We present a new method for GADT type inference that improves the precision of previous approaches. In particular, our approach accepts more type-correct programs than previous approaches when they do not employ type annotations. A side benefit of our approach is that can detect a wide range of runtime errors that are missed by previous approaches.

Our method is based on the idea to represent type refinements in pattern-matching branches by choice types, which facilitate a separation of the typing and reconciliation phases and thus support for case expressions. This idea is formalized in a type system, which is both sound and a conservative extension of the classical Hindley-Milner system. We present the results of an empirical evaluation that compares our algorithm with previous approaches.