{-# LANGUAGE FlexibleInstances #-}

import Data.DList
import Control.Monad.Trans.Writer (Writer)
import Data.Functor.ProductIsomorphic

data PH a = PH

newtype WithPhT r a =
  WithPhT { runWithPhT :: Writer (DList Int) (r a)  }

instance ProductIsoFunctor (WithPhT PH) where
  _ |$| wx = WithPhT $ runWithPhT wx *> return PH

instance ProductIsoApplicative (WithPhT PH) where
  pureP _   = WithPhT $ return PH
  wx |*| wy = WithPhT $ runWithPhT wx *> runWithPhT wy *> return PH