Abstract

Invariants allow a rigorous treatment of types as sets in the refinement calculus, a method for developing imperative programs. The interaction of procedures and invariants is explored, resulting in a practical formalisation of existing programming practice. 1 Introduction The notion of local invariants [9] was introduced to give rigorous treatment to types in the refinement calculus [7, 6, 8, 10]. Typing is a special kind of invariant. For example, in the scope of the declaration n : N, which introduces a new local variable n of type N (the natural numbers), the invariant is n 2 N, and all commands preserve it. The exploration [9] of the interaction between invariants and statements of a simple language---Dijkstra's language [2] with extensions---considered only language constructs including assignment, iteration, selection and recursion. We extend that work by examining a more complex language structure: the procedure. Although this paper deals only with parameterless procedures, th...

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