Reasoning About Static and Dynamic Properties in Alloy: A Purely Relational Approach

FRIAS, MARCELO FABIAN; LOPEZ POMBO, CARLOS GUSTAVO; BAUM, GABRIEL; AGUIRRE, NAZARENO; MAIBAUM, THOMAS STEPHEN EDWARD

ACM TRANSACTIONS ON SOFTWARE ENGINEERING AND METHODOLOGY

Association for Computing Machinery

Año: 2005 vol. 14 p. 478 - 526

1049-331X

We study a number of restrictions associated with the first-order relational specification language Alloy. The main shortcomings we address are: \begin{itemize} \item the lack of a complete calculus for deduction in Alloy's underlying formalism, the so called relational logic, \item the inappropriateness of the Alloy language for describing (and analysing) properties regarding execution traces. \end{itemize} 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 characterisation of executions. We propose to overcome the first problem by translating the relational logic to the equational calculus of the \emph{fork algebras}. Fork algebras provide a (purely relational) formalism close to Alloy, that possesses a complete equational deductive calculus. Regarding the second problem, we propose to extend Alloy by adding \emph{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 to state properties of execution traces at an appropriate level of abstraction. Since automatic analysis is one of Alloy's main features, and this paper aims to provide a deductive calculus for Alloy, we show that: \begin{itemize} \item the extension hereby proposed does not sacrifice the possibility of using SAT solving techniques for automated analysis, \item the obtained complete calculus for the relational logic is straightforwardly extended to a complete calculus for the extension of Alloy. \end{itemize}