Fair termination of binary sessions

Abstract

A binary session is a private communication channel that connects two processes, each adhering to a protocol description called session type . In this work, we study the first type system that ensures the fair termination of binary sessions. A session fairly terminates if all of the infinite executions admitted by its protocol are deemed unrealistic because they violate certain fairness assumptions . Fair termination entails the eventual completion of all pending input/output actions, including those that depend on the completion of an unbounded number of other actions in possibly different sessions. This form of lock freedom allows us to address a large family of natural communication patterns that fall outside the scope of existing type systems. Our type system is also the first to adopt fair subtyping , a liveness-preserving refinement of the standard subtyping relation for session types that so far has only been studied theoretically. Fair subtyping is surprisingly subtle not only to characterize concisely but also to use appropriately, to the point that the type system must carefully account for all usages of fair subtyping to avoid compromising its liveness-preserving properties.

An Infinitary Proof Theory of Linear Logic Ensuring Fair Termination in the Linear $π$-Calculus

“…As a consequence, the forwarder in Example 24 is ill typed according to those typing disciplines because it applies subtyping (in an implicit way, whenever it sends a tag) an unbounded number of times. At the same time, a "compulsive" variant of the player in Example 25 that keeps playing until it wins is well typed in previous type systems [10,8] but ill typed in the present one. This difference stems, at least in part, from the fact that the previous type systems support processes defined using general recursion, whereas πLIN's type system relies on the duality between recursion and corecursion.…”

“…Fair subtyping [32,34] is a refinement of the standard subtyping relation for session types [19] that preserves fair termination and that plays a key role in our previous type system ensuring fair termination for binary sessions [10]. Given the rich literature exploring the connections between linear logic and session types, πLIN and its type system might provide the right framework for investigating the logical foundations of fair subtyping.…”

“…As a consequence, it is not necessary to reduce cuts guarded by prefixes or to push cuts deep into the derivation tree to enable key reductions in πLIN processes. Some previous works [10,8] have studied type systems ensuring the fair termination of binary and multiparty sessions. Although the enforced property is the same and the communication models of these works are closely related to the one we consider here, the used techniques are quite different and the families of well-typed processes induced by the two type systems are not comparable.…”

“…One aspect that is shared among all of these works, including the present one, is the use of a rank annotation or function that estimates how far a process is from termination. In previous works for session-based communications [10,8], ranks account for the number of sessions that processes create and the number of times they use subtyping before they terminate. Since ranks are required to be finite, this means that deterministic processes can only create a finite number of sessions and can only use subtyping a finite number of times.…”

“…In previous work [10] we have proposed a type system ensuring the fair termination of binary sessions. The present work achieves the same objective using a more basic process calculus and exploiting its strong logical connection with µMALL ∞ .…”