Interpretation and Instantiation of Theories for Reasoning about Formal Speciications Interpretation and Instantiation of Theories for Reasoning about Formal Speciications

In this paper an outline is given of an approach to formally reasoning about importation , parameterisation and instantiation of speciications written in a modular extension of the Z language (called Sum). Interpretation and instantiation of theories in rst order logic are well understood. We illustrate how to use these results directly to provide a framework within which we can soundly and eeciently reason about modular speciications. A reasoning environment within the Ergo 4:1 theorem prover has been constructed that provides the theory management, construction and extension facilities needed to support such a reasoning process. Sum speciications are mapped to the appropriate Ergo structures by a straightforward translation process. A simple example in Sum is presented to demonstrate the use of these theory extension mechanisms. As far as the authors are aware, no other system ooers interpreted automated support for reasoning about parameterisation and instantiation of modular model-oriented speciications.