Copyright (c) Brent Yorgey 2016 BSD3 (see LICENSE) byorgey@gmail.com Safe Haskell2010

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 Source #

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

Methods

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

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 Source #

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] Source #

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] Source #

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

See randoms for details.

Instances

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

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 Source #

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

See split for details.

Instances

class MonadRandom m => MonadInterleave m where Source #

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 Source #

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

# Sampling functions

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

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) Source #

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 Source #

Sample a value uniformly from a nonempty collection of elements.

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

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 Source #

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) Source #

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