State monad done wrong

State.hs

{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}

module State where

import Control.Monad
import Control.Monad.Free.Church
import qualified Control.Monad.State.Class as MTL
import Data.Functor.Coyoneda
import Data.Kind

data State :: Type -> Type -> Type where
  Get :: State s s
  Put :: s -> State s ()

type StateF s = Coyoneda (State s)

type MonadState s m = MonadFree (StateF s) m

get :: MonadState s m => m s
get = liftF $ liftCoyoneda Get

put :: MonadState s m => s -> m ()
put = liftF . liftCoyoneda . Put

runState ::
     forall s m a. (MTL.MonadState s m)
  => (forall m0. MonadState s m0 =>
                   m0 a)
  -> m a
runState =
  iterM
    (join .
     lowerCoyoneda .
     hoistCoyoneda
       (\case
          Get -> MTL.get
          (Put s) -> MTL.put s))