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Coq

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description Coq Overview

Coq is a powerful interactive proof assistant used extensively in mathematics and computer science. It allows users to write rigorous mathematical proofs by constructing them step-by-step, using a combination of logic and programming techniques. Its ability to generate executable code from proofs has revolutionized research in areas like cryptography and algorithm design.

help Coq FAQ

What programming language does Coq use?

Coq uses its own specification language called Gallina, which is based on a typed lambda calculus called the Calculus of Inductive Constructions. Users write proofs in a tactic language and can extract verified code to OCaml, Haskell, or Scheme.

Is Coq the same as Coq proof assistant and Rocq?

In 2024, the Coq proof assistant was officially renamed to Rocq to avoid confusion with inappropriate English connotations. The project, originally developed at INRIA in France, remains the same software under the new name.

What is Coq used for in software verification?

Coq has been used to formally verify major mathematical results like the Four Color Theorem and the Feit-Thompson Theorem. In software, it was used to develop CompCert, a formally verified C compiler that provably produces correct assembly code.

How is Coq different from Lean or Agda?

Coq, Lean, and Agda are all interactive proof assistants based on dependent type theory, but they differ in their foundational systems and usability. Lean, developed by Microsoft Research, has gained popularity for its mathlib library and machine learning integration, while Coq has a longer track record in industrial verification.

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