The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, and also their classification as a special type of formal grammar (which he called phrase-structure grammars).
In Chomsky's generative grammar framework, the syntax of natural language was described by a context-free rules combined with transformation rules. In later work (e.g. Chomsky 1981), the idea of formulating a grammar consisting of explicit rewrite rules was abandoned. In other generative frameworks, e.g. Generalized Phrase Structure Grammar (Gazdar et al. 1985), context-free grammars were taken to be the mechanism for the entire syntax, eliminating transformations.
—Formal language theory, the discipline which studies formal grammars and languages, is a branch of applied mathematics . Its applications are found in theoretical computer science, theoretical linguistics, formal semantics, mathematical logic, and other areas.
The linguistic formalism derived from Chomsky can be characterized by a focus on innate universal grammar (UG), and a disregard for the role of stimuli.
—The formalist propositions regarding innateness and stimuli do fit extensively with the cognitive opposition to behaviouristic psychology
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