Isabelle vs Rocq

Isabelle is a free proof assistant for expressing mathematical formulas in a formal language and proving them within a logical calculus. Its main applications are formalizing mathematics and verifying properties of hardware, software, programming languages, and protocols. Isabelle/HOL provides a higher-order logic environment for large applications, with tools for reasoning, simplification, linear arithmetic, algebraic decision procedures, and access to external first-order provers through Sledgehammer. Proofs can be written in Isar, a structured language intended to be understandable to people and computers. Isabelle/HOL can generate SML, OCaml, Haskell, and Scala code from executable specifications. Isabelle/jEdit is the default interface, providing ongoing proof checking and real-time feedback; the Isabelle2025-2 release also includes Isabelle/VSCode with panels for documentation, symbols, and Sledgehammer. The distribution includes a library of verified mathematics, supplemented by the Archive of Formal Proofs. Isabelle runs on Linux, macOS, Windows, and self-hosted deployments. Its main code base is subject to BSD-style regulations. Windows lacks developer signatures and certificates and is rejected by Microsoft by default at first launch; macOS requires users to allow the unsigned application to open.

Rocq is a free interactive theorem prover and proof assistant for building mathematical proofs, formal specifications and programs, including proofs that programs meet specifications. Its Gallina language supports specification and mathematical work and is based on the Polymorphic, Cumulative Calculus of Inductive Constructions. A relatively small certification kernel machine-checks proofs. Rocq also offers interactive proof methods, decision and semi-decision algorithms, and a tactic language for defining methods. Certified programs can be extracted to OCaml, Haskell or Scheme, and the system can connect with external computer algebra systems or theorem provers. The Rocq Platform bundles the core prover with libraries and plugins for development and teaching. Its scripts install Rocq and packages on macOS, Windows and many Linux distributions; precompiled installers are available for macOS and Windows, but not Linux. Editor options include the VsRocq Visual Studio Code extension, RocqIDE, Proof General and Coqtail. Rocq is written in OCaml and distributed under the GNU Lesser General Public Licence Version 2.1.