Extending Hindley-Milner Type Inference with Coercive Structural Subtyping

Dmitriy Traytel, Stefan Berghofer, Tobias Nipkow


We investigate how to add coercive structural subtyping to a type system for simply-typed lambda calculus with Hindley-Milner polymorphism. Coercions allow to convert between different types, and their automatic insertion can greatly increase readability of terms. We present a type inference algorithm that, given a term without type information, computes a type assignment and determines at which positions in the term coercions have to be inserted to make it type-correct according to the standard Hindley-Milner system (without any subtypes). The algorithm is sound and, if the subtype relation on base types is a disjoint union of lattices, also complete. Also, a sound but incomplete extension of the algorithm to type classes is given. The algorithm has been implemented in the proof assistant Isabelle.

The final publication is available at link.springer.com.

short version long version APLAS 2011 slides