Difference between revisions of "New monads/MonadRandomSplittable"

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== Laws ==
 
== Laws ==
   
It is not clear to me exactly what [[Monad laws|laws]] <hask>splitRandom</hask> should satisfy, besides monadic variations of the "split laws" from the Haskell Library Report [http://haskell.org/onlinereport/random.html]
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It is not clear to me exactly what [[Monad laws|laws]] <hask>splitRandom</hask> should satisfy, besides monadic variations of the "split laws" from the [http://haskell.org/onlinereport/random.html Haskell Library Report]
   
 
For all terminating <hask>ma</hask> and <hask>mb</hask>, it should hold that
 
For all terminating <hask>ma</hask> and <hask>mb</hask>, it should hold that

Revision as of 20:04, 17 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)

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.