Monad van Laarhoven lenses can maintain invariants on the content.

MonadLens.hs

{-# LANGUAGE RankNTypes #-}

import Control.Monad.Trans.Writer
import Data.Functor.Identity

type MonadLens a b = forall m. Monad m => (b -> m b) -> a -> m a

get :: MonadLens a b -> a -> [b]
get l = execWriter . l (\b -> do tell [b]; return b)

modify :: MonadLens a b -> (b -> b) -> a -> a
modify l f = runIdentity . l (Identity . f)

set :: MonadLens a b -> b -> a -> a
set l = modify l . const


ordlist :: Ord a => MonadLens [a] a
ordlist _ [] = return []
ordlist f (x:xs) = do
  y <- f x
  ys <- ordlist f xs
  return $ insert y ys

insert :: Ord a => a -> [a] -> [a]
insert x [] = [x]
insert x (y:ys) = if x <= y then x:y:ys else y:(insert x ys)