Difference between revisions of "New monads/MonadRandomSplittable"
(splitRandoms, getRandoms, getRandomRs) 
(Fancify the tree example (hm, too fancy perhaps?)) 

Line 94:  Line 94:  
In <hask>replicateM 100 (splitRandom expensiveAction)</hask> There are no RNGdependencies between the different expensiveActions, so they may be computed in parallel. 
In <hask>replicateM 100 (splitRandom expensiveAction)</hask> There are no RNGdependencies between the different expensiveActions, so they may be computed in parallel. 

+  The following constructs a tree of infinite depth and width: 

<haskell> 
<haskell> 

−  data Tree a = Branch a (Tree a) (Tree a)  Leaf deriving (Eq, Show) 

+  import Data.Tree 

+  import Data.List 

−  makeRandomTree = do 

+  makeRandomTree = liftM2 Node (getRandomR ('a','z')) (splitRandoms $ repeat makeRandomTree) 

−  this < getRandomR (0,9) 

−  left < splitRandom makeRandomTree 

−  right < splitRandom makeRandomTree 

−  return $ Branch this left right 

</haskell> 
</haskell> 

By removing the RNGdependencies, infinite random data structures can be constructed lazily. 
By removing the RNGdependencies, infinite random data structures can be constructed lazily. 

Line 107:  Line 105:  
And for completeness the nonmonadic version: 
And for completeness the nonmonadic version: 

<haskell> 
<haskell> 

−  randomTree g = 
+  randomTree g = Node a (map randomTree gs) 
where 
where 

−  (a, g') = randomR ( 
+  (a, g') = randomR ('a','z') g 
−  +  gs = unfoldr (Just . split) g' 

</haskell> 
</haskell> 

−  Note that the monadic version 
+  Note that the monadic version does more split operations, so yields different results. 
Revision as of 00:06, 19 November 2006
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 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 RNGdependencies 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 RNGdependencies, infinite random data structures can be constructed lazily.
And for completeness the nonmonadic 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.