SAT-Based Arithmetic Support for Alloy

Formal specifications in Alloy are organized around user-defined data domains, associated with signatures, with almost no support for built-in datatypes. This minimality in the built-in datatypes provided by the language is one of its main features, as it contributes to the automated analyzability of models. One of the few built-in datatypes available in Alloy specifications are integers, whose SAT-based treatment allows only for small bit-widths. In many contexts, where relational datatypes dominate, the use of integers may be auxiliary, e.g., in the use of cardinality constraints and other features. However, as the applications of Alloy are increased, e.g., with the use of the language and its tool support as backend engine for different analysis tasks, the provision of efficient support for numerical datatypes becomes a need. In this work, we present our current preliminary approach to providing an efficient, scalable and user-friendly extension to Alloy, with arithmetic support for numerical datatypes. Our implementation allows for arithmetic with varying precisions, and is implemented via standard Alloy constructions, thus resorting to SAT solving for resolving arithmetic constraints in models.