Agda vs Isabelle

Agda has no write-up on Specifiction yet; its figures are above.

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.