random-fu-0.2.6.2: Random number generation

Safe HaskellNone
LanguageHaskell98

Data.Random

Contents

Description

Flexible modeling and sampling of random variables.

The central abstraction in this library is the concept of a random variable. It is not fully formalized in the standard measure-theoretic language, but rather is informally defined as a "thing you can get random values out of". Different random variables may have different types of values they can return or the same types but different probabilities for each value they can return. The random values you get out of them are traditionally called "random variates".

Most imperative-language random number libraries are all about obtaining and manipulating random variates. This one is about defining, manipulating and sampling random variables. Computationally, the distinction is small and mostly just a matter of perspective, but from a program design perspective it provides both a powerfully composable abstraction and a very useful separation of concerns.

Abstract random variables as implemented by RVar are composable. They can be defined in a monadic / "imperative" style that amounts to manipulating variates, but with strict type-level isolation. Concrete random variables are also provided, but they do not compose as generically. The Distribution type class allows concrete random variables to "forget" their concreteness so that they can be composed. For examples of both, see the documentation for RVar and Distribution, as well as the code for any of the concrete distributions such as Uniform, Gamma, etc.

Both abstract and concrete random variables can be sampled (despite the types GHCi may list for the functions) by the functions in Data.Random.Sample.

Random variable sampling is done with regard to a generic basis of primitive random variables defined in Data.Random.Internal.Primitives. This basis is very low-level and the actual set of primitives is still fairly experimental, which is why it is in the "Internal" sub-heirarchy. User-defined variables should use the existing high-level variables such as Uniform and Normal rather than these basis variables. Data.Random.Source defines classes for entropy sources that provide implementations of these primitive variables. Several implementations are available in the Data.Random.Source.* modules.

Synopsis

Random variables

Abstract (RVar)

type RVar = RVarT Identity

An opaque type modeling a "random variable" - a value which depends on the outcome of some random event. RVars 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 RVars:

runRVar (uniform 1 100) DevRandom :: IO Int
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)

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

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

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

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

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 RVars would have to use higher-ranked types to enforce the same kind of isolation and polymorphism.

Concrete (Distribution)

class Distribution d t where Source

A Distribution is a data representation of a random variable's probability structure. For example, in Data.Random.Distribution.Normal, the Normal distribution is defined as:

data Normal a
    = StdNormal
    | Normal a a

Where the two parameters of the Normal data constructor are the mean and standard deviation of the random variable, respectively. To make use of the Normal type, one can convert it to an rvar and manipulate it or sample it directly:

x <- sample (rvar (Normal 10 2))
x <- sample (Normal 10 2)

A Distribution is typically more transparent than an RVar but less composable (precisely because of that transparency). There are several practical uses for types implementing Distribution:

  • Typically, a Distribution will expose several parameters of a standard mathematical model of a probability distribution, such as mean and std deviation for the normal distribution. Thus, they can be manipulated analytically using mathematical insights about the distributions they represent. For example, a collection of bernoulli variables could be simplified into a (hopefully) smaller collection of binomial variables.
  • Because they are generally just containers for parameters, they can be easily serialized to persistent storage or read from user-supplied configurations (eg, initialization data for a simulation).
  • If a type additionally implements the CDF subclass, which extends Distribution with a cumulative density function, an arbitrary random variable x can be tested against the distribution by testing fmap (cdf dist) x for uniformity.

On the other hand, most Distributions will not be closed under all the same operations as RVar (which, being a monad, has a fully turing-complete internal computational model). The sum of two uniformly-distributed variables, for example, is not uniformly distributed. To support general composition, the Distribution class defines a function rvar to construct the more-abstract and more-composable RVar representation of a random variable.

Minimal complete definition

Nothing

Methods

rvar :: d t -> RVar t Source

Return a random variable with this distribution.

rvarT :: d t -> RVarT n t Source

Return a random variable with the given distribution, pre-lifted to an arbitrary RVarT. Any arbitrary RVar can also be converted to an 'RVarT m' for an arbitrary m, using either lift or sample.

