MonadRandom-0.5.1: Random-number generation monad.

Copyright | (c) Brent Yorgey 2016
License | BSD3 (see LICENSE)
Maintainer | byorgey@gmail.com
Safe Haskell | Safe
Language | Haskell2010

Control.Monad.Random.Class

Contents

- MonadRandom
- MonadSplit
- MonadInterleave
- Sampling functions

Description

The `MonadRandom`, `MonadSplit`, and `MonadInterleave` classes.

- `MonadRandom` abstracts over monads with the capability of generating random values.
- `MonadSplit` abstracts over random monads with the ability to get a split generator state. It is not very useful but kept here for backwards compatibility.
- `MonadInterleave` abstracts over random monads supporting an `interleave` operation, which allows sequencing computations which do not depend on each other's random generator state, by splitting the generator between them.

This module also defines convenience functions for sampling from a given collection of values, either uniformly or according to given weights.

Synopsis

- class Monad m => MonadRandom m where
- class Monad m => MonadSplit g m | m -> g where
- class MonadRandom m => MonadInterleave m where
- fromList :: MonadRandom m => [(a, Rational)] -> m a
- fromListMay :: MonadRandom m => [(a, Rational)] -> m (Maybe a)
- uniform :: (Foldable t, MonadRandom m) => t a -> m a
- uniformMay :: (Foldable t, MonadRandom m) => t a -> m (Maybe a)
- weighted :: (Foldable t, MonadRandom m) => t (a, Rational) -> m a
- weightedMay :: (Foldable t, MonadRandom m) => t (a, Rational) -> m (Maybe a)

# MonadRandom

class Monad m => MonadRandom m where #

With a source of random number supply in hand, the `MonadRandom` class allows the programmer to extract random values of a variety of types.

Minimal complete definition

getRandomR, getRandom, getRandomRs, getRandoms

Methods

getRandomR :: Random a => (a, a) -> m a #

Takes a range (lo,hi) and a random number generator g, and returns a computation that returns a random value uniformly distributed in the closed interval [lo,hi], together with a new generator. It is unspecified what happens if lo>hi. For continuous types there is no requirement that the values lo and hi are ever produced, but they may be, depending on the implementation and the interval.

See `randomR` for details.

getRandom :: Random a => m a #

The same as `getRandomR`, but using a default range determined by the type:

- For bounded types (instances of `Bounded`, such as `Char`), the range is normally the whole type.
- For fractional types, the range is normally the semi-closed interval `[0,1)`.
- For `Integer`, the range is (arbitrarily) the range of `Int`.

See `random` for details.

getRandomRs :: Random a => (a, a) -> m [a] #

Plural variant of `getRandomR`, producing an infinite list of random values instead of returning a new generator.

See `randomRs` for details.

getRandoms :: Random a => m [a] #

Plural variant of `getRandom`, producing an infinite list of random values instead of returning a new generator.

See `randoms` for details.

