# New monads/MonadRandomSplittable

### From HaskellWiki

< New monads(Difference between revisions)

(The infinite random tree example now compiles without extra code) |
(splitRandoms, getRandoms, getRandomRs) |
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Line 15: | Line 15: | ||

newtype Rand g a = Rand { unRand :: RandomT g Identity a } | newtype Rand g a = Rand { unRand :: RandomT g Identity a } | ||

deriving (Functor, Monad, MonadRandom, MonadRandomSplittable) | deriving (Functor, Monad, MonadRandom, MonadRandomSplittable) | ||

+ | </haskell> | ||

+ | |||

+ | Some potentially useful functions | ||

+ | <haskell> | ||

+ | 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)) | ||

</haskell> | </haskell> | ||

## Revision as of 23:39, 18 November 2006

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))

## 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 lawssplitRandom

ma

mb

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

Rand

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

## 3 Why?

InreplicateM 100 (splitRandom expensiveAction)

data Tree a = Branch a (Tree a) (Tree a) | Leaf deriving (Eq, Show) makeRandomTree = do this <- getRandomR (0,9) left <- splitRandom makeRandomTree right <- splitRandom makeRandomTree return $ Branch this left right

By removing the RNG-dependencies, infinite random data structures can be constructed lazily.

And for completeness the non-monadic version:

randomTree g = Branch a (randomTree gl) (randomTree gr) where (a, g') = randomR (0, 9) g (gl, gr)= split g'

Note that the monadic version needs one split operation more, so yields different results.