Session types, types for structuring communication between endpoints in distributed systems, are recently being integrated into mainstream programming languages. In practice, a very important notion for dealing with such types is that of subtyping, since it allows for typing larger classes of system, where a program has not precisely the expected behavior but a similar one. Unfortunately, recent work has shown that subtyping for session types in an asynchronous setting is undecidable. To cope with this negative result, the only approaches we are aware of either restrict the syntax of session types or limit communication (by considering forms of bounded asynchrony). Both approaches are too restrictive in practice, hence we proceed differently by presenting an algorithm for checking subtyping which is sound, but not complete (in some cases it terminates without returning a decisive verdict). The algorithm is based on a tree representation of the coinductive definition of asynchronous subtyping; this tree could be infinite, and the algorithm checks for the presence of finite witnesses of infinite successful subtrees. Furthermore, we provide a tool that implements our algorithm and we apply it to many examples that cannot be managed with the previous approaches.
Conclusions and future work We have proposed a sound algorithm for checking asynchronous session subtyping, showing that it is still possible to decide whether two types are related for many nontrivial examples. Our algorithm is based on a (potentially infinite) tree representation of the coinductive definition of asynchronous subtyping; it checks for the presence of finite witnesses of infinite successful subtrees. We have provided an implementation and applied it to examples that cannot be recognised by previous approaches. Although the (worst-case) complexity of our algorithm is rather high (the termination condition expects to encounter a set of states already encountered, of which there may be exponentially many), our implementation shows that it actually terminates under a second for machines of size comparable to typical communication protocols used in real programs, e.g., Go programs feature between three and four communication primitives per channel and whose branching construct feature two branches, on average @cite_7 .
@cite_7
2610085676 2754865860 2023127104 2786270130
Asynchronous session subtyping has been studied extensively ini?ź[9, 10, 28---31] and applied ini?ź[23, 32, 33, 35]. An open question was whether this subtyping relation is decidable. This paper settles the question in the negative. To prove this result, we first introduce a new sub-class of two-party communicating finite-state machines CFSMs, called asynchronous duplex ADs, which we show to be Turing complete. Secondly, we give a compatibility relation over CFSMs, which is sound and complete wrt. safety for ADs, and is equivalent to the asynchronous subtyping. Then we show that the halting problem reduces to checking whether two CFSMs are in the relation. In addition, we show the compatibility relation to be decidable for three sub-classes of ADs. 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 largest 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. Both the synchronous and the asynchronous calculus are first considered with lin ear channels only, and then they are extended with session initialisations and c ommunications of expressions (including shared channels). 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. Abstract Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become popular in mainstream programming languages in which asynchronous communication is the norm rather than the exception, it is crucial to detect significant decidable subtyping relations. Previous work considered extremely restrictive fragments in which limitations were imposed to the size of communication buffer (at most 1) or to the possibility to express multiple choices (disallowing them completely in one of the compared types). In this work, for the first time, we show decidability of a fragment that does not impose any limitation on communication buffers and allows both the compared types to include multiple choices for either input or output, thus yielding a fragment which is more significant from an applicability viewpoint. In general, we study the boundary between decidability and undecidability by considering several fragments of subtyping. Notably, we show that subtyping remains undecidable even if restricted to not using output covariance and input contravariance.