Implementing the Zc Logic in

Henson and Reeves have recently proposed a new kernel logic, Z C HR98b, HR98a] for the Z Spi89] speciication language. They have proved that their logic is sound and have shown how a complete schema calculus can be derived within the logic. An important next step is to investigate the practicality of the logic, to determine whether it could be used to reason about typical Z speciications in a practical fashion. Ongoing work is investigating how this logic can be implemented in the Isabelle and JAPE theorem provers. In this paper, we describe work we have been doing on implementing the logic in Ergo 5. Initially, we have chosen to implement the ZUM'98 version of the logic HR98b], which uses explicit Curry-style typing rules, rather than the more recent Church-style presentation HR98a], because the former is more suited to mechanization. Ergo 5 UW94, MNU97] is the latest version of a series of interactive proof tools that have been designed and implemented at the Software Veriication Research Centre (Brisbane, Australia) over the last ten years. It is implemented in Qu-Prolog SRP + 89, RH97] and is designed to be extensible, so that users can add new theories, tactics and user interfaces. It is a generic prover that can be instantiated by providing a collection of axiomatic and/or deenitional theories. Proofs are tree-structured and are built up in a backwards fashion by applying inference rules in a style reminiscent of natural deduction. The rst step in implementing the Z C logic within Ergo is to create a new Ergo theory, which we call zc.