[applicative]

It doesn't affect your objection to MaleKitten but not all types are occupied in Haskell. You are thinking of kind * By contrast,

    {-#LANGUAGE DataKinds#-}
    a :: 'Nothing
    a = a

and

    {-#LANGUAGE MagicHash#-}
    import GHC.Prim
    a :: Int#
    a = a

don't typecheck, though I cant say I understand the ins and outs of the latter.