Communicating and trusting proofs: Towards a broad spectrum proof certificate

Proofs, both formal and informal, are documents that circulate within societies of human and machine agents distributed across time and space in order to provide trust. Such trust might lead one mathematician to accept a certain statement as true or it might help convince a consumer of the quality and reliability of a safety-critical computer system. By exploiting recent results about focused proof systems, we develop an approach to proof certificates that is designed to provide a notation for proof that is (1) checkable by simple proof checkers, (2) flexible enough that most existing provers can directly produce such certificates, (3) directly related to proof formalisms used within the structural proof theory literature, and (4) permits a trade-off between proof checking and proof search. Proof certificates that satisfy such criteria should allow, in principle, any theorem prover to trust the output of any other theorem prover.