A sequential real-time refinement calculus

We present a comprehensive refinement calculus for the development of sequential, real-time programs from real-time specifications. A specification may include not only execution time limits, but also requirements on the behaviour of outputs over the duration of the execution of the program. The approach allows refinement steps that separate timing constraints and functional requirements. New rules are provided for handling timing constraints, but the refinement of components implementing functional requirements is essentially the same as in the standard refinement calculus. The product of the refinement process is a program in the target programming language extended with timing deadline directives. The extended language is a machine-independent, real-time programming language. To provide valid machine code for a particular model of machine, the machine code produced by a compiler must be analysed to guarantee that it meets the specified timing deadlines.