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Section: New Results

Formally certified computation of definite integrals

Assia Mahboubi and Thomas Sibut-Pinote, in collaboration with Guillaume Melquiond (Toccata), have developed a Coq library for the computation of intervals approximating the value of definite integrals for elementary mathematical functions. This library provides an automated tool which builds automatically a formal proof of the correctness of the output, that is: a formal proof that the interval contains the mathematical values and a formal proof of the integrability of the input function on the input interval. A description of this work was published in the proceeding of the ITP 2016 conference [13]. An extension to domains including singularities of the integrand is in progress.