We study the need for complex circular assume-guarantee (AG) rules in formalisms that already provide the simple precongruence rule. We first investigate the question for two popular formalisms: Labeled Transition Systems (LTSs) with weak simulation and Interface Automata (IA) with alternating simulation. We observe that, in LTSs, complex circular AG rules cannot always be avoided, but, in the IA world, the simple precongruence rule is all we need. Based on these findings, we introduce modal IA with cut states, a novel formalism that not only generalizes IA and LTSs but also allows for compositional reasoning without complex AG rules.

Interface theories (ITs) enable us to analyse the compatibility interfaces and refine them while preserving their compatibility. However, most ITs are for finite state interfaces, whereas computing systems are often parametrised involving components, the number of which cannot be fixed. We present, to our knowledge, the first IT that allows us to specify a parametric number of interfaces. Moreover, we provide a fully algorithmic procedure, implemented in a tool, for checking the compatibility of and refinement between parametrised interfaces. Finally, we show that the restrictions of the technique are necessary; removing any of them renders the refinement checking problem undecidable.