Lean

Lean is a programming language and proof assistant for people who need to formalize mathematics or verify software. It is strongest for mathematicians, theorem provers and developers prepared to work with proof tooling; its formal methods focus is a poor fit for ordinary coding without verification needs.

Overview

Lean brings functional programming and theorem proving into one environment, allowing users to write code and formalize mathematical claims. Its minimal trusted kernel checks proofs, supporting correctness arguments in mathematics, software verification and hardware verification. That makes it a considered choice when correctness needs a formal basis, rather than a substitute for a general-purpose language when conventional development is enough.

Created by Leonardo de Moura in 2013, Lean is open source under Apache 2.0. The Lean FRO became a nonprofit under Convergent Research in July 2023.

Key features

Mathlib, a community-driven library of more than a million lines, covers algebra, analysis, topology, probability and computer science. That breadth gives formalization work a substantial foundation, especially in mathematics, though its benefit depends on the subject area and willingness to work in Lean.

The Grind tool automates complex pattern matching, case analysis and systems of linear inequalities, which can reduce repetitive proof work. Metaprogramming lets users add domain-specific notation and proof automation, making Lean adaptable for specialized work but placing more responsibility on users to build what they need.

Projects are initialized and managed with Lake, bundled with Lean. The recommended VS Code setup and Lean 4 extension provide syntax highlighting and code completion. Neovim with lean.nvim is also well-supported, while VSCodium and Cursor support is unofficial. These editor options offer flexibility, but the recommended path is clearest for users comfortable with VS Code.

Lean4Web runs Lean code in a browser, providing a way to work without a local installation. Learning materials include textbooks, tutorials, interactive games, core documentation and an API reference. The Lean Community Zulip is the central place for questions and collaboration, and Lean FRO hosts weekly technical office hours.

Lean is used in a security context: AWS uses it to formally verify Cedar, an authorization policy language, proving security properties and validating them against production code through differential testing. This is a concrete example of verification work, not a promise that Lean automatically secures arbitrary software.

Pricing

Lean 4 costs nothing. It is open-source software under Apache 2.0, with no paid plans stated and no free trial. The free plan is the product itself, rather than a capped tier, making it suitable for individual learning, research and formalization without a subscription decision.

Its price removes a financial barrier, not the learning and proof-work investment. There are no paid plans to choose for additional capabilities.

Platforms

Lean supports Linux, macOS, Windows and web use. Linux, Apple Silicon macOS and x86-64 Windows are Tier 1; x86-64 macOS and Emscripten WebAssembly are Tier 2. The browser option is useful for trying Lean code, while users choosing a local setup should note the distinction between Tier 1 and Tier 2 support.

Who it's for

Lean is a strong fit for mathematicians formalizing results, theorem provers, and programmers building or checking code where formal verification matters. Its learning page separates core resources for programmers, theorem provers and mathematicians, reflecting that each group approaches the language differently. Developers seeking a conventional coding environment without proof obligations should look elsewhere.

Pros and cons

• Pro: The trusted kernel checks proofs, giving formal correctness work a clear foundation.
• Pro: Mathlib’s breadth offers substantial reusable formalized mathematics across several disciplines.
• Pro: Open-source access at no cost avoids plan caps and subscription costs.
• Con: Formalization and proof tooling make Lean specialized; users who do not need proofs may find its core strengths beside the point.
• Con: Some macOS and browser-target support is Tier 2, so platform support is not uniform.
• Con: VSCodium and Cursor support is unofficial, making them less assured choices than the recommended VS Code setup.

Alternatives

Choose Rocq if you want a free interactive theorem prover and dependently typed programming language with broader listed platform coverage, including extensions.

Z3 is a free alternative if you need an MIT-licensed solver, with Android, API and self-hosted options among its listed platforms. Boogie is another free choice for users who can work with its .NET and supported SMT-solver requirements.

cvc5 suits readers seeking a free open-source solver; optional GPL-licensed dependencies affect the license of the combined work. HOL4 is a free choice under the Modified (3-clause) BSD licence.

PVS offers a free noncommercial plan, while commercial use has custom pricing; its Allegro runtime requires accepting a click-through license. Why3 is a free option under the GNU Lesser General Public License version 2.1 with a special linking exception. Alloy Analyzer is a free, open-source project distributed as a self-contained executable.

See Formal Verification Tools for more options.

Verdict

Choose Lean if you are a mathematician, theorem prover or developer who wants machine-checked proofs, a trusted kernel and a substantial mathematical library without a license fee. Its combination of formalization and general coding is compelling for verification-led work; if you mainly need a conventional programming language or a different kind of solver, a more focused alternative may suit you better.