Instances

Distribution StdUniform Bool 
Distribution StdUniform Char 
Distribution StdUniform Double 
Distribution StdUniform Float 
Distribution StdUniform Int 
Distribution StdUniform Int8 
Distribution StdUniform Int16 
Distribution StdUniform Int32 
Distribution StdUniform Int64 
Distribution StdUniform Ordering 
Distribution StdUniform Word 
Distribution StdUniform Word8 
Distribution StdUniform Word16 
Distribution StdUniform Word32 
Distribution StdUniform Word64 
Distribution StdUniform () 
Distribution Uniform Bool 
Distribution Uniform Char 
Distribution Uniform Double 
Distribution Uniform Float 
Distribution Uniform Int 
Distribution Uniform Int8 
Distribution Uniform Int16 
Distribution Uniform Int32 
Distribution Uniform Int64 
Distribution Uniform Integer 
Distribution Uniform Ordering 
Distribution Uniform Word 
Distribution Uniform Word8 
Distribution Uniform Word16 
Distribution Uniform Word32 
Distribution Uniform Word64 
Distribution Uniform () 
(Floating a, Distribution StdUniform a) => Distribution Exponential a 
(Floating a, Distribution StdUniform a) => Distribution StretchedExponential a 
Distribution Normal Double 
Distribution Normal Float 
(Floating a, Ord a, Distribution Normal a, Distribution StdUniform a) => Distribution Gamma a 
Distribution Beta Double 
Distribution Beta Float 
(Fractional t, Distribution Gamma t) => Distribution ChiSquare t 
(RealFloat a, Distribution StdUniform a) => Distribution Rayleigh a 
(Floating a, Distribution Normal a, Distribution ChiSquare a) => Distribution T a 
(RealFloat a, Ord a, Distribution StdUniform a) => Distribution Triangular a 
(Floating a, Distribution StdUniform a) => Distribution Weibull a 
(Floating a, Distribution StdUniform a) => Distribution Pareto a 
HasResolution r => Distribution StdUniform (Fixed r) 
HasResolution r => Distribution Uniform (Fixed r) 
(Fractional a, Distribution Gamma a) => Distribution Dirichlet [a] 
(Fractional b, Ord b, Distribution StdUniform b) => Distribution (Bernoulli b) Bool 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Word64 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Word32 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Word16 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Word8 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Word 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Int64 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Int32 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Int16 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Int8 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Int 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Integer 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Double 
Distribution (Bernoulli b0) Bool => Distribution (Bernoulli b) Float 
(Fractional p, Ord p, Distribution Uniform p) => Distribution (Categorical p) a 
(Num t, Ord t, Vector v t) => Distribution (Ziggurat v) t 
(Integral a, Floating b, Ord b, Distribution Normal b, Distribution StdUniform b) => Distribution (Erlang a) b 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Word64 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Word32 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Word16 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Word8 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Word 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Int64 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Int32 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Int16 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Int8 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Int 
(Floating b0, Ord b0, Distribution Beta b0, Distribution StdUniform b0) => Distribution (Binomial b) Integer 
Distribution (Binomial b0) Integer => Distribution (Binomial b) Double 
Distribution (Binomial b0) Integer => Distribution (Binomial b) Float 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word64) b0, Distribution (Binomial b0) Word64) => Distribution (Poisson b) Word64 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word32) b0, Distribution (Binomial b0) Word32) => Distribution (Poisson b) Word32 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word16) b0, Distribution (Binomial b0) Word16) => Distribution (Poisson b) Word16 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word8) b0, Distribution (Binomial b0) Word8) => Distribution (Poisson b) Word8 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Word) b0, Distribution (Binomial b0) Word) => Distribution (Poisson b) Word 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int64) b0, Distribution (Binomial b0) Int64) => Distribution (Poisson b) Int64 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int32) b0, Distribution (Binomial b0) Int32) => Distribution (Poisson b) Int32 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int16) b0, Distribution (Binomial b0) Int16) => Distribution (Poisson b) Int16 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int8) b0, Distribution (Binomial b0) Int8) => Distribution (Poisson b) Int8 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Int) b0, Distribution (Binomial b0) Int) => Distribution (Poisson b) Int 
(RealFloat b0, Distribution StdUniform b0, Distribution (Erlang Integer) b0, Distribution (Binomial b0) Integer) => Distribution (Poisson b) Integer 
Distribution (Poisson b0) Integer => Distribution (Poisson b) Double 
Distribution (Poisson b0) Integer => Distribution (Poisson b) Float 
(Distribution (Bernoulli b) Bool, RealFloat a) => Distribution (Bernoulli b) (Complex a) 
(Distribution (Bernoulli b) Bool, Integral a) => Distribution (Bernoulli b) (Ratio a) 
(Num a, Eq a, Fractional p, Distribution (Binomial p) a) => Distribution (Multinomial p) [a] 

