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How do phrase-structure rules analyze the parts of a sentence in Syntactic Structures?

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Noam Chomsky wearing glasses and a dark sweater, looking slightly to the side during an interview. — Noam Chomsky American linguist and philosopher Noam Chomsky, 2010.

In Syntactic Structures, Noam Chomsky defines phrase-structure rules as a formal system of "rewrite" instructions that analyze a sentence by breaking it down into its hierarchical constituent parts.12

These rules function by taking a symbol on the left side of an arrow and defining it as a string of symbols on the right. For example, a rule might rewrite a Verb Phrase (VP) as a Verb plus a Noun Phrase (NP), indicating that these are the immediate constituents of that construction. By applying these rules systematically, the grammar generates a constituent-structure analysis, which organizes the smallest units of a sentence into layers of increasingly inclusive units.12

This process results in a phrase marker—a tree diagram that serves as a structural description of the sentence. These phrase-structure rules provide the essential underlying structure upon which subsequent transformational rules operate to account for more complex syntactic relationships, such as those between active and passive sentences.12