Random number generating in haskell - haskell

When running genRandTupe I continuously get the same random numbers, however when running genrandList with gen as the argument i get a new set of numbers every time. How would I solve this? Why doesn't g = newStdGen generate a new random number?
import System.Random
import System.IO.Unsafe
type RandTupe = (Int,Int)
genRandTupe :: IO RandTupe
genRandTupe = let [a,b] = genrandList g in return (a,b) where g = newStdGen
genrandList gen = let g = unsafePerformIO gen in take 2 (randomRs (1, 20) g)
gen = newStdGen

genRandTupe is a constant applicative form. That means any local variables in its let or where blocks are memoised. Usually quite a convenient feat!
In your case, it means that the list [a,b] is only computed once in your whole program. The way it is computed is actually illegal (don't use unsafePerformIO!), but it doesn't really matter because it only happens once anyway. Wrapping this constant tuple then into IO with return is actually completely superfluent, you could as well have written
genRandTupe' :: RandTupe
genRandTupe' = let [a,b] = genrandList g in (a,b)
where g = newStdGen
OTOH, when you evaluate genrandList gen (not a CAF) in multiple separate places, the result will not necessarily be stored. Instead, that function is calculated anew, using unsafePerformIO to unsafely modify the global state (or maybe not... the compiler is actually free to optimise this away since, you know, genRandList is supposedly a pure function...) and therefore yield a different result each time.
The correct thing, of course, is to stay the heck away from unsafePerformIO. There's actually no need at all to do IO in genRandList, since it already accepts a random generator... just bind that generator out from IO before passing it:
genRandTupe'' :: IO RandTupe
genRandTupe'' = do
g <- newStdGen
let [a,b] = genrandList g
return (a,b)
randListFrom :: RandomGen g => g -> [Int]
randListFrom g = take 2 (randomRs (1, 20) g)
Note that, because the let [a,b] = ... now is in a do block, it's now in the IO monad, decoupled from the CAF closure of genRandTupe''.

Related

Haskell random numbers

I am trying to generate a sample of random numbers in Haskell
import System.Random
getSample n = take n $ randoms g where
g = newStdGen
but it seems I am not quite using newStdGen the right way. What am I missing?
First off, you probably don't want to use newStdGen. The biggest problem is that you'll get a different seed every time you run your program, so no results will be reproducible. In my opinion, mkStdGen is a better choice as it requires you to give it a seed. This means you will get the same sequence of (pseudo)random numbers every time. If you want a different sequence, just change the seed.
The second problem with newStdGen is that since it's impure, you'll end up in the IO monad which can be a bit inconvenient.
sample :: Int -> IO [Int]
sample n = do
gen <- newStdGen
return $ take n $ randoms gen
You can use do-notation to 'extract' the values and then sum them:
main :: IO ()
main = do
xs <- sample 10
s = sum xs
print s
Or you could 'fmap' the function over the result (but notice that at some point you will probably need to extract the value):
main :: IO ()
main = do
s <- fmap sum $ sample 10
print s
The fmap function is a generalized version of map. Just like map applies a function to the values inside a list, fmap can apply a function to values inside IO.
Another problem with this sample function is that if we call it again, it starts with a fresh seed instead of continuing the previous (pseudo)random sequence. Again, this make reproducing results impossible. In order to fix this problem, we need to pass in the seed and return a new seed. Unfortunately, randoms does not return the next seed for us, so we'll have to write this from scratch using random.
sample :: Int -> StdGen -> ([Int],StdGen)
sample n seed1 = case n of
0 -> ([],seed1)
k -> let (rs,seed2) = sample (k-1) seed1
(r, seed3) = random seed2
in ((r:rs),seed3)
Our main function is now
main :: IO ()
main = do
let seed1 = mkStdGen 123456
(xs,seed2) = sample 10 seed1
s = sum xs
(ys,seed3) = sample 10 seed2
t = sum ys
print s
print t
I know this seems like an awful lot of work just to to use random numbers, but the advantages are worth it. We can generate all of our randomness with a single seed which guarantees that the results can be reproduced.
Of course, this being Haskell, we can take advantage of Monads to get rid of all the manual threading of the seed values. This is a slightly more advanced method, but well worth learning since monads are ubiquitous in Haskell code.
We need these imports:
import System.Random
import Control.Monad
import Control.Applicative
Then we'll create a newtype which represents the action of turning a seed into a value and the next seed.
newtype Rand a = Rand { runRand :: StdGen -> (a,StdGen) }
We need Functor and Applicative instances or GHC will complain, but we can avoid implementing them for this example.
instance Functor Rand
instance Applicative Rand
And now for the Monad instance. This is where the magic happens. The >>= function (called bind) is the one place where we specify how to thread the seed value through the computation.
instance Monad Rand where
return x = Rand ( \seed -> (x,seed) )
ra >>= f = Rand ( \s1 -> let (a,s2) = runRand ra s1
in runRand (f a) s2 )
newRand :: Rand Int
newRand = Rand ( \seed -> random seed )
Now our sample function is extremely simple! We can take advantage of replicateM from Control.Monad which repeats a given action and accumulates the results in a list. All that funny business with the seed values is taken care of behind the scenes
sample :: Int -> Rand [Int]
sample n = replicateM n newRand
main :: IO ()
main = do
let seed1 = mkStdGen 124567
(xs,seed2) = runRand (sample 10) seed1
s = sum xs
print s
We can even stay inside the Rand monad if we need to generate random values multiple times.
main :: IO ()
main = do
let seed1 = mkStdGen 124567
(xs,seed2) = flip runRand seed1 $ do
x <- newRand
bs <- sample 5
cs <- sample 10
return $ x : (bs ++ cs)
s = sum xs
print s
I hope this helps!

