Lean vs PVS

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.

PVS is a mechanized environment for formal specification and verification, intended for work such as mathematical formalization and hardware or algorithm verification. Its language is based on typed higher-order logic and supports predicate subtypes, dependent types, and parameterized theories. The system combines predefined theories, a type checker, interactive theorem prover, symbolic model checker, utilities, libraries, documentation, and examples. Proof support includes induction, rewriting, simplification with decision procedures, abstraction, and symbolic model checking; command-line tools can re-prove theories and libraries in batch mode. PVS also integrates the Yices SMT solver, supports random testing during proofs, and includes PVSio for evaluation and animation. GNU or X Emacs provides the integrated interface, with Tcl/Tk displays for proof trees and theory hierarchies. It runs on Linux, macOS, and Windows and is self-hosted. Noncommercial use is listed at free. Sources are under GPL, but the Allegro runtime has a separate click-through license, and commercial users need a current PVS license or must contact SRI about licensing.