On Sessions and Infinite Data

Abstract

We define a novel calculus that combines a call-by-name functional core with session-based communication primitives. We develop a typing discipline that guarantees both normalisation of expressions and progress of processes and that uncovers an unexpected interplay between evaluation and communication. CC Creative Commons2 SEVERI ET AL.Proof. By case analysis on the derivation.Proof. By induction on the structure of processes. We only discuss the case of rule [thread].The interesting observation is that we need to use the hypothesis dom(Γ 2 ) ∩ dom(∆) = ∅ to ensure that the name of the thread does not belong to its own body. We also use Lemma 4.4 to type the body of the thread itself. Lemma 5.13 (Evaluation Contexts for Processes). If Γ C[e] : • n (IO s), then Γ = Γ 1 + Γ 2 and Γ 1 , x : • n (IO t) C[x] : • n (IO s) and Γ 2 e : • n (IO t).Proof. By induction on the structure of evaluation contexts for processes. ON SESSIONS AND INFINITE DATA 21A useful consequence of the previous lemma is the following property of contexts filled by communication expressions.Lemma 5.14. If Γ , a p :Proof. We only consider the case Γ , a p : • n T C[send a p e] : • m (IO t). By Lemma 5.13 Γ = Γ 1 + Γ 2 and Γ 1 , x : • m (IO s) C[x] : • m (IO t) and Γ 2 , a p : • n T send a p e : • m (IO s). Since rule [→E] requires at least n bullets in front of the type of send we get n ≤ m.

Choreography Automata

“…The example (10) cannot be expressed in global graphs [35] either, again due to the intersecting loops. We note that the infinite unfolding of the c-automaton (10) is regular and therefore it fits in the session type system considered in [34]. However, this type system has not been conceived for choreographies (it is binary session type system) and does not allow non-determinism.…”