Sequence of tenses with infinitives
An infinitive is the base form of a verb preceded by to. Use the present infinitive (to be, to understand) to show action at the same time as or later than the action of the verb in the sentence.
The action expressed in the infinitive (to raise) occurred later than the action of the sentence’s verb (had hoped).
Use the perfect form of an infinitive (to have followed by the past participle: to have begun, to have walked) for an action occurring earlier than that of the verb in the sentence.
The liking occurs in the present; the joining would have occurred in the past.
Sequence of tenses with participles
Like the tense of an infinitive, the tense of a participle is governed by the tense of the sentence’s verb. Use the present participle (acting, lying) for an action occurring at the same time as that of the sentence’s verb.
Use the past participle (given, helped) or the present perfect participle (having started) for an action occurring before that of the verb.