What is this non finite describing "to have third form of verb " e.g,to have been,to have crossed etc.Is this showing any completeness of a work or something else.
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As miltonaut tells you, the verbform which you call the ‘third form’ is ordinarily called the 'past participle' (PaPpl). I urge you to discard the numbered term, which has no evident inherent meaning and is not in general use.
The construction HAVE + VERBPaPpl is the perfect construction; it signifies a state arising out of the prior eventuality named by VERB.
When HAVE is cast in a ‘finite’ (tensed) form, the resultant construction is named a present perfect or past perfect.
PRESENT PERFECT: John has now written the Anderson report.
PAST PERFECT: John had already written the Anderson report last week.
When HAVE is cast in the infinitive form, with or without the ‘infinitive marker’ to, the resulting construction is called the perfect infinitive. This construction is employed in the same uses as other infinitives, for instance:
As the complement of a modal verb: John may have written the report by tonight.
As the complement of a catenative verb: John wants to have written the report by tomorrow.
As a subject complement: To have written it so quickly is quite an accomplishment.
Note that HAVE can also be cast in the -ing form, having VERBPaPpl, and this construction can be used as either a gerund or participle. But the had in had VERBPaPpl can only represent the past form of HAVE, not the past participle form.
You may find a great deal more about perfect constructions at What is the perfect, and how should I use it?.
I think what you call the 'third form of the verb', I call the 'past participle'.
'To have + past participle' is the 'present perfect' tense. It has many uses. All of those uses involve actions completed in the past. However, they are different from past simple.
Past simple is usually used for one-time events, or when talking about a specific event in the past ("I went to China last year."). One of the uses of the present perfect is talking about an experience in the past that might be repeated in the future ("I have been to China, and I want to go again.").
Totally right, oerkelens! Guess that's the final sign I need to log off and go to bed.
OP, I'm sorry, I totally did not answer your question.