In [6, p. 317] Curry described a formal system assigning types to terms of the type-free λ-calculus. In [11] Scott gave a natural semantics for this type assignment and asked whether a completeness result holds.Inspired by [4] and [5] we extend the syntax and semantics of the Curry types in such a way that filters in the resulting type structure form a domain in the sense of Scott [12]. We will show that it is possible to turn the domain of types into a λ-model, among other reasons because all λ-terms possess a type. This model gives the completeness result for the extended system. By a conservativity result the completeness for Curry's system follows.Independently Hindley [8], [9] has proved both completeness results using term models. His method of proof is in some sense dual to ours.For λ-calculus notation see [1].

Abstract.A multiparty session forms a unit of structured interactions among many participants which follow a prescribed scenario specified as a global type signature. This paper develops, besides a more traditional communication type system, a novel static interaction type system for global progress in dynamically interleaved multiparty sessions.

A multiparty session forms a unit of structured communication among many participants which follow communication sequences specified as a global type. When a process is engaged in two or more sessions simultaneously, different sessions can be interleaved and can interfere at runtime. Previous work on multiparty session types has ignored session interleaving, providing a limited progress property ensured only within a single session, by assuming non-interference among different sessions and by forbidding delegation. This paper develops, besides a more traditional, compositional communication type system, a novel static interaction type system for global progress in dynamically interleaved and interfered multiparty sessions. The interaction type system infers causalities of channels making sure that processes do not get stuck at intermediate stages of sessions also in presence of delegation.

No abstract

No abstract