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New monads/MonadRandomSplittable

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(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 RNG-dependencies between the different expensiveActions, so they may be computed in parallel.
 
In <hask>replicateM 100 (splitRandom expensiveAction)</hask> 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:
 
<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 RNG-dependencies, infinite random data structures can be constructed lazily.
 
By removing the RNG-dependencies, infinite random data structures can be constructed lazily.
Line 103: Line 104:
 
And for completeness the non-monadic version:
 
And for completeness the non-monadic version:
 
<haskell>
 
<haskell>
randomTree g = Branch a (randomTree gl) (randomTree gr)
+
randomTree g = Node a (map randomTree gs)
 
where
 
where
(a, g') = randomR (0, 9) g
+
(a, g') = randomR ('a','z') g
(gl, gr)= split g'
+
gs = unfoldr (Just . split) g'
 
</haskell>
 
</haskell>
Note that the monadic version needs one split operation more, so yields different results.
+
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))

1 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)

2 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)

3 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.