Generic programming of all kinds

Datatype-generic programming is a widely used technique to define functions that work regularly over a class of datatypes. Examples include deriving serialization of data, equality or even functoriality. The state-of-the-art of generic programming still lacks handling GADTs, multiple type variables, and some other features. This paper exploits modern GHC extensions, including TypeInType, to handle arbitrary number of type variables, constraints, and existentials. We also provide an Agda model of our construction that does not require Russel’s paradox, proving the construction is consistent