Copyright	(c) Brent Yorgey 2016
License	BSD3 (see LICENSE)
Maintainer	byorgey@gmail.com
Stability	experimental
Portability	non-portable (multi-param classes, functional dependencies, undecidable instances)
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Monad.Trans.Random.Lazy

Contents

The Rand monad transformer
The RandT monad transformer
Lifting other operations
StatefulGen interface
Examples
- Random monads

Description

Lazy random monads, passing a random number generator through a computation. See below for examples.

For a strict version with the same interface, see Control.Monad.Trans.Random.Strict.

Synopsis

type Rand g = RandT g Identity
liftRand :: (g -> (a, g)) -> Rand g a
runRand :: Rand g a -> g -> (a, g)
evalRand :: Rand g a -> g -> a
execRand :: Rand g a -> g -> g
mapRand :: ((a, g) -> (b, g)) -> Rand g a -> Rand g b
withRand :: (g -> g) -> Rand g a -> Rand g a
evalRandIO :: Rand StdGen a -> IO a
data RandT g (m :: Type -> Type) a
liftRandT :: (g -> m (a, g)) -> RandT g m a
runRandT :: RandT g m a -> g -> m (a, g)
evalRandT :: Monad m => RandT g m a -> g -> m a
execRandT :: Monad m => RandT g m a -> g -> m g
mapRandT :: (m (a, g) -> n (b, g)) -> RandT g m a -> RandT g n b
withRandT :: forall g (m :: Type -> Type) a. (g -> g) -> RandT g m a -> RandT g m a
liftCallCC :: CallCC m (a, g) (b, g) -> CallCC (RandT g m) a b
liftCallCC' :: CallCC m (a, g) (b, g) -> CallCC (RandT g m) a b
liftCatch :: Catch e m (a, g) -> Catch e (RandT g m) a
liftListen :: Monad m => Listen w m (a, g) -> Listen w (RandT g m) a
liftPass :: Monad m => Pass w m (a, g) -> Pass w (RandT g m) a
evalRandTIO :: MonadIO m => RandT StdGen m a -> m a
data RandGen g = RandGen
withRandGen :: g -> (RandGen g -> RandT g m a) -> m (a, g)
withRandGen_ :: Monad m => g -> (RandGen g -> RandT g m a) -> m a

The Rand monad transformer

type Rand g = RandT g Identity Source #

A random monad parameterized by the type g of the generator to carry.

The return function leaves the generator unchanged, while >>= uses the final generator of the first computation as the initial generator of the second.

liftRand Source #

Arguments

:: (g -> (a, g))	pure random transformer
-> Rand g a	equivalent generator-passing computation

Construct a random monad computation from a function. (The inverse of runRand.)

runRand Source #

Arguments

:: Rand g a	generator-passing computation to execute
-> g	initial generator
-> (a, g)	return value and final generator

Unwrap a random monad computation as a function. (The inverse of liftRand.)

evalRand Source #

Arguments

:: Rand g a	generator-passing computation to execute
-> g	initial generator
-> a	return value of the random computation

Evaluate a random computation with the given initial generator and return the final value, discarding the final generator.

```
evalRand m s = fst (runRand m s)
```

execRand Source #

Arguments

:: Rand g a	generator-passing computation to execute
-> g	initial generator
-> g	final generator

Evaluate a random computation with the given initial generator and return the final generator, discarding the final value.

```
execRand m s = snd (runRand m s)
```

mapRand :: ((a, g) -> (b, g)) -> Rand g a -> Rand g b Source #

Map both the return value and final generator of a computation using the given function.

```
runRand (mapRand f m) = f . runRand m
```

withRand :: (g -> g) -> Rand g a -> Rand g a Source #

withRand f m executes action m on a generator modified by applying f.

```
withRand f m = modify f >> m
```

evalRandIO :: Rand StdGen a -> IO a Source #

Evaluate a random computation in the IO monad, splitting the global standard generator to get a new one for the computation.

The RandT monad transformer

data RandT g (m :: Type -> Type) a Source #

A random transformer monad parameterized by:

g - The generator.
m - The inner monad.

The return function leaves the generator unchanged, while >>= uses the final generator of the first computation as the initial generator of the second.

