applying layout modifiers to existentially quantified layouts

Experiment.hs

{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE RankNTypes #-}
import XMonad
import Data.Constraint

-- supplied: seems to be the pattern for layout modifier instances
typicalEntailment :: Read (l' a) :- Read (Mirror l' a)
typicalEntailment = Sub Dict

-- | this newtype captures the idea that `m l a` is 
-- a layout if `l a` is a layout. IE. Being a layout is
-- a shorter way to say that a given type has Read and LayoutClass
-- instances.
newtype RLS m a = RLS (forall l. l a -- ^ always ignored (not Proxy because we always have an (l a))
                                  -> (Read (l a), LayoutClass l a)
                                          :- (Read (m l a), LayoutClass (m l) a))

wrap :: forall m a. RLS m a
      -> (forall l. (LayoutClass l a, Read (l a)) => l a -> m l a)
      -> (Layout a -> Layout a)
wrap (RLS rS) m (Layout la) = case rS la of
    Sub Dict -> Layout (m la)

-- there seems to be no way to partially apply the wrap function
-- (since the RLS argument seems to be the same no matter what the layout modifier happens to be)
wrappedMirror :: Layout a -> Layout a
wrappedMirror x = wrap (RLS (\_ -> Sub Dict)) Mirror x