(13) these diligent workers
In (13) the adjective diligent is a modifier of the head noun workers. Modifier is a general term for optional elements in a phrase that add descriptive information about the head word. We have already seen some modifiers in the verb phrase: the adjuncts. The noun phrase also resembles the verb phrase in that it can contain contain complements. Distinguishing modifiers from complements in noun phrases, however, is much trickier than distinguishing them in verb phrases, and we will not do so in this course. Instead, we will content ourselves with simply lumping noun-phrase modifiers and complements into the broader category of dependent.
(7) Garth's reply
This NP looks almost the same as the NPs above, but Garth is a proper noun, not a determiner. And yet Garth seems to occupy the same "slot" in the noun phrase. Notice that we can use either a determiner or the proper noun, but not both:
(7a) the reply
(7b) *the Garth's reply
(7c) *Garth's the reply
At this point, you may be ready to assume that Garth’s actually is a determiner, but that conclusion leads to some unfortunate consequences. First, we would have to say that any noun could change its part of speech simply by adding the genitive inflection. In other words, the category of determiner, which we have already described as containing a small number of words that have a principally grammatical function becomes an open-ended set. Further, this slot isn't just occupied by genitive nouns. It can be occupied by entire phrases:
Only a little more complex is the case of a noun appearing with a determiner. Determiners are extremely common in noun phrases. You will encounter a great many noun phrases that contain them. If you are still unclear about the category of determiner, you may want to review the relevant section of chapter 3 at this point
The definite article, the, is used to introduce something that can be identified uniquely within the context of the utterance or of general knowledge. For that reason, the is typically used for "old" information. If I say "bring the chair," I assume you already know which chair I'm talking about.