Reasoning About Partial Functions in the Formal Development of Programs

Partial functions and operators are used extensively in the formal development of programs and thus development methods have to clarify how to reason about them. There are a number of approaches which cover up the fact that “First Order Predicate Calculus” does not handle undefined logical values. There is also at least one specific “Logic of Partial Functions” (LPF) which tackles the issue at its root by using a weaker logic. Recently, we have come to realise that LPF fits a particular way of developing programs. This paper explains why LPF is a suitable logic for “posit and prove” development and explores some problems that other approaches present.