A refinement-based approach to large scale reflection for algebra

National audienceLarge scale reflection tactics are often implemented with ad-hoc data-structures and in a way which is specific to the problematic. This makes it hard to add improvements and to implement variations without writing an extensive theory of the specific data-structures involved. We suggest to replace the core of such tactics with procedures that are proven correct using CoqEAL refinement framework, and to build a modular methodology around it. This refinement framework addresses the problem of duplication by promoting the use of one extensive proof-oriented library together with one or several more efficient implementations, with a reduced amount of proofs, but destined to computation and proven correct with regard to the proof-oriented library. We show on the example of the ring tactic of Coq that this gain in flexibility opens the door to different improvements. This is a presentation to trigger discussion about ideas for a prototype based on the existing but improved CoqEAL refinement framework, described in [5] and [3]