[Haskell-beginners] state and randomness, Rand, RandT

[Amy de Buitléir]

I'm experimenting with different ways of working with both state and
randomness at the same time. I put together this simple little example
as a starting point, where the state in question is a list of Ints,
and I want to be able to push a random number onto the stack.

{-# LANGUAGE PackageImports #-}

import "mtl" Control.Monad.State
import Control.Monad.Random

type Stack = [Int]

-- push a random number onto the stack
pushRandom:: State (Stack, StdGen) ()
pushRandom = do
     (xs,gen) <- get
     (r,gen') <- return $ randomR (1,100) gen
     put(r:xs,gen')

That implementation works just fine.

GHCi> execState pushRandom ([5,4,3,2,1], mkStdGen 0)
([46,5,4,3,2,1],40014 40692)

But... I think it would be nicer to use Rand. Unfortunately, I can't
figure out how to write the correct type signature. (Compiler message
is: `Rand g' is not applied to enough type arguments Expected kind
`*', but `Rand g' has kind `* -> *').

pushRandom2 :: (RandomGen g) => State (Stack, Rand g) ()
pushRandom2 = do
  (xs,gen) <- get
  (x,gen') <- getRandomR (0,100) gen
  put (1:xs,gen)

And I'd really like to try using RandT, because this seems like the
right situation for it. This compiles just fine.

pushRandom3 :: (RandomGen g) => RandT g (State Stack) ()
pushRandom3 = do
  xs <- get
  r <- getRandomR (1,100)
  put (r:xs)

But I don't know if it works, because I can't figure out the magic
incantation to get it to run!

GHCi> evalRandT $ pushRandom3 (mkStdGen 0) [5,4,3,2,1]

<interactive>:1:12:
    Couldn't match expected type `StdGen -> [t] -> RandT g m a'
           against inferred type `RandT g1 (State Stack) ()'
    In the second argument of `($)', namely
        `pushRandom3 (mkStdGen 0) [5, 4, 3, 2, ....]'
    In the expression:
          evalRandT $ pushRandom3 (mkStdGen 0) [5, 4, 3, 2, ....]
    In the definition of `it':
        it = evalRandT $ pushRandom3 (mkStdGen 0) [5, 4, 3, ....]

To summarise:

Q1: How can I fix pushRandom2?

Q2: How can I run pushRandom3?

Thank you in advance for anyone who can help.

Amy