Formal Specification and Development of Control System Input / Output

Abstract

This paper presents a formal specification in the Z notation for computations that calculate control system state variables from input / output device register contents (and vice-versa). The specification is motivated by a particular medical device but is quite generic and should be widely applicable. The specification is parameterised so that an implementation can be adapted to different control systems by providing tables of configuration data, rather than changing executable code. Specified behaviours include detection of errors (where clients invoke operations with invalid parameters) and faults (where input / output devices report invalid data). The specification is not merely descriptive, but is also used in the formal development (or “refinement”) of a detailed design. From an initial specification which naturally expresses the requirements, but is abstract and non-constructive, we derive a functionally equivalent specification (also in Z), which suggests a straightforward and efficient implementation in an imperative programming language. Formal justification is provided for each step in the derivation. Theorems are stated that formalise claims such as “All inputs are handled properly.” Proving the theorems checks for errors in the derivation, and provides confidence that the formal specification expresses the intended requirements.