Write list of random numbers to file. No Instance for (Show (IO a0))

I am trying to write to file a list of random Integers in a file. There seems to be a problem with writeFile here. When I use my function randomFile it says no instance for (Show (IO a0)). I see writeFile doesn't print anything to screen but IO(), so when I call the function randomFile 1 2 3 it says no Instance for Show (IO a0) but actually I just want to execute the function and not have to print anything but how can I avoid this problem. I might be making a lot of errors here. Any help.
import Control.Monad
import Control.Applicative
import System.Random
randNo mind maxd = randomRIO (mind,maxd)
randomFile mind maxd noe = do
let l=(replicate (fromInteger(noe ^ noe)) ( mind `randNo` maxd))
writeFile "RFile.txt" (show l)
I think you have a misunderstanding of what IO is. If you haven't done it, I strongly recommend going through the Input and Output section of Learn You a Haskell.
IO doesn't necessarily have anything to do with print. In Haskell every entry in memory that was made by your own code is considered "pure" while any entry that touches the rest of the computer lives in IO (with some exceptions you will learn about over time).
We model IO using something called a Monad. Which you will learn more about the longer you do Haskell. To understand this, let's look at an example of some code that does and doesn't use IO:
noIOused :: Int -> Int
noIOused x = x + 5
usesIO :: Int -> IO Int
usesIO x = print x >> return (x + 5)
usesIO2 :: Int -> IO Int
usesIO2 x = do
print x
return (x + 5)
The first function is "pure". The second and third functions have an IO "effect" that comes in the form of printing to the screen. usesIO and usesIO2 are just 2 different ways of doing the same thing (it's the same code but with different syntax). I'll use the second format, called do notation from here.
Here are some other ways you could have had IO effects:
add5WithFile :: Int -> IO Int
add5WithFile x = do
writeFile "someFile.txt" (show x)
return (x + 5)
Notice that in that function we didn't print anything, we wrote a file. But writing a file has a side effect and interacts with the rest of the system. So any value we return has to get wrapped in IO.
addRandom :: Int -> IO Int
addRandom x = do
y <- randomRIO (1,10)
return (x + y)
In addRandom we called randomRIO (1,10). But the problem is that randomRIO doesn't return an Int. It returns an IO Int. Why? Because in order to get true randomness we need to interact with the system in some way. To get around that, we have to temporarily strip away the IO. That's where this line comes in:
y <- randomRIO (1,10)
That <- arrow tells us that we want a y value outside of IO. For as long as we remain inside the do syntax that y value is going to be "pure". Now we can use it just like any other value.
So for example we couldn't do this:
let w = x + (randomRIO (1,10))
Because that would be trying to add Int to IO Int. And unfortunately our + function doesn't know how to do that. So first we have to "bind" the result of randomRIO to y before we can add it to x.
Now let's look at your code:
let l=(replicate (fromInteger(noe ^ noe)) ( mind `randNo` maxd))
writeFile "RFile.txt" (show l)
The type of l is actually IO a0. It's a0 because you haven't told the compiler what kind of number you want. So it doesn't know if you want a fraction, a double, a big integer or whatever.
So the first problem is to let the compiler know a little bit more about what kind of random number you want. We do this by adding a type annotation:
randNo :: Int -> Int -> IO Int
randNo mind maxd = randomRIO (mind,maxd)
Now both you and the compiler knows what kind of value randNo is.
Now we need to "bind" that value inside of the do notation to temporarily escape IO. You might think that would be simple, like this:
randomFile mind maxd noe = do
