Marcus,

Mostly, I bring up the issue of defining the quantifiers
via functors for the academic challenge of it, but also
thank you for looking up the singletons library.
Getting under the hood of that library will likely have some
beautiful code and likely a couple of balls-of-mud. Generally,
I am not sure the Hindley-Milner type system really even
supports such constructions, and so I would guess that a number
of pragmas in GHC need to be set to relax the type system.

Jon
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