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 is quite some handle for Modal forms in real time.
Let us begin with a picture for the infinitive and head time.
38. I care to exercise.
The exercise has made us physically fit and happy. To think about the workout as something prior, ■ANTECEDENT, we might say,
MAIN GRAMMATICAL TIME: THE PRESENT
38a. I am happy to HAVE exercised.
Auxiliary HAVE can make ancillary time extents that are antecedent to grammatical main time.
This ancillary extent may, but it does not have mean a past time. It is only antecedent to the main, and this 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 stalks, our theory time frame for finding them will be closed.
PROBABILITY
41. The handles MAY HAVE broken off.
41a. They MIGHT HAVE broken off.
41b. They 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. These here have stalks. We may guess,
44. This CAN / MAY / COULD / MIGHT be the handles.
The Modal frame here is open, with the likely handles in plain view. We could say, human cognizance allows theory, whereas not even theoretical physics would go on without data.
The Modal use depends much on what we think or expect. Feel welcome to ■9.2. The modal net.