- type RVar = RVarT Identity
- runRVar :: RandomSource m s => RVar a -> s -> m a
- data RVarT m a
- runRVarT :: (Lift n m, RandomSource m s) => RVarT n a -> s -> m a
- runRVarTWith :: RandomSource m s => (forall t. n t -> m t) -> RVarT n a -> s -> m a

# Documentation

type RVar = RVarT IdentitySource

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 a couple ways to sample `RVar`

s:

- In a monad, using a
`RandomSource`

:

sampleFrom DevRandom (uniform 1 100) :: IO Int

- As a pure function transforming a functional RNG:

sampleState (uniform 1 100) :: StdGen -> (Int, StdGen)

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

"Run" an `RVar`

- samples the random variable from the provided
source of entropy.

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, and then it can be sampled as usual:

do rw <- rwalkIO x <- sampleFrom DevURandom rw y <- sampleFrom DevURandom 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, but there is a gotcha lurking here: `sample`

and `runRVarT`

inherit the extreme generality of `lift`

, so there will almost always
need to be an explicit type signature lurking somewhere in any client
code making use of `RVarT`

with MTL types. In this example, the
inferred type of `start`

would be too general to be practical, so the
signature for `rwalk`

explicitly fixes it to `Double`

. Alternatively,
in this case `sample`

could be replaced with
`\x -> runRVarTWith MTL.lift x StdRandom`

.

rwalk :: Int -> Double -> StdGen -> ([Double], StdGen) rwalk count start gen = evalState (runStateT (sample (replicateM count rwalkState)) gen) start

MonadTrans RVarT | |

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

"Runs" an `RVarT`

, sampling the random variable it defines.

The `Lift`

context allows random variables to be defined using a minimal
underlying functor (`Identity`

is sufficient for "conventional" random
variables) and then sampled in any monad into which the underlying functor
can be embedded (which, for `Identity`

, is all monads).

The lifting 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.

For non-standard liftings or those where you would rather not introduce a
`Lift`

instance, see `runRVarTWith`

.

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

Like `runRVarT`

but allowing a user-specified lift operation. 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