a. PRO infinitive
Ex: I agreed (PRO) to do what she asked.
=> It was agreed that I should do what she asked.
Ex: She learned (PRO) to speak English.
Note, in these constructions, the subject is the doer of the action. Not all PRO constructs can be re-worded; e.g., PRO to do => I should do, but we can tell who the subject of the infinitive is by looking at the participants in the sentence; e.g., She learned to speak English.
b. For ... to-infinitive
Ex: It is rare for two people to talk about murder on a personal level.
Ex: It now remains for you to school your child.
(See more 'Full 'for to-infinitives' here http://www-personal.umich.edu/~jlawl...ershandout.pdf and here http://www.humanities.manchester.ac....S/cuyckens.pdf)
c. Nominative plus Infinitive Construction
THE NOMINATIVE WITH THE INFINITIVE , which consist of a noun / pronoun (in the Nominative) + Long Infinitive , is used:
1. with the following vb. In the passive: to accept , to believe , to expect , to find(out) , to hear , to imagine , to know , to notice , to say , to see , to suppose , etc.
She is said to be a very intelligent studentd. Accusative plus Infinitive Construction
2.with the following vb. in the activ voice: to appear , to chance , to happen , to prove , to seem etc.
The hunter changed to see the bear before I did.
3.with such constructions as : to be likely , to be certain /positive , to be lucky/unlucky , to be sure.
My son is likely to know what her new address is.
4. After ordinal numbers , superlatives and the only:
John was the first to finish the exercise.
Ex: I saw her go; we saw him leave.
Ex: She made me eat the vegetables.
Ex: The teacher let him stand outside the classroom
Note, in these constructions the subject (I, she, he, the teacher) isn't the doer of the actions go, leave, eat, stand.
THE ACCUSATIVE WITH THE NOMINATIVE , which consist of a noun/pronoun (in the Accusative) + an Infinitive , is used: 1.
with vb. of perception : to hear , to feel , to notice , to see , to perceive and after the vb to let and to make. After these vb , The Short Infinitive must be used: I saw him go into the house. That noise made her look back.
One should make the difference between: I heard her singing in the garden. (PRESENT PARTICIPLE) I heard her sing at the concert. (SHORT INFINITIVE) 2.
after vb expressing volition : to demand , to desire , to forbid ,to intend , to want ,to wish. I want him arrive there before noon. 3.
after vb expressing mental activities: to believe , to consider , to expect , to imagine , to know , to suppose , to think , to understand ,etc. They didnít expect her to arrive in time 4.
after vb of command or permission: to allow , to command , to force , to oblige ,to order, to permit ,etc. The teacher allowed me to leave the classroom. 5.
after impersonal constructions: Itís imposible for them to know where we are. 6
. after such vb as : to advise , to choose , to challenge , to convince , to send . Mother advised us not to run in the street.
Source: Present Tense, Past Tense, Future Tense, Infinitive constructions, Model verbs, Passive Voice referat