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 <pre>TypeInType</pre>, 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.