Reasoning about static and dynamic properties in alloy

We study a number of restrictions associated with the first-order relational specification language Alloy. The main shortcomings we address are:---the lack of a complete calculus for deduction in Alloy's underlying formalism, the so called relational logic,---the inappropriateness of the Alloy language for describing (and analyzing) properties regarding execution traces.The first of these points was not regarded as an important issue during the genesis of Alloy, and therefore has not been taken into account in the design of the relational logic. The second point is a consequence of the static nature of Alloy specifications, and has been partly solved by the developers of Alloy; however, their proposed solution requires a complicated and unstructured characterization of executions.We propose to overcome the first problem by translating relational logic to the equational calculus of fork algebras. Fork algebras provide a purely relational formalism close to Alloy, which possesses a complete equational deductive calculus. Regarding the second problem, we propose to extend Alloy by adding actions. These actions, unlike Alloy functions, do modify the state. Much the same as programs in dynamic logic, actions can be sequentially composed and iterated, allowing them to state properties of execution traces at an appropriate level of abstraction.Since automatic analysis is one of Alloy's main features, and this article aims to provide a deductive calculus for Alloy, we show that:---the extension hereby proposed does not sacrifice the possibility of using SAT solving techniques for automated analysis,---the complete calculus for the relational logic is straightforwardly extended to a complete calculus for the extension of Alloy.