Formal Language

A formal language is a set of strings defined by precise mathematical rules, studied in logic, computer science, and mathematics. Unlike natural languages, formal languages have unambiguous syntax and no native speakers — they are designed for computation, proof, or specification rather than communication between humans.

The concept underlies the theory of computation: the Chomsky hierarchy classifies formal languages by the power of the grammars that generate them, from finite-state languages to recursively enumerable languages equivalent to Turing machines. Natural language syntax occupies an intermediate position in this hierarchy, a fact that connects formal language theory directly to linguistics.

Formal languages are also the foundation of programming languages, database query languages, and communication protocols. Every compiler, parser, and verifier operates on formal languages. The distinction between syntax (well-formedness) and semantics (meaning) in formal languages has served as a template for analogous distinctions in the study of natural language — though whether the analogy holds without distortion is debated.