There have been a handful of papers about System FC, the internal language used within GHC (   , etc.). Each of these papers uses a different characterization of FC, with variations among the definitions and judgments. Unsurprisingly, each of these formalisms differs also from the actual implementation of FC within GHC. At ICFP, Simon PJ asked me to look at GHC’s implementation of System FC, and write it up using formal notation. The result of this work (developed using Ott) now lives in the GHC repo, in docs/core-spec. There are comments in various places reminding GHC contributors to update the formalization as they update the implementation.
Do you have a stake in this work? Are you planning on reasoning about GHC’s core language? Check out the formalism here. Any feedback is welcome!