Type inference with non-structural subtyping

Extending Hindley-Milner Type Inference with Coercive Structural Subtyping

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 whic...

Strong Normalization with Non-Structural Subtyping

We study a type system with a notion of subtyping that involves a largest type >, a smallest type ⊥, atomic coercions between base types, and the usual ordering of function types. We prove that any λ-term typable in this system is strongly normalizing; this solves an open problem of Thatte. We also prove that the fragment without ⊥ types strictly fewer terms. This demonstrates that ⊥ adds power...

Type Inference with Structural Subtyping: A Faithful Formalization of an Efficient Constraint Solver

We are interested in type inference in the presence of structural subtyping from a pragmatic perspective. This work combines theoretical and practical contributions: first, it provides a faithful description of an efficient algorithm for solving and simplifying constraints; whose correctness is formally proved. Besides, the framework has been implemented in Objective Caml, yielding a generic ty...

Extending Hindley-Milner Type Inference with Coercive Structural Subtyping (long version)

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 whic...

Type inference with structural subtyping: A faithful formalization of an efficient constraint solver