Further, the subject NP Colorless green ideas, the minor NP green ideas, and the VP sleep furiously are constituents. Phrase structure rules and the tree structures that are associated with them are a form of immediate constituent analysis. 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. Top down An important aspect of phrase structure rules is that they view sentence structure from the top down. The category on the left of the arrow is a greater constituent and the immediate constituents to the right of the arrow are lesser constituents. 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 Minimalism for instance, sentence structure is generated from the bottom up. The operation Merge merges smaller constituents to create greater constituents until the greatest constituent (i.e. the sentence) is reached. In this regard, theoretical syntax abandoned phrase structure rules long ago, although their importance for computational linguistics seems to remain intact. Alternative approaches Constituency vs. dependency Phrase structure rules as they are commonly employed result in a view of sentence structure that is constituency-based. Thus, grammars that employ phrase structure rules are constituency grammars (= phrase structure grammars), as opposed to dependency grammars, which view sentence structure as dependency-based. What this means is that for phrase structure rules to be applicable at all, one has to pursue a constituency-based understanding of sentence structure. The constituency relation is a one-to-one-or-more correspondence. For every word in a sentence, there is at least one node in the syntactic structure that corresponds to that word. The dependency relation, in contrast, is a one-to-one relation; for every word in the sentence, there is exactly one node in the syntactic structure that corresponds to that word. The distinction is illustrated with the following trees: The constituency tree on the left could be generated by phrase structure rules. The sentence