Asynchronous Subtyping by Trace Relaxation

Session subtyping answers the question of whether a program in a communicating system can be safely substituted for another, when their communication behaviours are described by session types. Asynchronous session subtyping is undecidable, hence the interest in devising sound, although incomplete, subtyping algorithms. State-of-the-art algorithms are formulated in terms of a data-structure called input trees. We show how input trees can be replaced by sets of traces, which opens up opportunities for applying techniques abstract interpretation techniques to the problem of asynchronous session subtyping. Sets of traces can be relaxed (enlarged) whilst still allowing subtyping to be observed, and one can choose relaxations that can be finitely represented, even when the input trees are arbitrarily large. We instantiate this strategy using regular expressions and show that it allows subtyping to be mechanically proven for communication patterns that were previously out of reach.