Type Inference with Nonstructural Subtyping

Abstract

We present an O(n^3) time type inference algorithm for a type system with a largest type !, a smallest type ?, and the usual ordering between function types. The algorithm infers type annotations of minimal size, and it works equally well for recursive types. For the problem of typability, our algorithm is simpler than the one of Kozen, Palsberg, and Schwartzbach for type inference without ?. This may be surprising, especially because the system with ? is strictly more powerful.