Instances

MonadRandom IO # |
Methods getRandomR :: Random a => (a, a) -> IO a # getRandom :: Random a => IO a # getRandomRs :: Random a => (a, a) -> IO [a] # getRandoms :: Random a => IO [a] #
MonadRandom m => MonadRandom (ListT m) # |
Methods getRandomR :: Random a => (a, a) -> ListT m a # getRandom :: Random a => ListT m a # getRandomRs :: Random a => (a, a) -> ListT m [a] # getRandoms :: Random a => ListT m [a] #
MonadRandom m => MonadRandom (MaybeT m) # |
Methods getRandomR :: Random a => (a, a) -> MaybeT m a # getRandom :: Random a => MaybeT m a # getRandomRs :: Random a => (a, a) -> MaybeT m [a] # getRandoms :: Random a => MaybeT m [a] #
(Error e, MonadRandom m) => MonadRandom (ErrorT e m) # |
Methods getRandomR :: Random a => (a, a) -> ErrorT e m a # getRandom :: Random a => ErrorT e m a # getRandomRs :: Random a => (a, a) -> ErrorT e m [a] # getRandoms :: Random a => ErrorT e m [a] #
MonadRandom m => MonadRandom (ExceptT e m) # |
Methods getRandomR :: Random a => (a, a) -> ExceptT e m a # getRandom :: Random a => ExceptT e m a # getRandomRs :: Random a => (a, a) -> ExceptT e m [a] # getRandoms :: Random a => ExceptT e m [a] #
MonadRandom m => MonadRandom (StateT s m) # |
Methods getRandomR :: Random a => (a, a) -> StateT s m a # getRandom :: Random a => StateT s m a # getRandomRs :: Random a => (a, a) -> StateT s m [a] # getRandoms :: Random a => StateT s m [a] #
MonadRandom m => MonadRandom (StateT s m) # |
Methods getRandomR :: Random a => (a, a) -> StateT s m a # getRandom :: Random a => StateT s m a # getRandomRs :: Random a => (a, a) -> StateT s m [a] # getRandoms :: Random a => StateT s m [a] #
(MonadRandom m, Monoid w) => MonadRandom (WriterT w m) # |
Methods getRandomR :: Random a => (a, a) -> WriterT w m a # getRandom :: Random a => WriterT w m a # getRandomRs :: Random a => (a, a) -> WriterT w m [a] # getRandoms :: Random a => WriterT w m [a] #
(MonadRandom m, Monoid w) => MonadRandom (WriterT w m) # |
Methods getRandomR :: Random a => (a, a) -> WriterT w m a # getRandom :: Random a => WriterT w m a # getRandomRs :: Random a => (a, a) -> WriterT w m [a] # getRandoms :: Random a => WriterT w m [a] #
MonadRandom m => MonadRandom (IdentityT * m) # |
Methods getRandomR :: Random a => (a, a) -> IdentityT * m a # getRandom :: Random a => IdentityT * m a # getRandomRs :: Random a => (a, a) -> IdentityT * m [a] # getRandoms :: Random a => IdentityT * m [a] #
(RandomGen g, Monad m) => MonadRandom (RandT g m) # |
Methods getRandomR :: Random a => (a, a) -> RandT g m a # getRandom :: Random a => RandT g m a # getRandomRs :: Random a => (a, a) -> RandT g m [a] # getRandoms :: Random a => RandT g m [a] #
(RandomGen g, Monad m) => MonadRandom (RandT g m) # |
Methods getRandomR :: Random a => (a, a) -> RandT g m a # getRandom :: Random a => RandT g m a # getRandomRs :: Random a => (a, a) -> RandT g m [a] # getRandoms :: Random a => RandT g m [a] #
MonadRandom m => MonadRandom (ContT * r m) # |
Methods getRandomR :: Random a => (a, a) -> ContT * r m a # getRandom :: Random a => ContT * r m a # getRandomRs :: Random a => (a, a) -> ContT * r m [a] # getRandoms :: Random a => ContT * r m [a] #
MonadRandom m => MonadRandom (ReaderT * r m) # |
Methods getRandomR :: Random a => (a, a) -> ReaderT * r m a # getRandom :: Random a => ReaderT * r m a # getRandomRs :: Random a => (a, a) -> ReaderT * r m [a] # getRandoms :: Random a => ReaderT * r m [a] #
(Monoid w, MonadRandom m) => MonadRandom (RWST r w s m) # |
Methods getRandomR :: Random a => (a, a) -> RWST r w s m a # getRandom :: Random a => RWST r w s m a # getRandomRs :: Random a => (a, a) -> RWST r w s m [a] # getRandoms :: Random a => RWST r w s m [a] #
(Monoid w, MonadRandom m) => MonadRandom (RWST r w s m) # |
Methods getRandomR :: Random a => (a, a) -> RWST r w s m a # getRandom :: Random a => RWST r w s m a # getRandomRs :: Random a => (a, a) -> RWST r w s m [a] # getRandoms :: Random a => RWST r w s m [a] #

# MonadSplit

class Monad m => MonadSplit g m | m -> g where #

The class `MonadSplit` proivides a way to specify a random number generator that can be split into two new generators.

