> type family F a b :: * -> *   -- F's arity is 2,
>                              -- although its overall kind is * -> * -> * -> *

I believe what you're missing is that with the definition F a b :: *
-> *, F needs three arguments (of kind *) in order to become kind *.
If F a b :: * -> * as stated, then F a :: * -> * -> * and F :: * -> *
-> * -> *, just like reported.

Cheers,

/Niklas
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