> ((a -> Void) -> Void) -> a

> However, this is exactly the type of Cont Void.

Defined where?

Not here: https://hackage.haskell.org/package/monads-tf-0.1.0.3/docs/C...

https://hackage.haskell.org/package/mtl-2.3.1/docs/Control-M...

The closest I find is

    cont :: ((a -> r) -> r) -> Cont r a

so cont (a -> Void) -> Void) :: Cont Void a

There is nothing "out of thin air", since `a` is the input, not the ouput, unless you just misread the type. But that can be said for any higher-order type, like

   map :: (a -> b) -> [a] -> [b]