Why does Maybe include Just?

Question

Thanks to some excellent answers here, I generally understand (clearly in a limited way) the purpose of Haskell\'s Maybe and that its definition is

Answer 1

Maybe a is designed so to have one more value than the type a. In type theory, sometimes it is written as 1 + a (up to iso), which makes that fact even more evident.

As an experiment, consider the type Maybe (Maybe Bool). Here we have 1 + 1 + 2 values, namely:

Nothing
Just Nothing
Just (Just False)
Just (Just True)

If we were allowed to define

data Maybe a = Nothing | a

we would lose the distinction between the cases Just Nothing and Nothing, since there is no longer Just to make them apart. Indeed, Maybe (Maybe a) would collapse into Maybe a. This would be an inconvenient special case.