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A number of representational phrase structure theories of grammar never acknowledged phrase structure rules, but have pursued instead an understanding of sentence structure in terms the notion of schema.

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.