Preposition, or verb particle?

[Linguist__]

I'm doing some grammatical analysis for uni, and I have come across this utterance which has thrown me off a little bit: "The lady gave them something to eat". So far I have analysed:

At the clause level:
The lady = Subject
gave = Verb
them = Indirect Object
something to eat = Direct Object

And at the phrase level:
The = determiner
lady = noun
gave = main verb
them = personal pronoun
something = indefinate pronoun
to = ?
eat = ?

My problem is the 'to eat' part. I think the 'to' is a prepostion, but the presence of the verb makes me think it might be the particle. Can you just have a verb sitting on its own like that?

[TheParser]

(Not a teacher) Before the experts answer you, may I make a few suggestions? Yes, in high-school level English analysis, most teachers would probably just call "to" a preposition or simply a "sign" of the infinitive, They would tell their students it's not important what you call it. On a higher level of study, you might be told the following: (l) Sometimes "to" is a real preposition that does NOT permit only a main verb (We look forward TO your visit; We look forward TO meetING you. In your example, you cannot say "Something to food" or "Something to eatING." Therefore, we can conclude that "to" in "Something to eat" is, indeed, a infinitival particle. (I wish to credit The Oxford Dictionary of English Grammar for this information.) Let's see what the experts say when they answer you.

[Frank Antonson]

The Parser has a good answer.
I have learned to call "to" a "function word" when it is introducing an infinitive.
Otherwise, it is a preposition.
Of course "to eat" is an infinitive (phrase) that is modifying "something" ie. acting as an adjective.
In a chart, available at the "competitive sentence diagrammers" website you can see that, when listed among the preposition, "to" is placed at the outside of the box. "That" ,when it is introducing a noun clause,is another example of what I have learned to call a "function word"
Linguist Farmer