST HAVE broken off.
CONTINGENCY
43. You SHOULD HAVE checked on the handle.
43a. The handle OUGHT TO HAVE BEEN checked.
43b. You NEEDN’T HAVE manipulated the handle.
Fortunately, there can be plenty of theory fruit. The one here has a stalk. We may guess,
44. This CAN / MAY / COULD / MIGHT be the handle.
The Modal frame here is open; we could say, the use for the stalk is an open matter, and altogether, when we see it, we can make more of some reasonable theory. Not even theoretical physics would go on without data.
The Modal use depends on what we think or expect. Feel welcome to ■9.2. THE MODAL NET.