What is an explicit example of a monad without a monad transformer? [duplicate]

Answer 1

This isn't an answer, but it's way too big for a comment. We can write

{-# LANGUAGE GeneralizedNewtypeDeriving
  , DeriveFunctor #-}

import Control.Monad.Free

-- All the IO primops you could ever need
data IOF a = PutStrLn String a
           | GetLine (String -> a)
           deriving Functor

newtype MyIO a = MyIO {unMyIO :: Free IOF a}
  deriving (Functor, Applicative, Monad)

But we can actually make a monad transformer out of this:

import Control.Monad.Trans.Free

newtype IOT m a = IOT {unIOT :: FreeT IOF m a}
  deriving (Functor, Applicative, Monad, MonadTrans)

So I don't really think even IO is excluded, although the isomorphism in that case is not "internal".