Isabelle vs PVS

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.

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.