l <- replicate (fromInteger(noe ^ noe)) ( mind `randNo` maxd)
writeFile "RFile.txt" (show l)
Surely that will "bind" the IO Int to l right? Unfortunately not. The problem here is that replicate is a function of the form Int -> a -> [a]. That is, given a number and a type, it will give you a list of that type.
If you give replicate an IO Int it's going to make [IO Int]. That actually looks more like this: List (IO Int) except we use [] as syntactic sugar for lists. Unfortunately if we want to "bind" an IO value to something with <- it has to be the out-most type.
So what you need is a way to turn an [IO Int] into an IO [Int]. There are two ways to do that. If we put \[IO a\] -> IO \[a\] into Hoogle we get this:
sequence :: Monad m => [m a] -> m [a]
As I mentioned before, we generalise IO to something called a Monad. Which isn't really that big a deal, we could pretend that sequence has this signature: sequence :: [IO a] -> IO [a] and it would be the same thing just specialised to IO.
Now your function would be done like this:
randomFile mind maxd noe = do
l <- sequence (replicate (fromInteger(noe ^ noe)) ( mind `randNo` maxd))
writeFile "RFile.txt" (show l)
But a sequence followed by replicate is something people have to do all the time. So someone went and made a function called replicateM:
replicateM :: Monad m => Int -> m a -> m [a]
Now we can write your function like this:
randomFile mind maxd noe = do
l <- replicateM (fromInteger(noe ^ noe)) ( mind `randNo` maxd)
writeFile "RFile.txt" (show l)
And for some real Haskell magic, you can write all 3 lines of code in a single line, like this:
randomFile mind maxd noe = randomRIO >>= writeFile "RFile.txt" . replicateM (fromInteger(noe ^ noe))
If that looks like gibberish to you, then there's a lot you need to learn. Here is the suggested path:
If you haven't already, start from the beginning with Learn You a Haskell
Then learn about how You could have invented Monads
Then learn more about how to use randomness in Haskell
Finally see if you can complete the 20 intermediate Haskell exercises

MonadRandom: why stack overflow happens?

This question is certainly for stackoverflow.com
here is the sample
module Main where
import Control.Monad.Random
import Control.Exception
data Tdata = Tdata Int Int Integer String
randomTdata :: (Monad m, RandomGen g) => RandT g m Tdata
randomTdata = do
a <- getRandom
b <- getRandom
c <- getRandom
return $ Tdata a b c "random"
manyTdata :: IO [Tdata]
manyTdata = do
g <- newStdGen
evalRandT (sequence $ repeat randomTdata) g
main = do
a <- manyTdata
b <- evaluate $ take 1 a
return ()
after compilation this return
Stack space overflow: current size 8388608 bytes.
Use `+RTS -Ksize -RTS' to increase it
How can it happen ? Is MonadRandom not lazy or what else ? And how to define the cause of stack overflow in cases like that ?
The issue arises because you are building IO into your manyTdata function.
The monad transformer ends up being of type RandT g IO Tdata. Because each element of
your infinite list can consist of IO actions, the entirety of the infinite list
returned by manyTdata must be evaluated completely before the function can return
any results.
The simplest solution would be to use Rand instead of RandT, as using the tranformer
isn't really useful here, anyway; you could also change the base monad to something like
the Identity monad by changing manyTdata to
manyTdata :: IO [Tdata]
manyTdata = do
g <- newStdGen
return $ runIdentity $ evalRandT (sequence $ repeat randomTdata) g
Which will terminate in a finite amount of time. The error concerning your stack size
is simply a result of recursively expanding your list of IO actions. Your code says to sequence all of these actions, so they all have to be performed, it has nothing to do with laziness.
Something else to think about, rather than using randomTdata, consider
making Tdata an instance of the Random class.

