Lean vs TLA+
Lean
lean-lang.orgTLA+
lamport.azurewebsites.netSide by side
| Figure | Lean | TLA+ |
|---|---|---|
| Price from | Free | Free |
| Free plan | Yes | Yes |
| Free trial | — | — |
| Open source | — | — |
| Web | Yes | — |
| Windows | Yes | Yes |
| macOS | Yes | Yes |
| Linux | Yes | Yes |
| Plans published | 1 | 1 |
| Spec score · Formal Verification Tools | 8.6 (#2) | 7.5 (#24) |
| Editor integration | The recommended setup uses VS Code and the official Lean 4 extension, which provides syntax highlighting and code completion. | A Visual Studio Code extension supports TLA+ and PlusCal syntax highlighting, translation, parsing, TLC runs, result visualization, code completion, and formatting. |
| 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 TLA+ tools and Toolbox repository is licensed under the MIT License. |
| Platforms | The reference lists Linux, macOS, and Windows among Lean’s supported platforms, with Tier 1 binary releases available through elan. | The Toolbox download instructions cover Windows, Mac OS, and Linux. |
| Proof checking | Lean's minimal trusted kernel is described as guaranteeing correctness in mathematical proof, software verification, and hardware verification. | TLAPS mechanically checks proofs written in TLA+. |
| Support | The Lean Community Zulip is described as the central hub for questions and collaboration, and Lean FRO hosts weekly technical office hours. | The TLA+ Foundation directs technical questions and issues to the appropriate GitHub issue tracker. |
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.
TLA+
TLA+ has no write-up on Specifiction yet; its figures are above.