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I just learned about phrase structure, but I can't figure out how to analyse an infinitive sentence.
For example, in the sentence "Mary tries to do her homework", I guess "try to do her homework" is a verb phrase, and "try" is the verb, but what about "to do her homework"? Considering that "to" belongs to preposition, is this a preposition phrase? However, I guess "to" in infinitive is not a preposition, so I think it should not be a preposition phrase. Therefore, I was thinking maybe "try to do" is the verb, and "her homework" is the noun phrase, but I'm really not sure. Could anyone help me with this question? Thank you!

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    You have answered it yourself. "To" is part of the infinitive there and not a preposition (since no noun follows directly). The infinitive phrase/ noun phrase "to do her homework" acts as the object of the transitive verb 'tries". – user392935 Aug 20 '20 at 18:45
  • Thanks for your answer, but I'm still kind of confused. What is the lexical category or functional category of "to do"? Is infinitive a lexical category or functional category? – Kieron Aug 20 '20 at 19:02
  • Are you a native speaker learing English formally or are you a native speaker of another language learning English as a foreign language? The context might affect some of the answers you get. – BoldBen Aug 20 '20 at 21:35
  • I'm not a native speaker of English and learning about structure of language now. – Kieron Aug 21 '20 at 4:37
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    "Tries to do her homework" is a verb phrase functioning as the predicate of the sentence. "To do her homework" is an infinitival clause functioning as complement of "tries". "To" is not a preposition here but a subordinator functioning as a marker for the clause. – BillJ Aug 21 '20 at 10:17
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Mary tries [to do her homework].

"Tries to do her homework" is a verb phrase functioning as the predicate of the sentence.

"Tries" is a catenative verb and the infinitival clause "to do her homework" is its catenative complement.

As Pax comments in their answer, "to" is not a preposition here but a subordinator, a special marker for VPs of infinitival clauses.

The term 'catenative' is derived from the Latin word for "chain", for the construction is repeatable in a way that forms a chain of verbs in which all except the last has a non-finite complement. In your example the chain is a short one consisting of just the two verbs "try" and "do".

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"to" is merely a marker of the infinitival clause "(to) do her homework", functioning here as complement of "tries". The to-infinitival clause is a clausal category, not a lexical category.

In the distant past the infinitive was inflected for nominative/accusative or dative, but with the decay of inflectional endings the preposition "to" was commandeered to mark the majority of infinitives, whether they were originally dative or not. It can therefore no longer be trusted to convey any kind of prepositional meaning, and may safely be analysed as a mere marker.

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