A proof term represents a proof as structured data in the formal language of a proof assistant. Under the propositions-as-types interpretation used by many systems, the term has a type corresponding to the theorem it proves.
Tactics and artificial intelligence tools can help construct a proof term without requiring the user to write every low-level step. The final term remains the authoritative artifact because the trusted kernel can validate it independently of how it was generated.
Acronyms and aliases
formal proof object variant
Related terms
Frequently asked questions
How is a proof term different from a written proof explanation?
A proof term has precise formal meaning and can be checked mechanically, while a natural-language explanation may omit steps or rely on informal interpretation.
Can proof tactics generate proof terms?
Yes. Tactics transform proof goals and construct the underlying proof term that the kernel ultimately checks for validity.
