A Logic for the Schema Calculus

Abstract

In this paper we introduce and investigate a logic for the schema calculus of Z. The schema calculus is arguably the reason for Z’s popularity but so far no true calculus (a sound system of rules for reasoning about schema expressions) has been given. Presentations to date have either failed to provide a calculus (e.g. the draft standard [3]) or have fallen back on informal descriptions at a syntactic level (most text books e.g. [7]). Alongside the calculus, we introduce a derived equational logic; this enables us to formalise properly the informal notions of schema expression equality to be found in the literature.