Enumerated types and type extensions for MiniZinc

Discrete optimisation problems often reason about finite sets of objects. While the underlying solvers will represent these objects as integer values, most modelling languages include enumerated types that allow the objects to be expressed as a set of names. Data attached to an object is made accessible through given arrays or functions from object to data. Enumerated types improve models by making them more self documenting, and by allowing type checking to point out modelling errors that may otherwise be hard to track down. But a frequent modelling pattern requires us to add new elements to a finite set of objects to represent extreme or default behaviour, or to combine sets of objects to reason about them jointly. Currently this requires us to map the extended object sets into integers, thus losing the benefits of using enumerated types. In this paper we introduce enumerated type extension, a restricted form of discriminated union types, to extend enumerated types without losing type safety, and default expressions to succinctly capture cases where we want to access data of extended types. The new language features allow for more concise and easily interpretable models that still support strong type checking and compilation to efficient solver-level models.