Section: New Results

Floating-Point and Numerical Programs

• S. Boldo, F. Clément, J.-C. Filliâtre, M. Mayero, G. Melquiond, and P. Weis, finished the formal proof of a numerical analysis program: the second order centered finite difference scheme for the one-dimensional acoustic wave [15] .

• S. Boldo developed a formal proof of an algorithm for computing the area of a triangle, an improvement of its error bound and new investigations in case of underflow [25] .

• S. Boldo, J.-H. Jourdan, X. Leroy, and G. Melquiond, extended CompCert to get the first formally verified compiler that provably preserves the semantics of floating-point programs [26] .

• S. Boldo and G. Melquiond wrote a chapter of the book [38] that describes the current state of the Mathematics/Computer science research in France.

• C. Lelay worked on formalizing power series for the Coq proof assistant [35] .

• Most 18-year old French students pass an exam called Baccalaureate which ends the high school and is required for attending the university. The idea was to try our Coq library Coquelicot on the 2013 mathematics test of the scientific Baccalaureate. C. Lelay went to the “Parc de Vilgénis” high school in Massy, France and took the 2013 test at the same time as the students, but had to formally prove the answers. There was therefore no possible cheating: the Coq library was already developed and it was tested as is during the four hours of the test. This experiment shows that Coquelicot is able to cope with basic real analysis: it has the necessary definitions and lemmas, and its usability and efficiency have been demonstrated in a test with a limited time [45] (see also https://www.lri.fr/~lelay/ ).

• D. Ishii and G. Melquiond applied methods of deductive program verification to ensure the safety of hybrid automata [34] .

• É. Martin-Dorel, G. Hanrot, M. Mayero, L. Théry, showed how to generate and formally check certificates in the Coq proof assistant to solve myriads of instances of the Integer Small Value Problem (ISValP). This problem is directly related to solving the Table Maker's Dilemma with hardest-to-round computations [50] . A new version of the formalized library has been released (http://tamadi.gforge.inria.fr/CoqHensel/ ).

• É. Martin-Dorel, G. Melquiond, and J.-M. Muller, studied issues related to double rounding in the implementation of error-free transformations [16] .