Isabelle

Isabelle is a feminine given name, a variant of Isabel and Elizabeth, used in many cultures. In the field of computer science, Isabelle refers to a generic interactive theorem prover and proof assistant.

Isabelle is designed to support formal reasoning in a variety of logics within a single framework. It follows the LCF-style architecture, featuring a small, trusted kernel that checks all proofs and a rich set of tools built around it. The user-facing proof language Isar provides a readable, structured way to develop formal arguments, while the implementation relies on Standard ML.

The system supports multiple object logics, with Isabelle/HOL (higher-order logic) being the most widely used instance. Other available instantiations include Isabelle/ZF (set theory) and Isabelle/FOL (first-order logic). This flexibility allows users to formalize mathematics, model software and hardware systems, and verify properties within different logical settings.

Key features include Sledgehammer, which integrates automated theorem provers to discharge goals, and Nitpick, a counterexample finder for finite models. Quickcheck is available for generating test cases in certain contexts. Isabelle also maintains the Archive of Formal Proofs, a large library of formalized results contributed by researchers and practitioners.

Isabelle is cross-platform, running on Windows, macOS, and Linux, and it is supported by an international community of developers and users. It is commonly employed in academic research, formal verification projects, and advanced teaching to demonstrate rigorous formal reasoning and machine-checked proofs.