MiniZinc with Functions

Functional relations are ubiquitous in combinatorial problems – the Global Constraint Catalog lists 120 functional constraints. This paper argues that the ability to express functional constraints with functional syntax leads to more elegant and readable models, and that it enables a better translation of the models to different underlying solving technologies such as CP, MIP, or SAT. Yet, most modelling languages only support built-in functions, such as arithmetic, Boolean, or array access operations. Custom, user-defined functions are either not catered for at all, or they have an ad-hoc implementation without a useful semantics in Boolean contexts and not exploiting potential optimisations. This paper develops a translation from MiniZinc with user-defined functions to FlatZinc. The translation respects the relational semantics of MiniZinc, correctly dealing with partial functions in arbitrary Boolean contexts. At the same time, it takes advantage of the full potential of common subexpression elimination.