Alternatives to Lean

{"intro": "Lean combines functional programming with interactive theorem proving, covering general coding, formalized mathematics, and software or hardware verification. Its minimal trusted kernel checks proofs, while Grind automates selected pattern matching, case analysis, and linear-inequality work. Mathlib supplies a community mathematical library, Lake manages projects, and VS Code, Neovim, or Lean4Web provide ways to work. Lean is free, open source, and available on Linux, macOS, Windows, and the web, with deductive verification and Lean 4 as its input language.\n\nReaders may switch when they need a specialized verifier, a different proof language, or solver-focused automation. Compare whether you need program extraction, SMT or model-checking support, external prover connections, or a particular editor and deployment style. Check platform fit and setup requirements too: some alternatives require separate compilers, runtimes, solvers, or external provers. Each option below is free, but its scope and workflow differ from Lean’s combination of a programming language, proof assistant, package manager, and mathematical library.", "rows": [{"ref": "sw:pvs", "name": "PVS", "best_for": "Formal specifications with interactive proving and model checking", "pricing": "Free plan", "key_difference": "PVS combines a specification language, interactive prover, symbolic model checker, SMT support, and random testing rather than Lean’s programming-centered environment.", "choose_when": "Choose PVS when integrated specification, model-checking, and Emacs-based proof work matter more than Lean’s general coding flexibility."}, {"ref": "sw:rocq", "name": "Rocq", "best_for": "Certified program extraction from formal proofs", "pricing": "Free plan", "key_difference": "Rocq uses Gallina and can extract certified programs to OCaml, Haskell, or Scheme, capabilities Lean’s entry does not describe.", "choose_when": "Choose Rocq when extracting verified programs to those languages or connecting external theorem provers is central."}, {"ref": "sw:cvc5", "name": "cvc5", "best_for": "Automatic SMT solving and function synthesis", "pricing": "Free; open source", "key_difference": "cvc5 focuses on automatic satisfiability and validity checking plus SyGuS function synthesis, rather than Lean’s interactive programming-and-proof workflow.", "choose_when": "Choose cvc5 when SMT-LIB or SyGuS inputs, solver APIs, or stand-alone library use fit your verification task."}, {"ref": "sw:why3", "name": "Why3", "best_for": "Deductive verification through multiple external provers", "pricing": "Free; open source", "key_difference": "Why3 writes specifications and programs in WhyML, sends conditions to separately installed provers, and extracts OCaml programs.", "choose_when": "Choose Why3 when verifying C, Java, Rust, or Ada through external provers and browser-based TryWhy3 is useful."}, {"ref": "sw:z3", "name": "Z3", "best_for": "SMT solving across many programming-language APIs", "pricing": "Free plan", "key_difference": "Z3 centers on SMTLIB2 solving with bindings for numerous languages, while Lean centers on writing and checking proofs in Lean 4.", "choose_when": "Choose Z3 when solver integration through your preferred API, SMTLIB2 input, or browser access outweighs Lean’s theorem-proving language."}, {"ref": "sw:boogie", "name": "Boogie", "best_for": "Building custom program verifiers atop SMT", "pricing": "Free; open source", "key_difference": "Boogie is a modeling layer that generates verification conditions for SMT solvers, requiring .NET and a supported solver.", "choose_when": "Choose Boogie when you are constructing a verifier pipeline or modeling concurrent systems with Civl."}, {"ref": "sw:hol4", "name": "HOL4", "best_for": "Higher-order logic with interactive proof tooling", "pricing": "Free plan", "key_difference": "HOL4 targets higher-order logic with Standard ML tooling, external-program oracles, and Emacs or Vim integrations rather than Lean’s Lean 4 ecosystem.", "choose_when": "Choose HOL4 when higher-order logic, deduction-plus-execution, and Standard ML proof-tool development match your work."}]}