# 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)
```

Some potentially useful functions

```
splitRandoms :: MonadRandomSplittable m => [m a] -> m [a]
splitRandoms [] = splitRandom $ return []
splitRandoms (x:xs) = splitRandom $ liftM2 (:) x (splitRandoms xs)
getRandoms :: (MonadRandomSplittable m, Random a) => m [a]
getRandoms = liftM2 (:) getRandom (splitRandom getRandoms)
getRandomRs :: (MonadRandomSplittable m, Random a) => (a, a) -> m [a]
getRandomRs b = liftM2 (:) (getRandomR b) (splitRandom (getRandomRs b))
```

## 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 (splitRandom ma) getRandom
```

and

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

return the same pair.

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.

The following constructs a tree of infinite depth and width:

```
import Data.Tree
import Data.List
makeRandomTree = liftM2 Node (getRandomR ('a','z')) (splitRandoms $ repeat makeRandomTree)
```

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

And for completeness the non-monadic version:

```
randomTree g = Node a (map randomTree gs)
where
(a, g') = randomR ('a','z') g
gs = unfoldr (Just . split) g'
```

Note that the monadic version does more split operations, so yields different results.