Instances

Instances details

(MonadReader r m, MonadWriter w m, MonadState s m) => MonadRWS r w s (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

(RandomGen g, Monad m) => MonadSplit g (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

getSplit :: RandT g m g Source #

MonadError e m => MonadError e (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

throwError :: e -> RandT g m a

catchError :: RandT g m a -> (e -> RandT g m a) -> RandT g m a

MonadReader r m => MonadReader r (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

ask :: RandT g m r

local :: (r -> r) -> RandT g m a -> RandT g m a

reader :: (r -> a) -> RandT g m a

MonadState s m => MonadState s (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

get :: RandT g m s

put :: s -> RandT g m ()

state :: (s -> (a, s)) -> RandT g m a

MonadWriter w m => MonadWriter w (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

writer :: (a, w) -> RandT g m a

tell :: w -> RandT g m ()

listen :: RandT g m a -> RandT g m (a, w)

pass :: RandT g m (a, w -> w) -> RandT g m a

MonadTrans (RandT g) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

lift :: Monad m => m a -> RandT g m a #

(Monad m, RandomGen g) => RandomGenM (RandGen g) g (RandT g m) Source #

Since: 0.5.3

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

applyRandomGenM :: (g -> (a, g)) -> RandGen g -> RandT g m a

(Monad m, RandomGen g) => StatefulGen (RandGen g) (RandT g m) Source #

Since: 0.5.3

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

uniformWord32R :: Word32 -> RandGen g -> RandT g m Word32

uniformWord64R :: Word64 -> RandGen g -> RandT g m Word64

uniformWord8 :: RandGen g -> RandT g m Word8

uniformWord16 :: RandGen g -> RandT g m Word16

uniformWord32 :: RandGen g -> RandT g m Word32

uniformWord64 :: RandGen g -> RandT g m Word64

uniformShortByteString :: Int -> RandGen g -> RandT g m ShortByteString

(Monad m, RandomGen g) => MonadInterleave (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

interleave :: RandT g m a -> RandT g m a Source #

(RandomGen g, Monad m) => MonadRandom (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

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

getRandom :: Random a => RandT g m a Source #

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

getRandoms :: Random a => RandT g m [a] Source #

MonadIO m => MonadIO (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

liftIO :: IO a -> RandT g m a #

MonadPlus m => Alternative (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

empty :: RandT g m a

(<|>) :: RandT g m a -> RandT g m a -> RandT g m a

some :: RandT g m a -> RandT g m [a]

many :: RandT g m a -> RandT g m [a]

Monad m => Applicative (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

pure :: a -> RandT g m a

(<*>) :: RandT g m (a -> b) -> RandT g m a -> RandT g m b

liftA2 :: (a -> b -> c) -> RandT g m a -> RandT g m b -> RandT g m c

(*>) :: RandT g m a -> RandT g m b -> RandT g m b

(<*) :: RandT g m a -> RandT g m b -> RandT g m a

Functor m => Functor (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

fmap :: (a -> b) -> RandT g m a -> RandT g m b #

(<$) :: a -> RandT g m b -> RandT g m a #

Monad m => Monad (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

(>>=) :: RandT g m a -> (a -> RandT g m b) -> RandT g m b #

(>>) :: RandT g m a -> RandT g m b -> RandT g m b #

return :: a -> RandT g m a #

MonadPlus m => MonadPlus (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

mzero :: RandT g m a #

mplus :: RandT g m a -> RandT g m a -> RandT g m a #

MonadFail m => MonadFail (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

fail :: String -> RandT g m a #

MonadFix m => MonadFix (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

mfix :: (a -> RandT g m a) -> RandT g m a #

MonadCont m => MonadCont (RandT g m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Methods

callCC :: ((a -> RandT g m b) -> RandT g m a) -> RandT g m a

PrimMonad m => PrimMonad (RandT s m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

Associated Types

type PrimState (RandT s m)
Instance details Defined in Control.Monad.Trans.Random.Lazy type PrimState (RandT s m) = PrimState m

Methods

primitive :: (State# (PrimState (RandT s m)) -> (# State# (PrimState (RandT s m)), a #)) -> RandT s m a

type PrimState (RandT s m) Source #

Instance details

Defined in Control.Monad.Trans.Random.Lazy

type PrimState (RandT s m) = PrimState m

liftRandT Source #

Arguments

:: (g -> m (a, g))	impure random transformer
-> RandT g m a	equivalent generator-passing computation

Construct a random monad computation from an impure function. (The inverse of runRandT.)

runRandT Source #

Arguments

:: RandT g m a	generator-passing computation to execute
-> g	initial generator
-> m (a, g)	return value and final generator

Unwrap a random monad computation as an impure function. (The inverse of liftRandT.)

evalRandT :: Monad m => RandT g m a -> g -> m a Source #

Evaluate a random computation with the given initial generator and return the final value, discarding the final generator.

evalRandT m g = liftM fst (runRandT m g)

execRandT :: Monad m => RandT g m a -> g -> m g Source #

Evaluate a random computation with the given initial generator and return the final generator, discarding the final value.

execRandT m g = liftM snd (runRandT m g)

mapRandT :: (m (a, g) -> n (b, g)) -> RandT g m a -> RandT g n b Source #

Map both the return value and final generator of a computation using the given function.

