BSML is a pure functional library for the multi-paradigm language OCaml. BSML embodies the principles of the Bulk Synchronous Parallel (BSP) model, a model of scalable parallel computing. We propose a formalization of BSML primitives with WhyML, the specification language of Why3 and specify and prove the correctness of most of the BSML standard library. Finally, we develop and verify the correctness of a small BSML application.