We present a Hoare logic for a call-by-value programming language equipped with recursive, higher-order functions, algebraic data types, and a polymorphic type system in the style of Hindley and Milner. It is the theoretical basis for a tool that extracts proof obligations out of programs annotated with logical assertions. These proof obligations, expressed in a typed, higher-order logic, are discharged using off-the-shelf automated or interactive theorem provers. Although the technical apparatus that we exploit is by now standard, its application to functional programming languages appears to be new, and (we claim) deserves attention. As a sample application, we check the partial correctness of a balanced binary search tree implementation.