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We form the perfect infinitive with to have + the -ed form of a verb. We use the perfect infinitive after verbs such as claim, expect, hate, hope, like, lover, prefer, pretend:
1. He pretended to have lost her number and so had been unable to contact her.(or He pretended that he lost her number and so had been unable to contact her.)
2. We hope to have finished the building works by the end of March
(Cambridge English Grammar Today p.383)
Are the following sentences correct if we don't use the perfect infinitive? If no, please correct my English. Is it a rule that we must use the perfect infinitive after verbs such as claim, expect, hate, hope, like, lover, prefer, pretend?
1. He pretended to lose her number so that he could not contact her.
2. We hope to finish the building works by the end of March.
As an NES but not a teacher, I believe there is a logic fault in sentence #1.
As he only "pretended" that he'd lost her number, he actually still had her number and so could have contacted her had he wished to do so. What I believe you mean is ".... so that he had an excuse for not contacting her".
Sentence #2 sounds fine to me, as an NES.