[Haskell-beginners] understanding MTL

[Dennis Raddle]

I had an interaction on #haskell today which left me utterly confused but
desiring to understand what happened. I was talking about a program in
which I was using stacks of monad transformers, inspiration taken from the
paper "Monad Transformers: Step by Step". So for example I wanted to
combine state and error handling in a Monadic type called "Er".

data ErState = ErState StdGen

newtype Er a = Er { runEr :: ErrorT String (State ErState) a }
    deriving(Monad, MonadError String, MonadState ErState)

Note that ErState holds a random generator. I had the idea to make a
typeclass of monadic types that hold random generators because I'll be
using them in other types all over my application. Something like

class Monad m => RandomMonad m where
  getGen :: m StdGen
  putGen :: StdGen -> m ()

Then I can write functions like this:

myRandoms :: (Random a, RandomMonad m) => m [a]
myRandoms = do
  g <- getGen
  let (g1, g2) = split g
      values = randoms g1
  putGen g2
  return values

So then mm_freak on #haskell noticed that I had written a function with a
signature like

process :: Int -> Er Int

He said, no no no functions should be agnostic with regard to data
structure. It should look something like
process :: (RandomMonad m, MonadError m, MonadState m) => Int -> m Int

He then said I don't want to put StateT and ErrorT in the same newtype
declaration, so it would be something like
newtype Er m a = Er { runEr :: StateT ErState m a }

On this point I'm confused. I don't know how to get from a line like the
above to eventually making a type that combines error handling and state.
Furthermore I need to define instances for things like MonadError. He got
me started with the line

instance MonadError e m => MonadError e (Er m) where
... define throwError and catchError which I have no idea how to do ...

So where we left it, I was confused and didn't understand anything.

Rather than just getting the answers, I want to try to understand this, but
I feel like I must need more background. This must be the kind of code that
is in the monad transformer library. Is there a guide to understanding that
somewhere?

D
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