(computing theory) A formal grammar in which every production rule is such that the left-hand side is exactly one non-terminal symbol and the right-hand side is zero or more terminal symbols and/or nonterminal symbols.

(formal theory) A language generated by a context-free grammar.

In formal language theory, deterministic context-free languages are a proper subset of context-free languages.

In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages.

In theoretical linguistics and computational linguistics, probabilistic context free grammars (PCFGs) extend context-free grammars, similar to how hidden Markov models extend regular grammars.