HOL Light vs Lean
HOL Light
hol-light.github.io
Lean
lean-lang.orgSide by side
| Figure | HOL Light | Lean |
|---|---|---|
| Price from | — | Free |
| Free plan | — | Yes |
| Free trial | — | — |
| Open source | — | — |
| Web | Yes | Yes |
| Windows | Yes | Yes |
| macOS | Yes | Yes |
| Linux | Yes | Yes |
| Self-hosted | Yes | — |
| Plans published | 0 | 1 |
| Spec score · Formal Verification Tools | 7.5 (#21) | 8.6 (#2) |
| Editor integration | The official site links to a Visual Studio Code extension for HOL Light. | The recommended setup uses VS Code and the official Lean 4 extension, which provides syntax highlighting and code completion. |
| Extensibility | HOL Light is fully programmable, allowing users to extend it with new theorems and inference rules without compromising soundness. | Lean's metaprogramming capabilities let users add domain-specific notation and proof automation. |
| Proof checking | The project describes HOL Light as an interactive theorem prover and proof checker. | Lean's minimal trusted kernel is described as guaranteeing correctness in mathematical proof, software verification, and hardware verification. |
| Security and trust | When compiling with HOLLIGHT_USE_MODULE=1, the repository documentation says the trusted base expands to include the inline_loads.ml script. | The Lean FRO privacy policy says it collects communication information when users contact it and describes practices for transferring, retaining, and protecting personal information. |
Plans
In their own words
HOL Light
HOL Light has no write-up on Specifiction yet; its figures are above.
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.