A Type-Safe Embedding of Constraint Handling Rules into Haskell

Two of the most exciting developments in programming languages research over the last decade have been constraint programming on the one hand, and typeful functional programming on the other hand. Constraint programming (CP) is an emergent software technology for declarative description and effective solving of large combinatorial problems, especially in the areas of planning and scheduling. Based on a strong theoretical foundation, this technology is also attracting widespread commercial interests. One key reason for its popularity is that constraints allow end-users to directly formalize the dependencies of the physical worlds; and through sound mathematical abstractions we can have the computers to understand and solve these dependencies. Higher-level programming languages have come a long way. One of the most promising technologies is advanced functional languages with a rich set of versatile features, such as higher-order functions, type generics, and algebraic structures. These features allow high-level language to function as better modular glues for constructing larger and yet safer software, providing precision and reusability to programming. In this thesis, we discuss how a constraint-solving technology, called Constraint-Handling Rules (CHR), can be embedded as an extension of a mainstream functional programming language, known as Haskell, in a type-safe fashion. We present various techniques used in the embedding which produces an excellent tool equipped with power from both worlds.