class Distribution d t => CDF d t where Source

Methods

cdf :: d t -> t -> Double Source

Return the cumulative distribution function of this distribution. That is, a function taking x :: t to the probability that the next sample will return a value less than or equal to x, according to some order or partial order (not necessarily an obvious one).

In the case where t is an instance of Ord, cdf should correspond to the CDF with respect to that order.

In other cases, cdf is only required to satisfy the following law: fmap (cdf d) (rvar d) must be uniformly distributed over (0,1). Inclusion of either endpoint is optional, though the preferred range is (0,1].

Note that this definition requires that cdf for a product type should _not_ be a joint CDF as commonly defined, as that definition violates both conditions. Instead, it should be a univariate CDF over the product type. That is, it should represent the CDF with respect to the lexicographic order of the product.

The present specification is probably only really useful for testing conformance of a variable to its target distribution, and I am open to suggestions for more-useful specifications (especially with regard to the interaction with product types).

Instances

CDF StdUniform Bool 
CDF StdUniform Char 
CDF StdUniform Double 
CDF StdUniform Float 
CDF StdUniform Int 
CDF StdUniform Int8 
CDF StdUniform Int16 
CDF StdUniform Int32 
CDF StdUniform Int64 
CDF StdUniform Ordering 
CDF StdUniform Word 
CDF StdUniform Word8 
CDF StdUniform Word16 
CDF StdUniform Word32 
CDF StdUniform Word64 
CDF StdUniform () 
CDF Uniform Bool 
CDF Uniform Char 
CDF Uniform Double 
CDF Uniform Float 
CDF Uniform Int 
CDF Uniform Int8 
CDF Uniform Int16 
CDF Uniform Int32 
CDF Uniform Int64 
CDF Uniform Integer 
CDF Uniform Ordering 
CDF Uniform Word 
CDF Uniform Word8 
CDF Uniform Word16 
CDF Uniform Word32 
CDF Uniform Word64 
CDF Uniform () 
(Real a, Distribution Exponential a) => CDF Exponential a 
(Real a, Distribution StretchedExponential a) => CDF StretchedExponential a 
(Real a, Distribution Normal a) => CDF Normal a 
(Real a, Distribution Gamma a) => CDF Gamma a 
(Real t, Distribution ChiSquare t) => CDF ChiSquare t 
(Real a, Distribution Rayleigh a) => CDF Rayleigh a 
(Real a, Distribution T a) => CDF T a 
(RealFrac a, Distribution Triangular a) => CDF Triangular a 
(Real a, Distribution Weibull a) => CDF Weibull a 
(Real a, Distribution Pareto a) => CDF Pareto a 
HasResolution r => CDF StdUniform (Fixed r) 
HasResolution r => CDF Uniform (Fixed r) 
(Distribution (Bernoulli b) Bool, Real b) => CDF (Bernoulli b) Bool 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Word64 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Word32 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Word16 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Word8 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Word 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Int64 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Int32 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Int16 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Int8 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Int 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Integer 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Double 
