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The Rocq Prover is an interactive theorem prover, or proof assistant. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive development of machine-checked proofs.
A Proof-oriented Programming Language
Formal verification for AI: a Lean 4 + Dafny proof checker that catches fake AI proofs (reward hacking), and verified recursive self-improvement (RSI) for coding agents. AI for math, physics and software engineering.
Lean certificates accompanying Navier-Stokes and Euler results
An axiom-free formalization of category theory in Coq for personal study and practical work
Mathematical Components
formally verified category theory library
Mathematical Components compliant Analysis Library
Verifying Signal's security at the machine-code level
Theorem statements about OSS-Fuzz fuzz targets as compiled RISC-V binaries, and machine-checked Rocq proofs of them
A Coq specification of ECMAScript 5 (JavaScript) with verified reference interpreter
A library of abstract interfaces for mathematical structures in Coq [maintainer=@spitters,@Lysxia]
A Lean formalization of the Classification of Finite Simple Groups
A foundational framework for modular cryptographic proofs in Coq
Prime numbers for Coq
Library for Classical Coq
Coq formalization of algorithms due to Tarjan and Kosaraju for finding strongly connected graph components using Mathematical Components and SSReflect [maintainers=@CohenCyril,@palmskog]
Coqtail is a library of mathematical theorems and tools proved inside the Coq proof assistant. Results range mostly from arithmetic to real and complex analysis. [maintainer=@jmadiot]