PVS vs Rocq

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.

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.