In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma,[1] is a lemma that gives a property shared by all context-free languages and generalizes the pumping lemma for regular languages.
The pumping lemma can be used to construct a refutation by contradiction that a specific language is not context-free. Conversely, the pumping lemma does not suffice to guarantee that a language is context-free; there are other necessary conditions, such as Ogden's lemma, or the Interchange lemma.