A proof assistant provides a formal language, libraries and interactive tools for constructing mathematical or software proofs. Users define objects and theorems, then provide proof steps that the system reduces to a form its trusted checker can validate.
Proof assistants can verify programs, protocols and mathematics with high assurance. They require precise specifications and specialized knowledge, although automation and AI can help propose lemmas, choose tactics and fill routine proof steps.
ELI5
A proof assistant is software that helps people write mathematical proofs in a precise formal language and checks every logical step. It acts like a very strict reviewer that accepts a proof only when it follows the rules of the chosen logical system.
For example, a programmer can formally state that an algorithm never produces a negative result and build a proof inside the assistant. AI may suggest steps, but the assistant's small trusted checker verifies the final proof independently.
Is a proof assistant the same as an automated theorem prover?
Not exactly. A proof assistant supports interactive construction and checking, while an automated theorem prover attempts to find proofs with less direct human guidance.
What are examples of proof assistants?
Lean, Coq, Isabelle and Agda are widely used systems with different logical foundations, languages, libraries and automation approaches.
