# New monads/MonadRandomSplittable

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m (fix a MonadRandomSplittable "law") |
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newtype Rand g a = Rand { unRand :: RandomT g Identity a } |
newtype Rand g a = Rand { unRand :: RandomT g Identity a } |
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deriving (Functor, Monad, MonadRandom, MonadRandomSplittable) |
deriving (Functor, Monad, MonadRandom, MonadRandomSplittable) |
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+ | </haskell> |
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+ | |||

+ | Some potentially useful functions |
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+ | <haskell> |
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+ | splitRandoms :: MonadRandomSplittable m => [m a] -> m [a] |
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+ | splitRandoms [] = splitRandom $ return [] |
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+ | splitRandoms (x:xs) = splitRandom $ liftM2 (:) x (splitRandoms xs) |
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+ | |||

+ | getRandoms :: (MonadRandomSplittable m, Random a) => m [a] |
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+ | getRandoms = liftM2 (:) getRandom (splitRandom getRandoms) |
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+ | |||

+ | getRandomRs :: (MonadRandomSplittable m, Random a) => (a, a) -> m [a] |
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+ | getRandomRs b = liftM2 (:) (getRandomR b) (splitRandom (getRandomRs b)) |
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</haskell> |
</haskell> |
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== Laws == |
== Laws == |
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− | It is not clear to me exactly what [[Monad laws|laws]] <hask>splitRandom</hask> should satisfy. |
+ | 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 |
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<haskell> |
<haskell> |
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− | liftM3 (\a _ c -> (a,c)) getRandom ma getRandom === liftM3 (\a _ c -> (a,c)) getRandom mb getRandom |
+ | liftM3 (\a _ c -> (a,c)) getRandom (splitRandom ma) getRandom |

</haskell> |
</haskell> |
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+ | and |
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+ | <haskell> |
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+ | liftM3 (\a _ c -> (a,c)) getRandom (splitRandom mb) getRandom |
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+ | </haskell> |
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+ | return the same pair. |
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For [[monad transformer]]s, it would also be nice if |
For [[monad transformer]]s, it would also be nice if |
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== Why? == |
== Why? == |
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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. |
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+ | |||

+ | The following constructs a tree of infinite depth and width: |
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+ | <haskell> |
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+ | import Data.Tree |
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+ | import Data.List |
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+ | |||

+ | makeRandomTree = liftM2 Node (getRandomR ('a','z')) (splitRandoms $ repeat makeRandomTree) |
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+ | </haskell> |
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+ | By removing the RNG-dependencies, infinite random data structures can be constructed lazily. |
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+ | |||

+ | And for completeness the non-monadic version: |
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+ | <haskell> |
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+ | randomTree g = Node a (map randomTree gs) |
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+ | where |
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+ | (a, g') = randomR ('a','z') g |
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+ | gs = unfoldr (Just . split) g' |
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+ | </haskell> |
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+ | Note that the monadic version does more split operations, so yields different results. |

## Latest revision as of 22:10, 27 November 2007

MonadRandom

RandomGen

split

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))

## [edit] 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)

## [edit] 2 Laws

It is not clear to me exactly what lawssplitRandom

ma

mb

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

Rand

>runRand (splitRandom undefined >> return ()) (mkStdGen 0) ((),40014 2147483398)

## [edit] 3 Why?

InreplicateM 100 (splitRandom expensiveAction)

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.