How to nondeterministically put a value in a state?

Question

In the following code, how can I replace put 1 with some code that insert nondeterministically 1 or 2 in the state?

import Control.Monad.List
import Control.Monad.Trans.State

test :: StateT Int [] Int
test = do
  put 1
  v <- get
  return v

Answer 1

Your monad stack signature is already the correct one.

Lift a computation from the [] monad and bind to its value. This will fork the computation:

test :: StateT Int [] Int
test = do
  s <- lift [1,2,3]
  put s
  v <- get
  return v

Testing to see it works:

*Main> runStateT test 10
[(1,1),(2,2),(3,3)]

Not only there are many results, but the state gets included in the nondeterminism as well.

If test had had type ListT (State Int) Int , only the results would have been nondetermistic, the state would have been shared among all the branches in the computation:

test :: ListT (State Int) Int
test = do
  s <- ListT $ return [1,2,3]
  put s
  v <- get
  return v

The result:

*Main> runState (runListT test) 10
([1,2,3],3)

Answer 2

maybe you want something like this instead:

import Control.Monad.List
import Control.Monad.Trans.State
import System.Random (randomIO)

test :: StateT Int IO Int
test = do
  put1 <- liftIO $ randomIO
  put (if put1 then 1 else 2)
  v <- get
  return v

This will use the global generator to set 1 or 2 at random