Lean vs Rocq
Lean
lean-lang.org
Rocq
rocq-prover.orgSide by side
| Figure | Lean | Rocq |
|---|---|---|
| Price from | Free | Free |
| Free plan | Yes | Yes |
| Free trial | — | — |
| Open source | — | — |
| Web | Yes | Yes |
| Windows | Yes | Yes |
| macOS | Yes | Yes |
| Linux | Yes | Yes |
| Plans published | 1 | 1 |
| Spec score · Formal Verification Tools | 8.6 (#2) | 8.5 (#3) |
| Founded | 2013 | 1984 |
| License | Lean is released under the Apache 2.0 license, which the documentation describes as allowing others to use and extend the code and mathematical libraries freely. | The Rocq Prover is distributed under the GNU Lesser General Public Licence Version 2.1 (LGPL). |
| Proof checking | Lean's minimal trusted kernel is described as guaranteeing correctness in mathematical proof, software verification, and hardware verification. | Rocq machine-checks proofs using a relatively small certification kernel. |
| Support | The Lean Community Zulip is described as the central hub for questions and collaboration, and Lean FRO hosts weekly technical office hours. | Users can report installation trouble or extension bugs in the dedicated Rocq Zulip stream. |
| Supported systems | Tier 1 platforms include Linux, Apple Silicon macOS, and x86-64 Windows; x86-64 macOS and Emscripten WebAssembly are Tier 2. | The Rocq Platform provides installation support for Windows, macOS, and many Linux distributions. |
| What it does | Lean is an open-source programming language and proof assistant for writing correct, maintainable, formally verified code. | Rocq is an interactive theorem prover for developing mathematical proofs and formal specifications, including proofs that programs meet their specifications. |
Plans
In their own words
Lean
Lean is an open-source programming language and proof assistant for formalizing mathematics, verifying software, and writing general code. Its minimal trusted kernel checks proofs, and the project describes it as supporting correctness in mathematical, software, and hardware verification. Lean includes the Grind tool for automating some pattern matching, case analysis, and systems of linear inequalities; metaprogramming lets users add notation and proof automation. Projects are managed with Lake, the package manager bundled with Lean. Mathlib is a community-driven library with over a million lines spanning areas including algebra, analysis, topology, probability, and computer science. The recommended setup uses VS Code with the Lean 4 extension for syntax highlighting and code completion, while Neovim with lean.nvim is also well-supported. Lean runs on Linux, macOS, and Windows, and Lean4Web lets users run code in a browser. The software is free under the Apache 2.0 license. Learning resources include textbooks, tutorials, interactive games, documentation, and an API reference.
Rocq
Rocq is a free interactive theorem prover and proof assistant for building mathematical proofs, formal specifications and programs, including proofs that programs meet specifications. Its Gallina language supports specification and mathematical work and is based on the Polymorphic, Cumulative Calculus of Inductive Constructions. A relatively small certification kernel machine-checks proofs. Rocq also offers interactive proof methods, decision and semi-decision algorithms, and a tactic language for defining methods. Certified programs can be extracted to OCaml, Haskell or Scheme, and the system can connect with external computer algebra systems or theorem provers. The Rocq Platform bundles the core prover with libraries and plugins for development and teaching. Its scripts install Rocq and packages on macOS, Windows and many Linux distributions; precompiled installers are available for macOS and Windows, but not Linux. Editor options include the VsRocq Visual Studio Code extension, RocqIDE, Proof General and Coqtail. Rocq is written in OCaml and distributed under the GNU Lesser General Public Licence Version 2.1.