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There are four main types of grammars in formal language theory, classified by the Chomsky hierarchy: Type 0 (recursively enumerable grammars), Type 1 (context-sensitive grammars), Type 2 (context-free grammars), and Type 3 (regular grammars). Each type has different generative power and constraints, with Type 3 being the simplest and Type 0 being the most complex. These grammars are used to define and analyze the syntax of programming languages and natural languages.

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