Is mapM in Haskell strict? Why does this program get a stack overflow?

The following program terminates correctly:
import System.Random
randomList = mapM (\_->getStdRandom (randomR (0, 50000::Int))) [0..5000]
main = do
randomInts <- randomList
print $ take 5 randomInts
Running:
$ runhaskell test.hs
[26156,7258,29057,40002,26339]
However, feeding it with an infinite list, the program never terminates, and when compiled, eventually gives a stack overflow error!
import System.Random
randomList = mapM (\_->getStdRandom (randomR (0, 50000::Int))) [0..]
main = do
randomInts <- randomList
print $ take 5 randomInts
Running,
$ ./test
Stack space overflow: current size 8388608 bytes.
Use `+RTS -Ksize -RTS' to increase it.
I expected the program to lazily evaluate getStdRandom each time I pick an item off the list, finishing after doing so 5 times. Why is it trying to evaluate the whole list?
Thanks.
Is there a better way to get an infinite list of random numbers? I want to pass this list into a pure function.
EDIT: Some more reading revealed that the function
randomList r = do g <- getStdGen
return $ randomRs r g
is what I was looking for.
EDIT2: after reading camccann's answer, I realized that getStdGen is getting a new seed on every call. Instead, better to use this function as a simple one-shot random list generator:
import System.Random
randomList :: Random a => a -> a -> IO [a]
randomList r g = do s <- newStdGen
return $ randomRs (r,g) s
main = do r <- randomList 0 (50::Int)
print $ take 5 r
But I still don't understand why my mapM call did not terminate. Evidently not related to random numbers, but something to do with mapM maybe.
For example, I found that the following also does not terminate:
randomList = mapM (\_->return 0) [0..]
main = do
randomInts <- randomList
print $ take 50000 randomInts
What gives? By the way, IMHO, the above randomInts function should be in System.Random. It's extremely convenient to be able to very simply generate a random list in the IO monad and pass it into a pure function when needed, I don't see why this should not be in the standard library.
Random numbers in general are not strict, but monadic binding is--the problem here is that mapM has to sequence the entire list. Consider its type signature, (a -> m b) -> [a] -> m [b]; as this implies, what it does is first map the list of type [a] into a list of type [m b], then sequence that list to get a result of type m [b]. So, when you bind the result of applying mapM, e.g. by putting it on the right-hand side of <-, what this means is "map this function over the list, then execute each monadic action, and combine the results back into a single list". If the list is infinite, this of course won't terminate.
If you simply want a stream of random numbers, you need to generate the list without using a monad for each number. I'm not entirely sure why you've used the design you have, but the basic idea is this: Given a seed value, use a pseudo-random number generator to produce a pair of 1) a random number 2) a new seed, then repeat with the new seed. Any given seed will of course provide the same sequence each time. So, you can use the function getStdGen, which will provide a fresh seed in the IO monad; you can then use that seed to create an infinite sequence in completely pure code.
In fact, System.Random provides functions for precisely that purpose, randoms or randomRs instead of random and randomR.
If for some reason you want to do it yourself, what you want is essentially an unfold. The function unfoldr from Data.List has the type signature (b -> Maybe (a, b)) -> b -> [a], which is fairly self-explanatory: Given a value of type b, it applies the function to get either something of type a and a new generator value of type b, or Nothing to indicate the end of the sequence.
You want an infinite list, so will never need to return Nothing. Thus, partially applying randomR to the desired range and composing it with Just gives this:
Just . randomR (0, 50000::Int) :: (RandomGen a) => a -> Maybe (Int, a)
Feeding that into unfoldr gives this:
unfoldr (Just . randomR (0, 50000::Int)) :: (RandomGen a) => a -> [Int]
...which does exactly as it claims: Given an instance of RandomGen, it will produce an infinite (and lazy) list of random numbers generated from that seed.
I would do something more like this, letting randomRs do the work with an initial RandomGen:
#! /usr/bin/env runhaskell
import Control.Monad
import System.Random
randomList :: RandomGen g => g -> [Int]
randomList = randomRs (0, 50000)
main :: IO ()
main = do
randomInts <- liftM randomList newStdGen
print $ take 5 randomInts
As for the laziness, what's happening here is that mapM is (sequence . map)
Its type is: mapM :: (Monad m) => (a -> m b) -> [a] -> m [b]
It's mapping the function, giving a [m b] and then needs to execute all those actions to make an m [b]. It's the sequence that'll never get through the infinite list.
This is explained better in the answers to a prior question: Is Haskell's mapM not lazy?

