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Section: New Software and Platforms

The Coquelicot library for real analysis

Participants : Sylvie Boldo [contact] , Catherine Lelay, Guillaume Melquiond.

Criteria for Software Self-Assessment: A-3, SO-4, SM-2, EM-3, SDL-4, OC-4.

The Coquelicot library is designed with three principles in mind. The first is the user-friendliness, achieved by implementing methods of automation, but also by avoiding dependent types in order to ease the stating and readability of theorems. This latter part was achieved by defining total function for basic operators, such as limits or integrals. The second principle is the comprehensiveness of the library. By experimenting on several applications, we ensured that the available theorems are enough to cover most cases. We also wanted to be able to extend our library towards more generic settings, such as complex analysis or Euclidean spaces. The third principle is for the Coquelicot library to be a conservative extension of the Coq standard library, so that it can be easily combined with existing developments based on the standard library. Moreover, we achieved this compatibility without adding any additional axiom.

The result is the Coquelicot library available at http://coquelicot.saclay.inria.fr . Latest version is 2.0.1 released in March 2014. It contains about 1,700 theorems and 37,000 lines of Coq.