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diff --git a/plug/src/Montis/StackSet.hs b/plug/src/Montis/StackSet.hs
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+module Montis.StackSet where
+
+import Control.Monad (void)
+import Data.Monoid (First(..))
+import Control.Monad.Identity
+import Control.Monad.Writer (MonadWriter (tell), execWriter)
+import Data.Maybe (isJust, mapMaybe)
+import Data.Maybe (isJust)
+
+-- | The root datastructure for holding the state of the windows.
+data StackSet s sd t l a = StackSet
+  { -- | The currently selected screen.
+    current :: Screen s sd t l a,
+    -- | Remaining visible screens.
+    visible :: [Screen s sd t l a],
+    -- | Workspaces that exist, but are not on a screen.
+    hidden :: [Workspace t l a]
+  }
+  deriving (Read, Show, Eq, Ord, Functor)
+
+class TraverseWorkspace f where
+  traverseWorkspaces ::
+    (Applicative m) => (Workspace t l a -> m (Workspace t' l' a')) -> f t l a -> m (f t' l' a')
+
+traverseWorkspaces_ :: (TraverseWorkspace f, Monad m) => (Workspace t l a -> m ()) -> f t l a -> m ()
+traverseWorkspaces_ f = void . traverseWorkspaces (\w -> f w >> pure w)
+
+foldMapWorkspaces ::
+  (Monoid m, TraverseWorkspace f) => (Workspace t l a -> m) -> f t l a -> m
+foldMapWorkspaces fn = execWriter . traverseWorkspaces_ (tell . fn)
+
+mapWorkspaces ::
+  (TraverseWorkspace f) =>
+  (Workspace t l a -> Workspace t' l' a') ->
+  f t l a ->
+  f t' l' a'
+mapWorkspaces fn = runIdentity . traverseWorkspaces (pure . fn)
+
+instance TraverseWorkspace Workspace where
+  traverseWorkspaces f = f
+
+instance TraverseWorkspace (Screen s sd) where
+  traverseWorkspaces f scr = (\w' -> scr {workspace = w'}) <$> f (workspace scr)
+
+instance TraverseWorkspace (StackSet s sd) where
+  traverseWorkspaces f (StackSet cur vis hid) =
+    StackSet
+      <$> traverseWorkspaces f cur
+      <*> traverse (traverseWorkspaces f) vis
+      <*> traverse (traverseWorkspaces f) hid
+
+instance Traversable Stack where
+  traverse f (Stack u d) =
+    Stack <$> traverse f u <*> traverse f d
+
+instance (TraverseWorkspace f) => Foldable (f t l) where
+  foldMap fn =
+    execWriter
+      . traverseWorkspaces_ (\(Workspace _ _ s) -> tell (foldMap (fn . windowInSeat) s))
+
+instance (Functor (f t l), TraverseWorkspace f) => Traversable (f t l) where
+  sequenceA =
+    traverseWorkspaces $
+      \(Workspace t l sf) -> Workspace t l <$> traverse sequenceA sf
+
+class HasFocus f where
+  focused :: f a -> Maybe a
+
+data Rectangle = Rectangle Int Int Int Int
+  deriving (Read, Show, Eq, Ord)
+
+instance HasFocus (StackSet s sd t l) where
+  focused (StackSet c _ _) = focused c
+
+data Screen s sd t l a = Screen
+  { screenDetail :: sd,
+    screenId :: s,
+    workspace :: Workspace t l a
+  }
+  deriving (Read, Show, Eq, Ord, Functor)
+
+instance HasFocus (Screen s sd t l) where
+  focused (Screen _ _ w) = focused w
+
+-- | Defines where a window should appear.
+data WindowSeat a = Floating Rectangle a | Tiled a
+  deriving (Read, Show, Eq, Ord, Functor, Foldable)
+
+windowInSeat :: WindowSeat a -> a
+windowInSeat (Floating _ a) = a
+windowInSeat (Tiled a) = a
+
+instance Traversable WindowSeat where
+  sequenceA (Floating r fa) = Floating r <$> fa
+  sequenceA (Tiled fa) = Tiled <$> fa
+
+instance HasFocus WindowSeat where
+  focused (Floating _ a) = Just a
+  focused (Tiled a) = Just a
+
+data Workspace t l a = Workspace
+  { tag :: t,
+    layout :: l,
+    stack :: Stack (WindowSeat a)
+  }
+  deriving (Read, Show, Eq, Ord, Functor)
+
+instance HasFocus (Workspace t l) where
+  focused (Workspace _ _ s) = windowInSeat <$> focused s
+
+data Stack a = Stack
+  { -- | The elements above the focused one.