runRandT (mapRandT f m) = f . runRandT m

withRandT :: forall g (m :: Type -> Type) a. (g -> g) -> RandT g m a -> RandT g m a Source #

withRandT f m executes action m on a generator modified by applying f.

```
withRandT f m = modify f >> m
```

Lifting other operations

liftCallCC :: CallCC m (a, g) (b, g) -> CallCC (RandT g m) a b Source #

Uniform lifting of a callCC operation to the new monad. This version rolls back to the original state on entering the continuation.

liftCallCC' :: CallCC m (a, g) (b, g) -> CallCC (RandT g m) a b Source #

In-situ lifting of a callCC operation to the new monad. This version uses the current state on entering the continuation. It does not satisfy the uniformity property (see Control.Monad.Signatures).

liftCatch :: Catch e m (a, g) -> Catch e (RandT g m) a Source #

Lift a catchE operation to the new monad.

liftListen :: Monad m => Listen w m (a, g) -> Listen w (RandT g m) a Source #

Lift a listen operation to the new monad.

liftPass :: Monad m => Pass w m (a, g) -> Pass w (RandT g m) a Source #

Lift a pass operation to the new monad.

evalRandTIO :: MonadIO m => RandT StdGen m a -> m a Source #

Evaluate a random computation that is embedded in the IO monad, splitting the global standard generator to get a new one for the computation.

StatefulGen interface

data RandGen g Source #

A proxy that carries information about the type of generator to use with RandT monad and its StatefulGen instance.

Since: 0.5.3

Constructors

RandGen

Instances

Instances details

(Monad m, RandomGen g) => RandomGenM (RandGen g) g (RandT g m)	Since: 0.5.3
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods applyRandomGenM :: (g -> (a, g)) -> RandGen g -> RandT g m a
(Monad m, RandomGen g) => RandomGenM (RandGen g) g (RandT g m) Source #	Since: 0.5.3
Instance details Defined in Control.Monad.Trans.Random.Strict Methods applyRandomGenM :: (g -> (a, g)) -> RandGen g -> RandT g m a
(Monad m, RandomGen g) => StatefulGen (RandGen g) (RandT g m)	Since: 0.5.3
Instance details Defined in Control.Monad.Trans.Random.Lazy Methods uniformWord32R :: Word32 -> RandGen g -> RandT g m Word32 uniformWord64R :: Word64 -> RandGen g -> RandT g m Word64 uniformWord8 :: RandGen g -> RandT g m Word8 uniformWord16 :: RandGen g -> RandT g m Word16 uniformWord32 :: RandGen g -> RandT g m Word32 uniformWord64 :: RandGen g -> RandT g m Word64 uniformShortByteString :: Int -> RandGen g -> RandT g m ShortByteString
(Monad m, RandomGen g) => StatefulGen (RandGen g) (RandT g m) Source #	Since: 0.5.3
Instance details Defined in Control.Monad.Trans.Random.Strict Methods uniformWord32R :: Word32 -> RandGen g -> RandT g m Word32 uniformWord64R :: Word64 -> RandGen g -> RandT g m Word64 uniformWord8 :: RandGen g -> RandT g m Word8 uniformWord16 :: RandGen g -> RandT g m Word16 uniformWord32 :: RandGen g -> RandT g m Word32 uniformWord64 :: RandGen g -> RandT g m Word64 uniformShortByteString :: Int -> RandGen g -> RandT g m ShortByteString

withRandGen Source #

Arguments

:: g	initial generator
-> (RandGen g -> RandT g m a)
-> m (a, g)	return value and final generator

A RandT runner that allows using it with StatefulGen restricted actions. Returns the outcome of random computation and the new pseudo-random-number generator

>>> withRandGen (mkStdGen 2021) uniformM :: IO (Int, StdGen)
(6070831465987696718,StdGen {unStdGen = SMGen 4687568268719557181 4805600293067301895})

Since: 0.5.3

withRandGen_ Source #

Arguments

:: Monad m
=> g	initial generator
-> (RandGen g -> RandT g m a)
-> m a	return value and final generator

Same as withRandGen, but discards the resulting generator.

>>> withRandGen_ (mkStdGen 2021) uniformM :: IO Int
6070831465987696718

Since: 0.5.3

Examples

Random monads

The die function simulates the roll of a die, picking a number between 1 and 6, inclusive, and returning it in the Rand monad transformer. Notice that this code will work with any random number generator g.

die :: (RandomGen g) => Rand g Int
die = getRandomR (1, 6)

The dice function uses replicate and sequence to simulate the roll of n dice.

dice :: (RandomGen g) => Int -> Rand g [Int]
dice n = sequence (replicate n die)

To extract a value from the Rand monad transformer, we can use evalRandIO.

main = do
  values <- evalRandIO (dice 2)
  putStrLn (show values)