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.