Section: New Results

Interoperability

F. Thiré has finished to implement a translation of an arithmetic library from Matita to OpenTheory. This work can be decomposed in two steps: A first step goes from Matita to a new logic called STTforall while a second step goes from STTforall to OpenTheory. This translation will be described in two separate papers. The first paper that will be submitted to FSCD 2018 describe the logic STTforall and its translation to HOL while the second paper explains the translation from Matita to STTforall. STTforall is a very simple logic and so, it is easy to translate proofs from this logic to other proofs assistants. For example, a translation from STTforall to Coq has also been implemented by F. Thiré. Two new tools have been implemented to make these translations:

• Dkmeta is a tool that translates terms thanks to the rewrite engine of Dedukti

• Ediloh is a tool that translates terms from STTforall them in OpenTheory

F.Gilbert developed a first prototype for the extraction of proofs from the proof assistant PVS that can be verified externally. The system PVS is based on the dichotomy between a type-checker and a prover. This proof extraction mechanism is built by instrumenting the PVS prover, but does not contain any typing information from the type-checker at this stage. Proofs can be built for any PVS theory. However, some reasoning steps rely on unverified assumptions. For a restricted fragment of PVS, the proofs are exported to Dedukti, and the unverified assumptions are proved externally using the automated theorem prover MetiTarski. This work has been published and presented in [15].