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Coq

Coq is a formal theorem-proving language and system. It uses a small set of core primitives for expressing logical statements. Built on top of the Calculus of Inductive Constructions, Coq allows users to define functions and predicates as well as prove properties about them in a machine-checkable way using expressive type systems that can capture complex mathematical notions directly, leading to non-trivial program verification. As one might expect from a programming environment that also serves as an interactive proof assistant, it is widely used in academic research related to formal methods and has also found some application in industry when strong guarantees are needed.

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