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 . 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).