Probabilistic Denotational Semantics for an Interrupt Modelling Language

Interrupts play an important role in real time and embedded systems. It is purposely designed to handle unexpected and emergent issues. However, the randomicity of interrupts brings some potential safety problems, i.e., too frequently interrupt handling would cause the interrupted program to miss its deadline. It is therefore difficult to precisely predict and formally reason about a program's behavior in the presence of interrupts. In this paper, we move one step forward by proposing a probabilistic denotational model for an interrupt modeling language that is capable of describing programs with nested interrupts, to characterise the formal semantics of such programs from a quantitative perspective under Hoare and He's UTP framework. On top of the denotational model, we also present a set of algebraic laws involving distinct features. Our model sets up a semantic foundation for the analysis and reasoning about programs with nested interrupts for embedded systems.