This class is not very useful in practice: typically, one cannot actually do anything with a generator. It remains here to avoid breaking existing code unnecessarily. For a more practically useful interface, see `MonadInterleave`.

Minimal complete definition

getSplit

Methods

getSplit :: m g #

The `getSplit` operation allows one to obtain two distinct random number generators.

See `split` for details.

Instances

MonadSplit StdGen IO # |
Methods getSplit :: IO StdGen #
MonadSplit g m => MonadSplit g (MaybeT m) # |
Methods getSplit :: MaybeT m g #
MonadSplit g m => MonadSplit g (ListT m) # |
Methods getSplit :: ListT m g #
(Monoid w, MonadSplit g m) => MonadSplit g (WriterT w m) # |
Methods getSplit :: WriterT w m g #
(Monoid w, MonadSplit g m) => MonadSplit g (WriterT w m) # |
Methods getSplit :: WriterT w m g #
MonadSplit g m => MonadSplit g (StateT s m) # |
Methods getSplit :: StateT s m g #
MonadSplit g m => MonadSplit g (StateT s m) # |
Methods getSplit :: StateT s m g #
MonadSplit g m => MonadSplit g (IdentityT * m) # |
Methods getSplit :: IdentityT * m g #
MonadSplit g m => MonadSplit g (ExceptT e m) # |
Methods getSplit :: ExceptT e m g #
(Error e, MonadSplit g m) => MonadSplit g (ErrorT e m) # |
Methods getSplit :: ErrorT e m g #
(RandomGen g, Monad m) => MonadSplit g (RandT g m) # |
Methods getSplit :: RandT g m g #
(RandomGen g, Monad m) => MonadSplit g (RandT g m) # |
Methods getSplit :: RandT g m g #
MonadSplit g m => MonadSplit g (ReaderT * r m) # |
Methods getSplit :: ReaderT * r m g #
MonadSplit g m => MonadSplit g (ContT * r m) # |
Methods getSplit :: ContT * r m g #
(Monoid w, MonadSplit g m) => MonadSplit g (RWST r w s m) # |
Methods getSplit :: RWST r w s m g #
(Monoid w, MonadSplit g m) => MonadSplit g (RWST r w s m) # |
Methods getSplit :: RWST r w s m g #

# MonadInterleave

class MonadRandom m => MonadInterleave m where #

The class `MonadInterleave` proivides a convenient interface atop a `split` operation on a random generator.

Minimal complete definition

interleave

Methods

interleave :: m a -> m a #

If `x :: m a` is a computation in some random monad, then `interleave x` works by splitting the generator, running `x` using one half, and using the other half as the final generator state of `interleave x` (replacing whatever the final generator state otherwise would have been). This means that computation needing random values which comes after `interleave x` does not necessarily depend on the computation of `x`. For example:

    >>> evalRandIO $ snd <$> ((,) <$> undefined <*> getRandom)
    *** Exception: Prelude.undefined
    >>> evalRandIO $ snd <$> ((,) <$> interleave undefined <*> getRandom)
    6192322188769041625

This can be used, for example, to allow random computations to run in parallel, or to create lazy infinite structures of random values. In the example below, the infinite tree `randTree` cannot be evaluated lazily: even though it is cut off at two levels deep by `hew 2`, the random value in the right subtree still depends on generation of all the random values in the (infinite) left subtree, even though they are ultimately unneeded. Inserting a call to `interleave`, as in `randTreeI`, solves the problem: the generator splits at each `Node`, so random values in the left and right subtrees are generated independently.

