On the Preciseness of Subtyping in Session Types

Abstract

Subtyping in concurrency has been extensively studied since early 1990s as one of the most interesting issues in type theory. The correctness of subtyping relations has been usually provided as the soundness for type safety. The converse direction, the completeness, has been largely ignored in spite of its usefulness to define the greatest subtyping relation ensuring type safety. This paper formalises preciseness (i.e. both soundness and completeness) of subtyping for mobile processes and studies it for the synchronous and the asynchronous session calculi. We first prove that the well-known session subtyping, the branching-selection subtyping, is sound and complete for the synchronous calculus. Next we show that in the asynchronous calculus, this subtyping is incomplete for type-safety: that is, there exist session types T and S such that T can safely be considered as a subtype of S, but T S is not derivable by the subtyping. We then propose an asynchronous subtyping system which is sound and complete for the asynchronous calculus. The method gives a general guidance to design rigorous channel-based subtypings respecting desired safety properties.

Subtyping Supports Safe Session Substitution

“…Demangeon and Honda actually define subtyping for input, which in their presentation is unified with branch, to be covariant in the message type, and conversely subtyping for output, which they unify with select, is contravariant. It seems that this is just a typographical error, as other papers in the Honda et al style, for example by Chen et al (2014), use the expected variance in the message type. In some definitions of subtyping, for example by Mostrous and Yoshida (2015), the variance depends on whether data or channels are being communicated; the technical details need further investigation to clarify this point.…”

Hybrid Session Verification Through Endpoint API Generation

“…async essentially allows the input transition in the local EFSM to be decoupled in the user program from the actual message input action in safe situations. (2) Postponing input actions supports natural communication patterns that exploit asynchronous messaging for safe permutations of I/O actions at an endpoint [25,3]. In the example, the input future allows C to safely permute the actions: send Ehlo first, then receive 220.…”

“…The former includes value-switched session branching and the abstraction of nominal state channel types as I/O interfaces. Examples of the latter are the generation of state-specific input futures to support aspects of non-blocking inputs [16], safe permutations of I/O actions [25,3] and affine inputs [33,24]; and the generation of Java subtype hierarchies for I/O interfaces to reflect session subtyping [11]. We have tested our framework by using our API generation to implement compliant clients and servers for real-world protocols such as HTTP and SMTP.…”

On Duality Relations for Session Types

“…Subtyping: Recent work by Chen et al [6] has considered preciseness of subtyping, meaning the combination of soundness and completeness. A subtyping relation is complete if it is the largest safe subtyping relation for a given type system.…”