  Multiparty session types (MP) are a type discipline for enforcing the
structured, deadlock-free communication of concurrent and message-passing
programs. Traditional MP have a limited form of choice in which alternative
communication possibilities are offered by a single participant and selected by
another. Mixed choice multiparty session types (MCMP) extend the choice
construct to include both selections and offers in the same choice. This paper
first proposes a general typing system for a mixed choice synchronous
multiparty session calculus, and prove type soundness, communication safety,
and deadlock-freedom.
  Next we compare expressiveness of nine subcalcli of MCMP-calculus by
examining their encodability (there exists a good encoding from one to another)
and separation (there exists no good encoding from one calculus to another). We
prove 8 new encodablity results and 20 new separation results. In summary, MCMP
is strictly more expressive than classical multiparty sessions (MP) and mixed
choice in mixed sessions. This contrasts earlier results where mixed sessions
do not add any expressiveness to non-mixed fundamental sessions, shedding a
light on expressiveness of multiparty mixed choice.
