Basic Laws of Object Modeling

Semantics-preserving model transformations are usually proposed in an ad hoc way because it is difficult to prove that they are sound with respect to a formal semantics. So, simple mistakes lead to incorrect transformations that might, for example, introduce inconsistencies to a model. In order to avoid that, we propose a set of simple modeling laws (which can be seen as bi-directional transformations) that can be used to safely derive more complex semanticspreserving transformations, such as refactorings which are useful, for example, to introduce design patterns into a model. Our laws are specific for Alloy, a formal object-oriented modeling language, but they can be leveraged to other object modeling notations. We illustrate their applicability by formally refactoring Alloy models with subtypes in order to improve the analysis performed by the Alloy Analyzer tool.