Functional dependencies are a popular extension to Haskell's type-class system because they provide fine-grained control over type inference, resolve ambiguities and even enable type-level computations. Unfortunately, several aspects of Haskell's functional dependencies are ill-understood. In particular, the GHC compiler does not properly enforce the functional dependency property, and rejects well-typed programs because it does not know how to elaborate them into its core language, System F-C. This paper presents a novel formalization of functional dependencies that addresses these issues: We explicitly capture the functional dependency property in the type system, in the form of explicit type equalities. We also provide a type inference algorithm and an accompanying elaboration strategy which allows all well-typed programs to be elaborated into System F-C.