CDF (Bernoulli b0) Bool => CDF (Bernoulli b) Float 
(Integral a, Real b, Distribution (Erlang a) b) => CDF (Erlang a) b 
(Real b0, Distribution (Binomial b0) Word64) => CDF (Binomial b) Word64 
(Real b0, Distribution (Binomial b0) Word32) => CDF (Binomial b) Word32 
(Real b0, Distribution (Binomial b0) Word16) => CDF (Binomial b) Word16 
(Real b0, Distribution (Binomial b0) Word8) => CDF (Binomial b) Word8 
(Real b0, Distribution (Binomial b0) Word) => CDF (Binomial b) Word 
(Real b0, Distribution (Binomial b0) Int64) => CDF (Binomial b) Int64 
(Real b0, Distribution (Binomial b0) Int32) => CDF (Binomial b) Int32 
(Real b0, Distribution (Binomial b0) Int16) => CDF (Binomial b) Int16 
(Real b0, Distribution (Binomial b0) Int8) => CDF (Binomial b) Int8 
(Real b0, Distribution (Binomial b0) Int) => CDF (Binomial b) Int 
(Real b0, Distribution (Binomial b0) Integer) => CDF (Binomial b) Integer 
CDF (Binomial b0) Integer => CDF (Binomial b) Double 
CDF (Binomial b0) Integer => CDF (Binomial b) Float 
(Real b0, Distribution (Poisson b0) Word64) => CDF (Poisson b) Word64 
(Real b0, Distribution (Poisson b0) Word32) => CDF (Poisson b) Word32 
(Real b0, Distribution (Poisson b0) Word16) => CDF (Poisson b) Word16 
(Real b0, Distribution (Poisson b0) Word8) => CDF (Poisson b) Word8 
(Real b0, Distribution (Poisson b0) Word) => CDF (Poisson b) Word 
(Real b0, Distribution (Poisson b0) Int64) => CDF (Poisson b) Int64 
(Real b0, Distribution (Poisson b0) Int32) => CDF (Poisson b) Int32 
(Real b0, Distribution (Poisson b0) Int16) => CDF (Poisson b) Int16 
(Real b0, Distribution (Poisson b0) Int8) => CDF (Poisson b) Int8 
(Real b0, Distribution (Poisson b0) Int) => CDF (Poisson b) Int 
(Real b0, Distribution (Poisson b0) Integer) => CDF (Poisson b) Integer 
CDF (Poisson b0) Integer => CDF (Poisson b) Double 
CDF (Poisson b0) Integer => CDF (Poisson b) Float 
(CDF (Bernoulli b) Bool, RealFloat a) => CDF (Bernoulli b) (Complex a) 
(CDF (Bernoulli b) Bool, Integral a) => CDF (Bernoulli b) (Ratio a) 

Sampling random variables

class Sampleable d m t where Source

A typeclass allowing Distributions and RVars to be sampled. Both may also be sampled via runRVar or runRVarT, but I find it psychologically pleasing to be able to sample both using this function, as they are two separate abstractions for one base concept: a random variable.

Methods

sampleFrom :: RandomSource m s => s -> d t -> m t Source

Directly sample from a distribution or random variable, using the given source of entropy.

Instances

Distribution d t => Sampleable d m t 
Lift m n => Sampleable (RVarT m) n t 

sample :: (Sampleable d m t, MonadRandom m) => d t -> m t Source

Sample a random variable using the default source of entropy for the monad in which the sampling occurs.

sampleState :: (Sampleable d (State s) t, MonadRandom (State s)) => d t -> s -> (t, s) Source

Sample a random variable in a "functional" style. Typical instantiations of s are System.Random.StdGen or System.Random.Mersenne.Pure64.PureMT.

sampleStateT :: (Sampleable d (StateT s m) t, MonadRandom (StateT s m)) => d t -> s -> m (t, s) Source

Sample a random variable in a "semi-functional" style. Typical instantiations of s are System.Random.StdGen or System.Random.Mersenne.Pure64.PureMT.

