Isabelle vs Lean
Isabelle
isabelle.in.tum.de
Lean
lean-lang.orgSide by side
| Figure | Isabelle | Lean |
|---|---|---|
| Price from | Free | Free |
| Free plan | Yes | Yes |
| Free trial | — | — |
| Open source | — | — |
| Web | — | Yes |
| Windows | Yes | Yes |
| macOS | Yes | Yes |
| Linux | Yes | Yes |
| Self-hosted | Yes | — |
| Plans published | 1 | 1 |
| Spec score · Formal Verification Tools | 7.9 (#13) | 8.6 (#2) |
| Platforms | The application bundles support Linux, Windows, and macOS; the site also provides a self-contained Docker image without GUI support. | The reference lists Linux, macOS, and Windows among Lean’s supported platforms, with Tier 1 binary releases available through elan. |
| Support | Support is available through official documentation, the isabelle-users and isabelle-dev mailing lists, Zulip, and Q&A sites listed by the project. | The Lean Community Zulip is described as the central hub for questions and collaboration, and Lean FRO hosts weekly technical office hours. |
| What it does | Isabelle is a generic proof assistant for expressing mathematical formulas in a formal language and proving them in a logical calculus. | Lean is an open-source programming language and proof assistant for writing correct, maintainable, formally verified code. |
Plans
In their own words
Isabelle
Isabelle is a free proof assistant for expressing mathematical formulas in a formal language and proving them within a logical calculus. Its main applications are formalizing mathematics and verifying properties of hardware, software, programming languages, and protocols. Isabelle/HOL provides a higher-order logic environment for large applications, with tools for reasoning, simplification, linear arithmetic, algebraic decision procedures, and access to external first-order provers through Sledgehammer. Proofs can be written in Isar, a structured language intended to be understandable to people and computers. Isabelle/HOL can generate SML, OCaml, Haskell, and Scala code from executable specifications. Isabelle/jEdit is the default interface, providing ongoing proof checking and real-time feedback; the Isabelle2025-2 release also includes Isabelle/VSCode with panels for documentation, symbols, and Sledgehammer. The distribution includes a library of verified mathematics, supplemented by the Archive of Formal Proofs. Isabelle runs on Linux, macOS, Windows, and self-hosted deployments. Its main code base is subject to BSD-style regulations. Windows lacks developer signatures and certificates and is rejected by Microsoft by default at first launch; macOS requires users to allow the unsigned application to open.
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.