Lean is a formal proof assistant and functional programming language for creating machine-checkable mathematical proofs and verifying software.
Why it matters
overview
Lean is a formal proof assistant and functional programming language tool that enables mathematicians, researchers, and software engineers to create machine-checkable proofs and formally verify code. It includes mathematical libraries and supports automated reasoning, including AI-driven tools. Lean is open-source and is used for mathematical proof development, software verification, and research collaboration.
features
Lean combines proof development and functional programming in a system for machine-checkable mathematics and formal code verification.
use cases
Lean is intended for people working with formal proofs, software verification, and mathematical research.
how to use
Start with Lean’s official website and documentation, then use the VS Code extension to work with Lean code. The available materials identify an API documentation site but do not specify API setup steps.
pricing
Lean is listed as freemium and includes a free tier. No specific prices, paid tier names, or paid-tier inclusions are provided in the available product information.
Similar Tools
Lean is a formal proof assistant and functional programming language with mathematical libraries, metaprogramming, and tactic-driven automation. The alternatives listed differ in their proof systems, automation approaches, or emphasis.
The most mature and widely cited proof assistant in computer science, featuring extraction to OCaml and Haskell and decades of formal verification libraries.
Coq lacks Lean's cohesive Mathlib ecosystem and modern metaprogramming framework, but it has a much larger body of verified software engineering proofs like CompCert.
Relies on classic higher-order logic (HOL) rather than dependent type theory and integrates heavily with automated Sledgehammer solvers for high-speed tactic dispatch.
Isabelle's automated proof finding via Sledgehammer is often faster out-of-the-box than Lean's tactics, but HOL cannot express certain constructive or dependently typed constructions as naturally as Lean's type theory.
A dependently typed functional language designed from the ground up for writing proofs as programs via Curry-Howard with tight Emacs-driven interactive development.
Agda emphasizes pure type-directed programming and pattern matching over tactic-based automation, meaning you lose Lean's rich ecosystem of tactic-driven automation and massive centralized math library.
A proof-oriented programming language designed for program verification that discharges proof obligations directly to the Z3 SMT solver and extracts to C.
F* is built for verified low-level systems programming rather than pure mathematics, giving you automatic SMT proofs at the cost of Lean's broader mathematical community.
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