Type family applications in Haskell must be fully saturated. This means that all type-level functions have to be first-order, leading to code that is both messy and longwinded. In this paper we detail an extension to GHC that removes this restriction. We augment Haskell’s existing type arrow, |->|, with an unmatchable arrow, | >|, that supports partial application of type families without compromising soundness. A soundness proof is provided. We show how the techniques described can lead to substantial code-size reduction (circa 80%) in the type-level logic of commonly-used type-level libraries whilst simultaneously improving code quality and readability.

@article{paperbot606,
  title = {Higher-order type-level programming in Haskell},
  author = {Csongor Kiss and Tony Field and Susan Eisenbach and Simon Peyton Jones},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {3},
  number = {ICFP},
  year = {2019},
  doi = {10.1145/3341706}
}