Haha you're putting me on the spot here, I guess I haven't really thought too deeply about the specifics!

Maybe flatMap would return true only if all chained booleans are true?

Bimap would allow you to provide functions for what to do in true and false case?

Fold would allow you to turn true or false into a single type?

I'm sure someone more experienced in FP can weigh in with something more correct! :p

I rather like that, `if condition` is a 0/1 iteration with no input. flatMap can return empty, what should map return when run on false, None?

I'd probably think of Bool as being isomorphic to Maybe (), which would mean your map implementation looks a bit like:

    map :: Bool -> (() -> b) -> Maybe b
    map True f = Just (f ())
    map False _ = Nothing

Or, in Haskell because you've got laziness you could go with:

    map :: Bool -> b -> Maybe b

Which already exists as a combination of Control.Monad.guard and Data.Functor.(<$).

    map tf b = b <$ guard tf