A Calculus for Schemas in Z

The popularity and flexibility of the Z notation can largely be attributed to its notion of schemas. We describe these schemas and illustrate their various common uses in Z. We also present a collection of logical laws for manipulating these schemas. These laws are capable of supporting reasoning about the Z schema calculus in its full generality. This is demonstrated by presenting some theorems about the removability of schemas from Z specifications, together with outline proofs. We survey briefly models against which this logical system may be proven sound, and other related logics for Z.