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  • The Inria's Research Teams produce an annual Activity Report presenting their activities and their results of the year. These reports include the team members, the scientific program, the software developed by the team and the new results of the year. The report also describes the grants, contracts and the activities of dissemination and teaching. Finally, the report gives the list of publications of the year.

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Section: New Results

Mathematical Components Analysis

Participants : Cyril Cohen, Damien Rouhling, Reynald Affeldt [AIST Japan] , Assia Mahboubi [Inria Gallinette] , Pierre-Yves Strub [Ecole Polytechnique] .

As a synthesis of the lessons learned in the usage of Mathematical Components and Coquelicot, we develop an extension of the Mathematical Components library to cover questions of analysis. This work includes a new tactic called near to handle reasoning steps around limits and filters and little-o notation (following Landau's style of asymptotic reasoning). This work is described in [6]. There also contains a new formalization of topoligical structures, Rolle's theorem, the intermediate value theorem, and Heine Borel's theorem. Ongoing work concentrates on a better design of the topological hierarchy and a simplification of the properties expected from real numbers (following a design by A. Mahboubi and P.-Y. Strub).

Some of this work also includes experiments performed with the Lean theorem prover (developed at Microsoft Research).