Functional real-time programming: the language Ruth and its semantics

Real-time systems are amongst the most safety critical systems involving computer software and the incorrect functioning of this software can cause great damage, up to and including the loss of life. If seems sensible therefore to write real-time software in a way that gives us the best chance of correctly implementing specifications. Because of the high level of functional programming languages, their semantic simplicity and their amenability to formal reasoning and correctness preserving transformation it thus seems natural to use a functional language for this task. This thesis explores the problems of applying functional programming languages to real-time by defining the real-time functional programming language Ruth. The first part of the thesis concerns the identification of the particular problems associated with programming real-time systems. These can broadly be stated as a requirement that a real-time language must be able to express facts about time, a feature we have called time expressibility. The next stage is to provide time expressibility within a purely functional framework. This is accomplished by the use of timestamps on inputs and outputs and by providing a real-time clock as an input to Ruth programs. The final major part of the work is the construction of a formal definition of the semantics of Ruth to serve as a basis for formal reasoning and transformation. The framework within which the formal semantics of a real-time language are defined requires time expressibility in the same way as the real-time language itself. This is accomplished within the framework of domain theory by the use of specialised domains for timestamped objects, called herring-bone domains. These domains could be used as the basis for the definition of the semantics of any real-time language