Promoting functions to type families in Haskell
Richard A. Eisenberg, Jan Stolarek · 2014
Haskell, as implemented in the Glasgow Haskell Compiler (GHC), is enriched with many extensions that support type-level programming, such as promoted datatypes, kind polymorphism, and type families. Yet, the expressiveness of the type-level language remains limited. It is missing many features present at the term level, including case expressions, anonymous functions, partially-applied functions, and let expressions. In this paper, we present an algorithm - with a proof of correctness - to encode these term-level constructs at the type level. Our approach is automated and capable of promoting a wide array of functions to type families. We also highlight and discuss those term-level features that are not promotable. In so doing, we offer a critique on GHC's existing type system, showing what it is already capable of and where it may want improvement.