Foundations of Modular SOS

Abstract

A novel form of labelled transition system is proposed, where the labels are the arrows of a category, and adjacent labels in computations are required to be composable. Such transition systems provide the foundations for modular SOS descriptions of programming languages. Three fundamental ways of transforming label categories, analogous to monad transformers, are provided, and it is shown that their applications preserve computations in modular SOS. The approach is illustrated with fragments taken from a modular SOS for ML concurrency primitives.