A few very common distributions

uniform :: Distribution Uniform a => a -> a -> RVar a Source

uniformT :: Distribution Uniform a => a -> a -> RVarT m a Source

stdUniform :: Distribution StdUniform a => RVar a Source

Get a "standard" uniformly distributed variable. For integral types, this means uniformly distributed over the full range of the type (there is no support for Integer). For fractional types, this means uniformly distributed on the interval [0,1).

stdUniformT :: Distribution StdUniform a => RVarT m a Source

Get a "standard" uniformly distributed process. For integral types, this means uniformly distributed over the full range of the type (there is no support for Integer). For fractional types, this means uniformly distributed on the interval [0,1).

data Normal a Source

A specification of a normal distribution over the type a.

Constructors

StdNormal

The "standard" normal distribution - mean 0, stddev 1

Normal a a

Normal m s is a normal distribution with mean m and stddev sd.

normal :: Distribution Normal a => a -> a -> RVar a Source

normal m s is a random variable with distribution Normal m s.

stdNormal :: Distribution Normal a => RVar a Source

stdNormal is a normal variable with distribution StdNormal.

normalT :: Distribution Normal a => a -> a -> RVarT m a Source

normalT m s is a random process with distribution Normal m s.

stdNormalT :: Distribution Normal a => RVarT m a Source

stdNormalT is a normal process with distribution StdNormal.

data Gamma a Source

Constructors

Gamma a a 

gamma :: Distribution Gamma a => a -> a -> RVar a Source

gammaT :: Distribution Gamma a => a -> a -> RVarT m a Source

Entropy Sources

class Monad m => MonadRandom m

A typeclass for monads with a chosen source of entropy. For example, RVar is such a monad - the source from which it is (eventually) sampled is the only source from which a random variable is permitted to draw, so when directly requesting entropy for a random variable these functions are used.

Minimum implementation is either the internal getRandomPrim or all other functions. Additionally, this class's interface is subject to extension at any time, so it is very, very strongly recommended that the monadRandom Template Haskell function be used to implement this function rather than directly implementing it. That function takes care of choosing default implementations for any missing functions; as long as at least one function is implemented, it will derive sensible implementations of all others.

To use monadRandom, just wrap your instance declaration as follows (and enable the TemplateHaskell and GADTs language extensions):

$(monadRandom [d|
        instance MonadRandom FooM where
            getRandomDouble = return pi
            getRandomWord16 = return 4
            {- etc... -}
    |])

class Monad m => RandomSource m s

A source of entropy which can be used in the given monad.

See also MonadRandom.

Minimum implementation is either the internal getRandomPrimFrom or all other functions. Additionally, this class's interface is subject to extension at any time, so it is very, very strongly recommended that the randomSource Template Haskell function be used to implement this function rather than directly implementing it. That function takes care of choosing default implementations for any missing functions; as long as at least one function is implemented, it will derive sensible implementations of all others.

To use randomSource, just wrap your instance declaration as follows (and enable the TemplateHaskell, MultiParamTypeClasses and GADTs language extensions, as well as any others required by your instances, such as FlexibleInstances):

$(randomSource [d|
        instance RandomSource FooM Bar where
            {- at least one RandomSource function... -}
    |])

data StdRandom :: *

A token representing the "standard" entropy source in a MonadRandom monad. Its sole purpose is to make the following true (when the types check):

runRVar x StdRandom === sampleRVar

Constructors

StdRandom 

Useful list-based operations

randomElement :: [a] -> RVar a Source

A random variable returning an arbitrary element of the given list. Every element has equal probability of being chosen. Because it is a pure RVar it has no memory - that is, it "draws with replacement."

shuffle :: [a] -> RVar [a] Source

A random variable that returns the given list in an arbitrary shuffled order. Every ordering of the list has equal probability.

shuffleN :: Int -> [a] -> RVar [a] Source

A random variable that shuffles a list of a known length (or a list prefix of the specified length). Useful for shuffling large lists when the length is known in advance. Avoids needing to traverse the list to discover its length. Each ordering has equal probability.

shuffleNofM :: Int -> Int -> [a] -> RVar [a] Source

A random variable that selects N arbitrary elements of a list of known length M.