  Choreographic Programming is a paradigm for developing
correct-by-construction concurrent programs, by writing high-level descriptions
of the desired communications and then synthesising process implementations
automatically. So far, choreographic programming has been explored in the
monadic setting: interaction terms express point-to-point communications of a
single value. However, real-world systems often rely on interactions of
polyadic nature, where multiple values are communicated among two or more
parties, like multicast, scatter-gather, and atomic exchanges. We introduce a
new model for choreographic programming equipped with a primitive for grouped
interactions that subsumes all the above scenarios. Intuitively, grouped
interactions can be thought of as being carried out as one single interaction.
In practice, they are implemented by processes that carry them out in a
concurrent fashion. After formalising the intuitive semantics of grouped
interactions, we prove that choreographic programs and their implementations
are correct and deadlock-free by construction.
