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The notion of intersubstitutability of subexpressions, or categorization of subexpressions into equivalence classes, is tightly related to the very idea of a grammar itself. Grammar formalisms differ in the ways that they compose these subexpressions (e.g. prefix‐suffix combinations, infix‐circumfix combinations), but this composition is mediated by categorization. Any interesting system of categorization involves isolating out the properties of a subexpression that affect its combinatory potential, and those that don't; those properties that need to be remembered or tracked, and those that can be safely ignored or forgotten. If everything is remembered and nothing is forgotten, a grammar reduces to a list of stored complete expressions (recall Figure 5.6); at the other extreme, a grammar that remembers nothing treats all subexpressions interchangeably, and therefore generates a set of expressions that exhibits no regularities. An interesting grammar is one that sits in between these two extremes, yielding constrained productivity.

The overall perspective that I have offered here is somewhat more optimistic about lasting contributions of the Chomsky hierarchy than linguists have generally been since the 1960s – not more optimistic about the role string‐generating grammars can play in linguistic theory, but more optimistic about the role that insights gleaned from the careful study of string‐generating grammars can play in an understanding of any kind of grammar.