proofassistants

Proof assistants, also known as interactive theorem provers, are software tools that help users develop and verify mathematical proofs. They allow users to write down formal specifications of mathematical objects and statements, and then interactively guide the system to construct proofs of these statements. The core idea is that the proof assistant checks each step of the proof for correctness, ensuring that the final proof is logically sound. This process can catch subtle errors that might be missed in traditional pen-and-paper proofs.

These systems typically employ a formal logic, such as higher-order logic or type theory, to represent mathematical statements and proofs. Users interact with the proof assistant through a specialized language, often called a proof language or tactic language. The assistant provides feedback on the state of the proof, guiding the user towards a complete and verified demonstration of the theorem. Proof assistants are used in various fields, including formal verification of software and hardware, foundational research in mathematics, and the development of complex logical systems.

Notable examples of proof assistants include Coq, Isabelle, Lean, and Agda. Each has its own underlying logic, syntax, and feature set, catering to different needs and communities. The development of proof assistants has been a significant area of research in computer science and logic, aiming to make formal methods more accessible and practical for a wider range of applications.