
coq
Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semiinteractive development of machinechecked proofs.
That's untrue. There are typesystems and typecheckers which can check for correctness, as specified by a mathematical formula. This is proof assistants such as Coq[1] work. For example, take a look at fiatcrypto [2], a project that generates code that is correct by mathematical proof, and is now deployed in Chrome. Another famous example is the CompCert [3] compiler, a C compiler along with a correctness proof that the compiler generates assembly which correctly simulates the C semantics.
[1] https://coq.inria.fr/

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