Towards an Isabelle Theory for Distributed, Interactive, Real-Time Systems Volume 2

In many applications, the behavior of a component depends on the time when messages are received. To model these in embedded systems, capabilities to specify time are required. This includes the capability to react to the absence of input. This report presents an encoding of FOCUS in the theorem prover Isabelle. This implementation extends our previous formalization of untimed streams. Similar to the untimed version, concepts such as timed stream bundles, timed stream processing functions, and corresponding functions and theorems are presented. The principle idea is to conceptualize the observable flow of messages over a channel as a stream and the behavior of a component as a stream processing function. A component’s specification is then given by a set of stream processing functions, allowing for the modeling of underspecified behavior. Refinement and composition of components are natural operations in this theory and are compatible. This is a great advantage when modular reuse, evolutionary optimization, or incremental development are required to develop highly reliable systems that must be certifiable or even verifiable. The theories are evaluated by proving the properties of a time-sensitive case study.