    data Tree = Leaf | Node Int Tree Tree deriving Show

    hew :: Int -> Tree -> Tree
    hew 0 _    = Leaf
    hew _ Leaf = Leaf
    hew n (Node x l r) = Node x (hew (n-1) l) (hew (n-1) r)

    randTree :: Rand StdGen Tree
    randTree = Node <$> getRandom <*> randTree <*> randTree

    randTreeI :: Rand StdGen Tree
    randTreeI = interleave $ Node <$> getRandom <*> randTreeI <*> randTreeI

    >>> hew 2 <$> evalRandIO randTree
    Node 2168685089479838995 (Node (-1040559818952481847) Leaf Leaf) (Node ^CInterrupted.
    >>> hew 2 <$> evalRandIO randTreeI
    Node 8243316398511136358 (Node 4139784028141790719 Leaf Leaf) (Node 4473998613878251948 Leaf Leaf)

Instances

MonadInterleave m => MonadInterleave (ListT m) # |
Methods interleave :: ListT m a -> ListT m a #
MonadInterleave m => MonadInterleave (MaybeT m) # |
Methods interleave :: MaybeT m a -> MaybeT m a #
(Error e, MonadInterleave m) => MonadInterleave (ErrorT e m) # |
Methods interleave :: ErrorT e m a -> ErrorT e m a #
MonadInterleave m => MonadInterleave (ExceptT e m) # |
Methods interleave :: ExceptT e m a -> ExceptT e m a #
MonadInterleave m => MonadInterleave (StateT s m) # |
Methods interleave :: StateT s m a -> StateT s m a #
MonadInterleave m => MonadInterleave (StateT s m) # |
Methods interleave :: StateT s m a -> StateT s m a #
(Monoid w, MonadInterleave m) => MonadInterleave (WriterT w m) # |
Methods interleave :: WriterT w m a -> WriterT w m a #
(Monoid w, MonadInterleave m) => MonadInterleave (WriterT w m) # |
Methods interleave :: WriterT w m a -> WriterT w m a #
MonadInterleave m => MonadInterleave (IdentityT * m) # |
Methods interleave :: IdentityT * m a -> IdentityT * m a #
(Monad m, RandomGen g) => MonadInterleave (RandT g m) # |
Methods interleave :: RandT g m a -> RandT g m a #
(Monad m, RandomGen g) => MonadInterleave (RandT g m) # |
Methods interleave :: RandT g m a -> RandT g m a #
MonadInterleave m => MonadInterleave (ContT * r m) # |
Methods interleave :: ContT * r m a -> ContT * r m a #
MonadInterleave m => MonadInterleave (ReaderT * r m) # |
Methods interleave :: ReaderT * r m a -> ReaderT * r m a #
(Monoid w, MonadInterleave m) => MonadInterleave (RWST r w s m) # |
Methods interleave :: RWST r w s m a -> RWST r w s m a #
(Monoid w, MonadInterleave m) => MonadInterleave (RWST r w s m) # |
Methods interleave :: RWST r w s m a -> RWST r w s m a #

# Sampling functions

fromList :: MonadRandom m => [(a, Rational)] -> m a #

Sample a random value from a weighted list. The list must be non-empty and the total weight must be non-zero.

fromListMay :: MonadRandom m => [(a, Rational)] -> m (Maybe a) #

Sample a random value from a weighted list. Return `Nothing` if the list is empty or the total weight is zero.

uniform :: (Foldable t, MonadRandom m) => t a -> m a #

Sample a value uniformly from a nonempty collection of elements.

uniformMay :: (Foldable t, MonadRandom m) => t a -> m (Maybe a) #

Sample a value uniformly from a collection of elements. Return `Nothing` if the collection is empty.

weighted :: (Foldable t, MonadRandom m) => t (a, Rational) -> m a #

Sample a random value from a weighted nonempty collection of elements. Crashes with a call to `error` if the collection is empty or the total weight is zero.

weightedMay :: (Foldable t, MonadRandom m) => t (a, Rational) -> m (Maybe a) #

Sample a random value from a weighted collection of elements. Returns `Nothing` if the collection is empty or the total weight is zero.