New monads/MonadRandom

From New monads, copied from old wiki.

MonadRandom

A simple monad transformer to allow computations in the transformed monad to generate random values.

"CaleGibbard/BSDLicense"

{-# OPTIONS_GHC -fglasgow-exts #-}

module MonadRandom (
    MonadRandom,
    getRandom,
    getRandomR,
    evalRandomT,
    evalRand,
    evalRandIO,
    fromList,
    Rand, RandomT -- but not the data constructors
    ) where

import System.Random
import Control.Monad.State
import Control.Monad.Identity

class (Monad m) => MonadRandom m where
    getRandom :: (Random a) => m a
    getRandomR :: (Random a) => (a,a) -> m a

newtype (RandomGen g) => RandomT g m a = RandomT { unRT :: StateT g m a }
    deriving (Functor, Monad, MonadTrans, MonadIO)

liftState :: (MonadState s m) => (s -> (a,s)) -> m a
liftState t = do v <- get
                 let (x, v') = t v
                 put v'
                 return x

instance (Monad m, RandomGen g) => MonadRandom (RandomT g m) where
    getRandom = (RandomT . liftState) random
    getRandomR (x,y) = (RandomT . liftState) (randomR (x,y))

evalRandomT :: (Monad m, RandomGen g) => RandomT g m a -> g -> m a
evalRandomT x g = evalStateT (unRT x) g

-- Boring random monad :)
newtype Rand g a = Rand { unRand :: RandomT g Identity a }
    deriving (Functor, Monad, MonadRandom)

evalRand :: (RandomGen g) => Rand g a -> g -> a
evalRand x g = runIdentity (evalRandomT (unRand x) g)

evalRandIO :: Rand StdGen a -> IO a
evalRandIO x = getStdRandom (runIdentity . runStateT (unRT (unRand x)))

fromList :: (MonadRandom m) => [(a,Rational)] -> m a
fromList [] = error "MonadRandom.fromList called with empty list"
fromList [(x,_)] = return x
fromList xs = do let s = fromRational $ sum (map snd xs) -- total weight
                     cs = scanl1 (\(x,q) (y,s) -> (y, s+q)) xs -- cumulative weight
                 p <- liftM toRational $ getRandomR (0.0,s)
                 return $ fst $ head $ dropWhile (\(x,q) -> q < p) cs

To make use of common transformer stacks involving Rand and RandomT, the following definitions may prove useful:

instance (MonadRandom m) => MonadRandom (StateT s m) where
    getRandom = lift getRandom
    getRandomR r = lift $ getRandomR r

instance (MonadRandom m, Monoid w) => MonadRandom (WriterT w m) where
    getRandom = lift getRandom
    getRandomR r = lift $ getRandomR r

instance (MonadRandom m) => MonadRandom (ReaderT r m) where
    getRandom = lift getRandom
    getRandomR r = lift $ getRandomR r


instance (MonadState s m, RandomGen g) => MonadState s (RandomT g m) where
    get = lift get
    put s = lift $ put s

instance (MonadReader r m, RandomGen g) => MonadReader r (RandomT g m) where
    ask = lift ask
    local f m = RandomT $ local f (unRT m)

instance (MonadWriter w m, RandomGen g, Monoid w) => MonadWriter w (RandomT g m) where
    tell w = lift $ tell w
    listen m = RandomT $ listen (unRT m)
    pass m = RandomT $ pass (unRT m)