a) I thought WILL could only have the form “WILL + present infinitive”! But in the following sentence WILL is used with perfect infinitive:
“I’m sure you will have noticed that attendance has fallen sharply.”
The main sentence does talk about present/future ( as in “You will notice now or soon” ), but why is PERFECT infinitive used instead of PRESENT infinitive?
a) Past form of CAN is COULD and of WILL is WOULD. Are these verbs actual past forms ( the same way wrote is past form of write ), or does is just mean that when used to describe past, we use COULD/WOULD instead of CAN/WILL?
b)I know that COULD is a past form of CAN when talking about some ability in the past, but what do we use instead of CAN when we want to express a request, an offer or permission that someone gave in the past? Or can in at least some of those cases CAN be used as it is?
c)when COULD is used as a past form of CAN, its form can only be “COULD + present infinitive”, but not COULD + perfect infinitive? If so, why?
3) “He could have sold cars.”
“You could have told me.”
a) The above two sentences can only talk about something in the past and not the present/future?
Thus is the form “COULD + perfect infinitive” used only when talking about something that should be done, but it wasn’t?
4) Perfect present tense has same form as perfect infinitive and yet perfect infinitive is used to talk about actions that happened before another action. Shouldn’t prefect infinitive also be used to describe the same time period as present perfect tense?
5) Among other things we also use present participle for building present continuous and present perfect continuous tenses. Then why couldn’t we also claim that present gerund is used for building those two tenses?
 Future perfect is also used to indicate a past likelihood, one that has consequences for the present or future:
- "As you will have already heard, the gym will be closed today"
- "You will have noticed that we no longer have a convertible."
I can't come over tonight. <present>
I couldn't come over last night. <past>
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 Click English Grammar Lessons
Use a present infinitive to express action at the same time as or later than that of the verb. "... why couldn't we also claim that present gerund is used for building those two tenses?"
Use a perfect infinitive to express action earlier than that of the verb.
Ex: I prefer to stay right here.The perfect infinitive combines to have with the verb’s past participle: to have kicked, to have
(Present infinitive to stay.)
Ex: She would have liked to join you.
(Present infinitive to join.)
written. It shows action that occurred earlier than that of the verb.
Ex: We now know human ancestors to have existed millions of years ago.
(Past infinitive to have existed.)
Ex: My father would like to have been an actor. (Perfect infinitive to have been.)
See also Perfect Infinitive. Fowler, H. W. 1908. The King's English
=>Becuase a gerund cannot function as a part of a verb. Gerunds are either subjects or objects.