Specifying reusable components using Z: realistic sets and dictionaries

We use the Z specification language to specify the designs of two reusable components and their interfaces. The components are based on set:3 and dictionaries from Smalltalk, each of which can provide surprises to users. We prove a significant property of desired behavior of the specifications under the precondition expected by the implementations. Specification and proof played an important role in our understanding of the components.