A trusted kernel forms the final acceptance boundary of a proof assistant. More complex tools may parse code, search tactics and generate candidate proofs, but the kernel applies a much smaller set of rules to decide whether the resulting proof term is valid.
Keeping the kernel small reduces the amount of software that must be trusted for the logical guarantee. A defect in an untrusted proof generator should produce a rejected proof, while a defect in the kernel could undermine every accepted theorem.
Acronyms and aliases
proof-checking kernel variant
Related terms
Frequently asked questions
Why should a proof kernel be small?
A small kernel is easier to inspect, test and reason about, reducing the trusted computing base responsible for accepting every proof.
Does the trusted kernel search for proofs?
Usually no. Tactics and external tools search for a proof, while the kernel checks the completed proof term against the logical rules.
