random-fu-0.2.1.0: Random number generation

Data.Random.RVar

Synopsis

# Documentation

type RVar = RVarT Identity

An opaque type modeling a "random variable" - a value which depends on the outcome of some random event. `RVar`s can be conveniently defined by an imperative-looking style:

``` normalPair =  do
u <- stdUniform
t <- stdUniform
let r = sqrt (-2 * log u)
theta = (2 * pi) * t

x = r * cos theta
y = r * sin theta
return (x,y)
```

OR by a more applicative style:

``` logNormal = exp <\$> stdNormal
```

Once defined (in any style), there are several ways to sample `RVar`s:

• In a monad, using a `RandomSource`:
``` runRVar (uniform 1 100) DevRandom :: IO Int
```
• In a monad, using a `MonadRandom` instance:
``` sampleRVar (uniform 1 100) :: State PureMT Int
```
• As a pure function transforming a functional RNG:
``` sampleState (uniform 1 100) :: StdGen -> (Int, StdGen)
```

(where `sampleState = runState . sampleRVar`)

runRVar :: RandomSource m s => RVar a -> s -> m a

"Run" an `RVar` - samples the random variable from the provided source of entropy.

data RVarT m a

A random variable with access to operations in an underlying monad. Useful examples include any form of state for implementing random processes with hysteresis, or writer monads for implementing tracing of complicated algorithms.

For example, a simple random walk can be implemented as an `RVarT` `IO` value:

``` rwalkIO :: IO (RVarT IO Double)
rwalkIO d = do
lastVal <- newIORef 0

let x = do
prev    <- lift (readIORef lastVal)
change  <- rvarT StdNormal

let new = prev + change
lift (writeIORef lastVal new)
return new

return x
```

To run the random walk it must first be initialized, after which it can be sampled as usual:

``` do
rw <- rwalkIO
x <- sampleRVarT rw
y <- sampleRVarT rw
...
```

The same random-walk process as above can be implemented using MTL types as follows (using `import Control.Monad.Trans as MTL`):

``` rwalkState :: RVarT (State Double) Double
rwalkState = do
prev <- MTL.lift get
change  <- rvarT StdNormal

let new = prev + change
MTL.lift (put new)
return new
```

Invocation is straightforward (although a bit noisy) if you're used to MTL:

``` rwalk :: Int -> Double -> StdGen -> ([Double], StdGen)
rwalk count start gen =
flip evalState start .
flip runStateT gen .
sampleRVarTWith MTL.lift \$
replicateM count rwalkState
```

Instances

 MonadTrans RVarT MonadPrompt Prim (RVarT n) Monad (RVarT n) Functor (RVarT n) Applicative (RVarT n) MonadIO m => MonadIO (RVarT m) MonadRandom (RVarT n) Lift m n => Sampleable (RVarT m) n t Lift (RVarT Identity) (RVarT m)

runRVarT :: (Lift n m, RandomSource m s) => RVarT n a -> s -> m aSource

Like `runRVarTWith`, but using an implicit lifting (provided by the `Lift` class)

runRVarTWith :: RandomSource m s => (forall t. n t -> m t) -> RVarT n a -> s -> m a

"Runs" an `RVarT`, sampling the random variable it defines.

The first argument lifts the base monad into the sampling monad. This operation must obey the "monad transformer" laws:

``` lift . return = return
lift (x >>= f) = (lift x) >>= (lift . f)
```

One example of a useful non-standard lifting would be one that takes `State s` to another monad with a different state representation (such as `IO` with the state mapped to an `IORef`):

``` embedState :: (Monad m) => m s -> (s -> m ()) -> State s a -> m a
embedState get put = \m -> do
s <- get
(res,s) <- return (runState m s)
put s
return res
```

The ability to lift is very important - without it, every `RVar` would have to either be given access to the full capability of the monad in which it will eventually be sampled (which, incidentally, would also have to be monomorphic so you couldn't sample one `RVar` in more than one monad) or functions manipulating `RVar`s would have to use higher-ranked types to enforce the same kind of isolation and polymorphism.