Definition
Plain language
A formal proof language, formerly called Coq, where the compiler refuses any proof that doesn't logically follow.
As stated in the literature
A dependently-typed proof assistant (renamed from Coq) supporting interactive theorem proving with the Admitted keyword for partial proofs; the verification substrate in the Inductive-Deductive Synthesis paper.
Why it matters: It provides a verifier you cannot fool, which makes it an ideal training signal for AI systems trying to learn rigorous mathematical reasoning.
For example, a proof of a theorem about sorting algorithms isn't accepted in Rocq unless every logical step type-checks, with no hand-waving permitted.
Heard on the show
“… equivalent of that on-site inspector, in this paper, is a feature of the proof assistant they use — Rocq, which used to be called Coq, and is a cousin of Lean and Isabelle if anyone's heard of those. …”Episode 075 — Growing Code and Proof Together: Verified Systems in Ten Hours Instead of a Year