Restoring Confluence for Functional Dependencies

Haskell-style functional dependencies allow the programmer to influence the type inference process by automatically deriving type improvement rules from class and instance declarations. Previous work demands that the dependency must fully cover all type parameters of a type class to guarantee confluence. Confluence is an important property to ensure that type inference is well-behaved. We restore confluence for non-full functional dependencies by giving a novel encoding of functional dependencies in terms of type families as supported by the Glasgow Haskell Compiler. We compare our method against another alternative constraint-propagation encoding due to Claus Reinke. Our work provides new insights in the connection between functional dependencies and type families, and in the relative trade-offs of rewriting based or constraint-propagation based type inference approaches.