Foundations of Modular SOS

Abstract

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.

Pragmatics of Modular SOS

“…Simple functors called basic label transformers can be used for adding new components to labels [13,14]. Surprisingly, it appears that this straightforward use of categories of labels had not previously been exploited in work on transition systems.…”

“…3. A previous paper on MSOS [13] gives a more formal presentation, focussing on points of theoretical interest.…”

“…operate (times, N1, N2) = N1 * N2 (13) operate (equals, N1, N2) = true when N1 = N2 else false (14) operate (greater , N1, N2) = true when N1 > N2 else false (15) …”

“…As the name suggests, Modular SOS (MSOS) [13,14] is a variant of SOS that ensures a high degree of modularity: the rules specifying the MSOS of individual language constructs can be given definitively, once and for all, since their formulation is completely independent of the presence or absence of other constructs in the described language. When extending a pure functional language with concurrency primitives and/or references, the MSOS rules for the functional constructs don't need even the slightest reformulation [17].…”

“…The original, rather abstract notation used for accessing and setting components of labels in MSOS rules [13,14] has been made more user-friendly, to increase perspicuity. Experimentally, derivation of computations according to MSOS rules is being simulated using Prolog, so that students can trace how the rules shown in examples actually work, and check whether their own rules for further language constructs provide the intended semantics.…”