## Section: New Results

### Integration of the GeoCoq library to Logipedia

Participants : Pierre Boutry, Gaspard Ferey [Inria Saclay Ile de France, Deducteam project team] .

We have proofs of independence of the parallel postulate for several models of hyperbolic geometry (among which the PoincarĂ© disk model). An objective is to provide formal proofs that these models are actually isomorphic. An issue for this objective is the question of re-usability, because the formal proofs that we have so far exist in the realms of different theorem provers. The Logipedia effort is an attempt to make proofs from different proofs systems work together, by using a tool called Dedukti as a go-between. A particular point is to be able to translate proofs already done in Coq, namely the GeoCoq library, into proofs verifiable by Dedukti. This requires handling tactics based on internal computation (reflective tactics), that we used intensively in our Coq proof. However, handling reflective tactics is currently not well supported by Dedukti. This is our current point of attention.