Haskell and random numbers

I've been messing with Haskell few days and stumbled into a problem.
I need a method that returns a random list of integers ( Rand [[Int]] ).
So, I defined a type: type Rand a = StdGen -> (a, StdGen).
I was able to produce Rand IO Integer and Rand [IO Integer] ( (returnR lst) :: StdGen -> ([IO Integer], StdGen) ) somehow. Any tips how to produce Rand [[Int]]?
How to avoid the IO depends on why it's being introduced in the first place. While pseudo-random number generators are inherently state-oriented, there's no reason IO needs to be involved.
I'm going to take a guess and say that you're using newStdGen or getStdGen to get your initial PRNG. If that's the case, then there's no way to completely escape IO. You could instead seed the PRNG directly with mkStdGen, keeping in mind that the same seed will result in the same "random" number sequence.
More likely, what you want to do is get a PRNG inside IO, then pass that as an argument to a pure function. The entire thing will still be wrapped in IO at the end, of course, but the intermediate computations won't need it. Here's a quick example to give you the idea:
import System.Random
type Rand a = StdGen -> (a, StdGen)
getPRNG = do
rng <- newStdGen
let x = usePRNG rng
print x
usePRNG :: StdGen -> [[Int]]
usePRNG rng = let (x, rng') = randomInts 5 rng
(y, _) = randomInts 10 rng'
in [x, y]
randomInts :: Int -> Rand [Int]
randomInts 0 rng = ([], rng)
randomInts n rng = let (x, rng') = next rng
(xs, rng'') = randomInts (n - 1) rng'
in (x:xs, rng'')
You might notice that the code using the PRNG gets pretty ugly due to passing the current value back and forth constantly. It's also potentially error prone, since it'd be easy to accidentally reuse an old value. As mentioned above, using the same PRNG value will give the same sequence of numbers, which is usually not what you want. Both problems are a perfect example of where it makes sense to use a State monad--which is getting off topic here, but you may want to look into it next.
You are recreating MonadRandom on Hackage. If this is more than just an experiment to see if you can do it, you might want to use that library instead.
If you want to get an infinite list of Integers you're going to run into problems as you won't ever get a StdGen value back out. What you want to do here is split the StdGen first, pass one half out again and 'use up' the other half to generate an infinite list of integers. Something like this:
infiniteRandomInts :: Rand [Int]
infiniteRandomInts g = (ints, g2) where
(g1,g2) = split g
ints = randoms g1
However, if you then repeat this approach to get an infinite matrix of Integers (which you seem to want, by using Rand [[Int]]), you might run into problems of a statistical nature: I don't know how well StdGen deals with repeated splitting. Maybe another implementation of RandomGen might be better, or you could try to use some sort of diagonal walk to turn a [Int] into a [[Int]].
Using monadic notation, you should be able to write something like
randomList gen = do
randomLength <- yourRandomInteger
loop gen (randomLength + 1)
where
loop gen 1 = gen
loop gen n = do { x <- gen; xs <- loop gen (n - 1); return (x:xs) }
And with this
randomInts :: Rand [Int]
randomInts = randomList yourRandomInteger
randomLists :: Rand [[Int]]
randomLists = randomList randomInts
Concerning the monadic computations itself, take a look at this article. Note that random generators are pure, you shouldn't need any IO just for this purpose.

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