prover

A prover is a person or a system that establishes the truth of a proposition by providing a proof. In mathematics and formal logic, a proof is a finite sequence of statements each justified by axioms or previously proven results, culminating in the target proposition. A prover may be a human mathematician or a computer program.

In computer science, a prover is typically a formal system that verifies proofs or attempts to construct them within a formal logic. Automated theorem provers (ATPs) try to establish the validity of a given statement with little or no human guidance, using inference rules and heuristics. Interactive theorem provers or proof assistants, such as Coq, Isabelle, Lean, and HOL, require user input to develop formal proofs, producing a machine-checkable proof object.

Common techniques include resolution, term rewriting, sequent calculi, and satisfiability modulo theories. Proof assistants often provide a rich language for defining mathematical structures and a system of tactics to guide proof development, while ATPs emphasize automation and may output a proof certificate or a refutation.

Applications include formal verification of software and hardware, safety-critical systems, cryptographic proofs, and the formalization of mathematics. They also serve as educational tools and research infrastructure for verifying assertions beyond manual reach.

Limitations include computational complexity, incompleteness in certain logical systems, and ensuring trustworthiness of automated proofs. Ongoing work aims to improve automation, expressiveness, and integration with human-guided proof development.