What's the form and function of?

Question

As the title says, what's the form and function of "for a walk" and "with a statue" in the following sentence? [John went for a walk to the park (with a statue.]

Answer 1

Both "for a walk" and "with a statue" are Prepositional Phrases in form. This is because both have a preposition ("for" and "with" respectively) as well as noun phrases that are the objects of those prepositions ("a walk" and "a statue" respectively).

The function of these two prepositional phrases within this sentence is different though.

The first prepositional phrase is an argument of the verb "went", and would, in my mind, be best categorized as having the function of DO (direct object).

The second prepositional phrase is a descriptor for the noun "park". Which park? the one WITH A STATUE. Because it is describing a noun, this prepositional phrase would be best labeled as having a function of "adjective" (postnominal adjective specifically).

And hopefully the above makes sense. The basic idea is that even though these phrases look very structurally similar when zoomed in (Preposition + indefinite article + noun), they are nonetheless fulfilling very different roles in the sentence. Or, using the vocabulary of the question prompt: their form might be identical, but their function is not.