Section: Scientific Foundations

Making the case for proof certificates

The team has been considering how it might be possible to define a universal format for proofs so that any existing theorem provers can have its proofs trusted by any other prover. This is a rather ambitious project and involves a great deal of work at the infrastructure level of computational logic. As a result, we have put significant energies into considering the high-level objectives and consequences of deploying such proof certificates.

Our current thinking on this point is roughly the following. Proofs, both formal and informal, are documents that are intended to circulate within societies of humans and machines distributed across time and space in order to provide trust. Such trust might lead a mathematician to accept a certain statement as true or it might help convince a consumer that a certain software system is secure. Using this general definition of proof, we have re-examined a range of perspectives about proofs and their roles within mathematics and computer science that often appears contradictory.

Given this view of proofs as both document and object, that need to be communicated and checked, we have attempted to define a particular approach to a broad spectrum proof certificate format that is intended as a universal language for communicating formal proofs among computational logic systems. We identify four desiderata for such proof certificates: they must be

  1. checkable by simple proof checkers,

  2. flexible enough that existing provers can conveniently produce such certificates from their internal evidence of proof,

  3. directly related to proof formalisms used within the structural proof theory literature, and

  4. permit certificates to elide some proof information with the expectation that a proof checker can reconstruct the missing information using bounded and structured proof search.

We consider various consequences of these desiderata, including how they can mix computation and deduction and what they mean for the establishment of marketplaces and libraries of proofs. More specifics can be found in Miller's papers [8] and [47] .