Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers is well understood and present in many programming languages today, polymorphism over type qualifiers remains an area less well examined. We explore how such a polymorphic system could arise by constructing a calculus, System F-sub-Q, which combines the higher-rank bounded polymorphism of System F-sub with the theory of type qualifiers. We explore how the ideas used to construct System F-sub-Q can be reused in situations where type qualifiers naturally arise---in reference immutability, function colouring, and capture checking. Finally, we re-examine other qualifier systems in the literature in light of the observations presented while developing System F-sub-Q.

@article{paperbot2536,
  title = {Qualifying System F<sub>&lt;:</sub>: Some Terms and Conditions May Apply},
  author = {Edward Lee and Yaoyu Zhao and Ondřej Lhoták and James You and Kavin Satheeskumar and Jonathan Immanuel Brachthäuser},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {8},
  number = {OOPSLA1},
  year = {2024},
  doi = {10.1145/3649832}
}