Modern functional languages rely on sophisticated type inference algorithms. However, there often exists a gap between the theoretical presentation of these algorithms and their practical implementations. Specifically, implementations employ techniques not explicitly included in formal specifications, causing undesirable consequences. First, this leads to confusion and unforeseen challenges for developers adhering to the formal specification. Moreover, theoretical guarantees established for a formal presentation may not directly translate to the implementation. This paper focuses on formalizing one such technique, known as levels , which is widely used in practice but whose theoretical treatment remains largely understudied. We present the first comprehensive formalization of levels and demonstrate their applicability to type inference implementations.

@article{paperbot3083,
  title = {Practical Type Inference with Levels},
  author = {Andong Fan and Han Xu and Ningning Xie},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {PLDI},
  year = {2025},
  doi = {10.1145/3729338}
}