Property Transformations For Translations

When translating a system description from one speciication language to another, it is, in many cases, inevitable that the underlying models of the original and the translated speciication will be diierent. The notion of property transformation can be used to deene the relation between the properties of the original and the translated model. In an earlier paper, deenitions of 'faithful' translations were given, along with motivation and examples. Here, a fuller theory of faithful property transformations is developed, including a calculus for combining translations and property transformations to obtain more complicated relations. Property transformations are required to be independent of the source model, and this is shown to be a necessary restriction so that the transformation reeects the quality of the model translation. Suucient conditions for proving the non-existence of property transformations are given. Generic translations are considered, derived directly from compilers that translate among formal methods model description languages. Property transformations for these translations are proven faithful for CTL*. The notion of an 'eeective' source language is deened in terms of the logic that can be used to express properties in a tool associated with the target of the translation. This notion is then used to show that the most general transformation is not always the best. Finally, compositions of model translation stages and, respectively, property transformations are considered. We prove that a composed property transformation is appropriate for sequentially composed model translations that each have faithful property transformations. Even when the translation of the model mixes translations of two previously analyzed stages non-sequentially, we deene conditions when the simple composition of the property transformations is still faithful for the result, and prove the conditions for an example.