-- |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.
module Data.Random
( -- * Random variables
-- ** Abstract ('RVar')
RVar, RVarT,
runRVar, runRVarT, runRVarTWith,
-- ** Concrete ('Distribution')
Distribution(..), CDF(..),
-- * Sampling random variables
Sampleable(..), sample, sampleState, sampleStateT,
-- * A few very common distributions
Uniform(..), uniform, uniformT,
StdUniform(..), stdUniform, stdUniformT,
Normal(..), normal, stdNormal, normalT, stdNormalT,
Gamma(..), gamma, gammaT,
-- * Entropy Sources
MonadRandom, RandomSource, StdRandom(..),
-- * Useful list-based operations
randomElement,
shuffle, shuffleN, shuffleNofM
) where
import Data.Random.Sample
import Data.Random.Source (MonadRandom, RandomSource)
import Data.Random.Source.IO ()
import Data.Random.Source.MWC ()
import Data.Random.Source.StdGen ()
import Data.Random.Source.PureMT ()
import Data.Random.Source.Std
import Data.Random.Distribution
import Data.Random.Distribution.Gamma
import Data.Random.Distribution.Normal
import Data.Random.Distribution.Uniform
import Data.Random.Lift ()
import Data.Random.List
import Data.Random.RVar