We define a new, more semantic interpretation of gradual types and use it to ``gradualize'' two forms of polymorphism: subtyping polymorphism and implicit parametric polymorphism. In particular, we use the new interpretation to define three gradual type systems ---Hindley-Milner, with subtyping, and with union and intersection types--- in terms of two preorders, subtyping and materialization. We define these systems both declaratively ---by adding two subsumption-like rules--- which yields clearer, more intelligible, and streamlined definitions, and algorithmically by reusing existing techniques such as unification and tallying.

@article{paperbot619,
  title = {Gradual typing: a new perspective},
  author = {Giuseppe Castagna and Victor Lanvin and Tommaso Petrucciani and Jeremy G. Siek},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {3},
  number = {POPL},
  year = {2019},
  doi = {10.1145/3290329}
}