  For many application-level distributed protocols and parallel algorithms, the
set of participants, the number of messages or the interaction structure are
only known at run-time. This paper proposes a dependent type theory for
multiparty sessions which can statically guarantee type-safe, deadlock-free
multiparty interactions among processes whose specifications are parameterised
by indices. We use the primitive recursion operator from G\"odel's System T to
express a wide range of communication patterns while keeping type checking
decidable. To type individual distributed processes, a parameterised global
type is projected onto a generic generator which represents a class of all
possible end-point types. We prove the termination of the type-checking
algorithm in the full system with both multiparty session types and recursive
types. We illustrate our type theory through non-trivial programming and
verification examples taken from parallel algorithms and Web services usecases.
