In transformational grammar, systems of phrase structure rules are supplemented by transformation rules, which act on an existing syntactic structure to produce a new one (performing such operations as negation, passivization, etc.).
These transformations are not strictly required for generation, as the sentences they produce could be generated by a suitably expanded system of phrase structure rules alone, but transformations provide greater economy and enable significant relations between sentences to be reflected in the grammar.
Constituents are successively broken down into their parts as one moves down a list of phrase structure rules for a given sentence.
This top-down view of sentence structure stands in contrast to much work done in modern theoretical syntax.
In this regard, theoretical syntax abandoned phrase structure rules long ago, although their importance for computational linguistics seems to remain intact.
The dependency tree on the right could not, in contrast, be generated by phrase structure rules (at least not as they are commonly interpreted).
Here phrase structures are not derived from rules that combine words, but from the specification or instantiation of syntactic schemata or configurations, often expressing some kind of semantic content independently of the specific words that appear in them.
This approach is essentially equivalent to a system of phrase structure rules combined with a noncompositional semantic theory, since grammatical formalisms based on rewriting rules are generally equivalent in power to those based on substitution into schemata.
So in this type of approach, instead of being derived from the application of a number of phrase structure rules, the sentence Colorless green ideas sleep furiously would be generated by filling the words into the slots of a schema having the following structure: And which would express the following conceptual content: Though they are non-compositional, such models are monotonic.