Machinechecked

Machinechecked, or machine-checked (sometimes written as machinechecked), refers to proofs, specifications, or verifications whose correctness has been verified by a computer using a formal proof system. In a machine-checked setting, mathematics or software correctness is formalized in a precise logic, and a proof assistant or automated verifier checks each inference against the kernel rules, producing a machine-verified certificate of correctness. This contrasts with traditional, paper-based proofs where verification rests on human review and trust in omitted details.

Machine-checked proofs are central to formal verification, formalized mathematics, and high-assurance software and hardware. Common tools include Coq, Lean, Isabelle/HOL, HOL Light, and other dependent type theory or higher-order logic frameworks. The process typically involves encoding statements into a formal language, constructing a proof with tactics or terms, and then relying on the proof kernel to accept only valid derivations, thereby producing an independently checkable artifact.

Notable milestones include projects that have achieved substantial machine-checked verification of complex mathematical results. The Flyspeck project completed a machine-checked verification of Thomas Hales's proof of the Kepler conjecture. The CompCert project provides a fully machine-checked C compiler, ensuring correctness up to its formal specifications. Other large formalizations include substantial work on the Feit–Thompson theorem and various areas of abstract algebra and analysis within proof assistants.

Machine-checked proofs increase confidence for large, intricate arguments where manual checking is error-prone and enable higher assurance in software and hardware systems. They also pose challenges, including the substantial formalization effort required, reliance on the soundness of proof assistants and their kernels, and the need to maintain and extend formalizations as tools evolve. As methods mature, machine-checked verification is increasingly integrated into mathematical practice and software development.