In the ManageHook I can define what should happen to windows that have specific xprops etc. For example, I can call doShift or doFloat.

How can I do the same to the currently focused window with a key binding?

The section looks like this:

`additionalKeys` ( [  -- Key bindings --
    -- Minimize window
      ((myModMask .|. shiftMask, xK_m     ), withFocused minimizeWindow)

As you can see, I can call the minimizedWindow function (which takes a Window as parameter) on the current window when pressing a combination of keys, but doFloat etc. do not work like this.