Section: New Results
Confluence
Confluence of parameterized rewrite systems
Participant : Jean-Pierre Jouannaud.
Together with Benjamin Monate (CEA), we are interested in proofs of properties of infinite families of specifications, like the family of dihedral groups of order n for some natural number n , or the family of a multicore harware with 2n cores for some natural number n . So far, we have shown the decidability of confluence when these families can be presented by parameterised words over a finite alphabet of parameterized size, as in the case of the example of dihedral groups.
Confluence of higher-order rewrite systems
Participant : Jean-Pierre Jouannaud.
Together with Femke van Raamsdonk from the Free University of Amsterdam, we have started a program to investigate decidable sufficient conditions for the confluence of higher-order rewrite systems when lefthand sides are patterns “a la Miller” which can be fired by using higher-order pattern matching [39] . The difficulty here lies in the fact that it is difficult to abstract from a particular syntax for lambda-terms, such as de Bruijn numbers, localy nameless variables, or freshness conditions. We have not been able yet to prove our results in an axiomatic setting capturing all these various syntax for binders.
Certified confluence
Participants : Jean-Pierre Jouannaud, Huiying Luo.
Decreasing diagrams are a technique due to van Oostrom for proving confluence results for abstract relations which captures both styles of proofs based respectively on strong and local confluence. Last year, Van Oostrom and Jouannaud developped a refinement of this technique in order to handle relations defined by rewrite systems [15] . We continue this work in order to get rid of some linearity restrictions, and plan to develop a Coq library in order to search for and certify confluence proofs.