+    up :: ![a],
+    -- | The elements below the focused one including the focused one itself.
+    down :: ![a]
+  }
+  deriving (Read, Show, Eq, Ord, Functor, Foldable)
+
+instance HasFocus Stack where
+  focused (Stack _ (a : _)) = Just a
+  focused _ = Nothing
+
+-- | Change the tag in a structure.
+mapTag :: (TraverseWorkspace f) => (t -> t') -> f t l a -> f t' l a
+mapTag fn = mapWorkspaces (\w -> w {tag = fn (tag w)})
+
+-- | Change the layout in a structure.
+mapLayout :: (TraverseWorkspace f) => (l -> l') -> f t l a -> f t l' a
+mapLayout fn = mapWorkspaces (\w -> w {layout = fn (layout w)})
+
+-- | Return all the tags in a structure.
+tags :: (TraverseWorkspace f) => f t l a -> [t]
+tags = foldMapWorkspaces ((: []) . tag)
+
+-- | Insert a new window into the StackSet. The optional rectangle indicates if
+-- the window should be floating or tiled.
+--
+-- The window is inserted just above the the currently focused window and is
+-- given focus.
+insert :: a -> Maybe Rectangle -> StackSet s sd t l a -> StackSet s sd t l a
+insert win rect =
+  runIdentity
+    . onCurrentStack
+      ( \(Stack u d) ->
+          return $
+            (\w -> Stack u (w : d)) $
+              maybe (Tiled win) (`Floating` win) rect
+      )
+
+-- | Find the tag associated with a window.
+findTag :: (TraverseWorkspace f, Eq a) => a -> f t l a -> Maybe t
+findTag a =
+  getFirst
+    . foldMapWorkspaces
+      ( \ws ->
+          foldMap
+            ( \a' ->
+                First $ if a' == a then Just (tag ws) else Nothing
+            )
+            ws
+      )
+
+-- | Return true if the window exist in a structure
+elem :: (TraverseWorkspace f, Eq a) => a -> f t l a -> Bool
+elem a = isJust . findTag a
+
+-- | Convenience function for inserting a window in stack set tiled.
+insertTiled :: a -> StackSet s sd t l a -> StackSet s sd t l a
+insertTiled win = insert win Nothing
+
+integrate :: Stack a -> [a]
+integrate (Stack u d) = u ++ d
+
+differentiate :: [a] -> Stack a
+differentiate = Stack []
+
+applyStack ::
+  (Monad m) =>
+  (Stack (WindowSeat a) -> m (Stack (WindowSeat a))) ->
+  Workspace t l a ->
+  m (Workspace t l a)
+applyStack fn (Workspace t l s) = Workspace t l <$> fn s
+
+-- | Apply a function to the currently focused stack.
+onCurrentStack ::
+  (Monad m) =>
+  (Stack (WindowSeat a) -> m (Stack (WindowSeat a))) ->
+  StackSet s sd t l a ->
+  m (StackSet s sd t l a)
+onCurrentStack fn (StackSet cur vis hid) =
+  StackSet <$> cur' cur <*> pure vis <*> pure hid
+  where
+    cur' (Screen s sd ws) = Screen s sd <$> ws' ws
+    ws' (Workspace t l s) = Workspace t l <$> fn s
+
+catMaybes :: StackSet s sd t l (Maybe a) -> StackSet s sd t l a
+catMaybes (StackSet cur hidden visible) =
+  StackSet (catMaybesS cur) (map catMaybesS hidden) (map catMaybesW visible)
+  where
+    catMaybesS (Screen a b ws) = Screen a b $ catMaybesW ws
+    catMaybesW (Workspace a b st) = Workspace a b $ catMaybesSt st
+    catMaybesSt (Stack up down) =
+      Stack (mapMaybe sequenceA up) (mapMaybe sequenceA down)
+
+filter :: (a -> Bool) -> StackSet s sd t l a -> StackSet s sd t l a
+filter ffn =
+  Montis.StackSet.catMaybes . fmap (\a -> if ffn a then Just a else Nothing)
+
+delete :: (Eq a) => a -> StackSet s sd t l a -> StackSet s sd t l a
+delete win = Montis.StackSet.filter (/=win)