Deriving via StateT s IO, (IO `Compose` State s) and (State s `Compose` IO)

state.hs

-- https://stackoverflow.com/questions/49587122/type-variable-location-in-transformers

{-# Language DerivingVia #-}

import Control.Applicative
import Control.Monad.State
import Data.Functor.Compose
import Data.Functor.Identity

-- >> :instances StateT _ IO
-- instance Alternative (StateT _ IO)
-- instance Applicative (StateT _ IO)
-- instance Monad (StateT _ IO)
-- instance MonadPlus (StateT _ IO)
-- instance MonadFix (StateT _ IO)
-- instance MonadFail (StateT _ IO)
-- instance MonadIO (StateT _ IO)
-- instance Functor (StateT _ IO)
newtype One s a = One (s -> IO (a, s))
 deriving (Functor, Applicative, Alternative, Monad, MonadPlus, MonadFix, MonadFail, MonadIO)
 via StateT s IO

-- >> :instances IO `Compose` State _
-- instance Functor (Compose IO (State _ Identity))
-- instance Alternative (Compose IO (State _))
-- instance Applicative (Compose IO (State _))
newtype Two s a = Two (IO (s -> (a, s)))
 deriving (Functor, Applicative, Alternative)
 via IO `Compose` State s

-- >> :instances State _ `Compose` IO
-- instance Applicative (Compose (State _) IO)
-- instance Functor (Compose (State _) IO)
newtype Three s a = Three (s -> (IO a, s))
 deriving (Functor, Applicative)
 via State s `Compose` IO