# New monads/MonadRandomSplittable

When using New monads/MonadRandom, one may also want to use a `MonadRandom`

equivalent of `RandomGen`

's `split`

function:

```
class (MonadRandom m) => MonadRandomSplittable m where
splitRandom :: m a -> m a
instance (Monad m, RandomGen g) => MonadRandomSplittable (RandomT g m) where
splitRandom ma = (RandomT . liftState) split >>= lift . evalRandomT ma
```

MonadRandomSplittable can then be derived for Rand by GHC:

```
newtype Rand g a = Rand { unRand :: RandomT g Identity a }
deriving (Functor, Monad, MonadRandom, MonadRandomSplittable)
```

## Example of usage

```
test :: Rand StdGen [Bool] -> (Int, [Bool], Int)
test ma = evalRand (liftM3 (,,) (getRandomR (0,99)) ma (getRandomR (0,99)))
(mkStdGen 0)
```

Then

```
*MonadRandom> test (replicateM 0 getRandom)
(45,[],55)
*MonadRandom> test (replicateM 2 getRandom)
(45,[True,True],0)
*MonadRandom> test (splitRandom $ replicateM 0 getRandom)
(45,[],16)
*MonadRandom> test (splitRandom $ replicateM 2 getRandom)
(45,[False,True],16)
*MonadRandom> case test undefined of (a,_,c) -> (a,c)
*** Exception: Prelude.undefined
*MonadRandom> case test (splitRandom undefined) of (a,_,c) -> (a,c)
(45,16)
```

## Laws

It is not clear to me exactly what laws `splitRandom`

should satisfy, besides monadic variations of the "split laws" from the Haskell Library Report

For all terminating `ma`

and `mb`

, it should hold that

```
liftM3 (\a _ c -> (a,c)) getRandom ma getRandom === liftM3 (\a _ c -> (a,c)) getRandom mb getRandom
```

For monad transformers, it would also be nice if

```
splitRandom undefined === splitRandom (return ()) >> lift undefined
```

For example,

```
>runIdentity $ runRandomT (splitRandom (return ()) >> lift undefined >> return ()) (mkStdGen 0)
((),40014 2147483398)
>runIdentity $ runRandomT (splitRandom undefined >> return ()) (mkStdGen 0)
((),40014 2147483398)
```

But

```
>runRandomT (splitRandom (return ()) >> lift undefined >> return ()) (mkStdGen 0)
*** Exception: Prelude.undefined
>runRandomT (splitRandom undefined >> return ()) (mkStdGen 0)
*** Exception: Prelude.undefined
```

I have no idea how to express this idea for monads that aren't transformers though. But for `Rand`

it means that:

```
>runRand (splitRandom undefined >> return ()) (mkStdGen 0)
((),40014 2147483398)
```

## Why?

In `replicateM 100 (splitRandom expensiveAction)`

There are no RNG-dependencies between the different expensiveActions, so they may be computed in parallel.

```
makeRandomTree = do this <- randomNode
left <- split $ randomLeftChild this
right <- split $ randomRightChild this
return $ Node this left right
```

By removing the RNG-dependencies, infinite random data structures can be constructed lazily.