## Section: New Results

### Refining the FPC framework

Participants : Roberto Blanco, Zakaria Chihani, Quentin Heath, Dale Miller, Fabien Renaud.

We have continued to develop our approach to Foundational Proof Certificates (FPCs). This framework allows defining proof evidence in a general fashion. Proofs in both intuitionistic and classical logics are definable in this framework. We originally have written two different kernels for checking these results but more recently we have found that we can exploit an encoding due to Chaudhuri [43] that enables us to only implement the intuitionistic kernel and then simply encode the classical formulas so that they operator directly on the intuitionistic kernel. This encoding allows for a much more precise and simple means for encoding classical logic into intuitionistic logic than the more familiar double negation translations.

We have also started to develop the second phase of defining proof evidence that was proposed in the ProofCert proposal: the definition of proofs that require fixed points (induction / co-induction). We now have two different kernels being developed on top of the Bedwyr model checker that are checking (and in some cases, proving) theorems involving induction, reachability, and bisimulation.