SIMPLE random number generation

Question

I'm writing this after a good while of frustrating research, and I'm hoping someone here can enlighten me about the topic.

I want to generate a simple random number in a haskell function, but alas, this seems impossible to do without all sorts of non-trivial elements, such as Monads, asignation in "do", creating generators, etc.

Ideally I was looking for an equivalent of C's "rand()". But after much searching I'm pretty convinced there is no such thing, because of how the language is designed. (If there is, please someone enlighten me). As that doesn't seem feasible, I'd like to find a way to get a random number for my particular problem, and a general explanation on how it works to get a random number.

prefixGenerator :: (Ord a, Arbitrary a) => Gen ([a],[a])
prefixGenerator = frequency [ 
    (1, return ([],[])),
    (2, do {
            xs1 <- orderedListEj13 ;
            xs2 <- orderedListEj13 ;
            return (xs1,xs2)
       }),
    (2, do {                
            xs2 <- orderedListEj13 ;
            return ((take RANDOMNUMBERHERE xs2),xs2)
       })
    ]

I'm trying to get to grips with QuickCheck but my inability to use random numbers is making it hard. I've tried something like this (by putting an drawInt 0 (length xs2) instead of RANDOMNUMBERHERE)but I get stuck with the fact that take requires an Int and that method leaves me with a IO Int, which seems impossible to transform to an Int according to this.

Answer 1

As haskell is a pure functional programming language, functions are referentially transparent which means essentially that only a function's arguments determine its result. If you were able to pull a random number out of the air, you can imagine how that would cause problems.

I suppose you need something like this:

prefixGenerator :: (Ord a, Arbitrary a) => Gen ([a],[a])
prefixGenerator = do
  randn <- choose (1,999) -- number in range 1-999
  frequency [ 
    (1, return ([],[])),
    (2, do {
            xs1 <- orderedListEj13 ;
            xs2 <- orderedListEj13 ;
            return (xs1,xs2)
       }),
    (2, do {                
            xs2 <- orderedListEj13 ;
            return ((take randn xs2),xs2)
       })
    ]

In general in haskell you approach random number generation by either pulling some randomness from the IO monad, or by maintaining a PRNG that is initialized with some integer seed hard-coded, or pulled from IO (gspr's comment is excellent).

Reading about how pseudo random number generators work might help you understand System.Random, and this might help as well (scroll down to section on randomness).

Answer 2

You're right in that nondeterministic random (by which I mean "pseudo-random") number generation is impossible without trickery. Functions in Haskell are pure which means that the same input will always produce the same output.

The good news is that you don't seem to need a nondeterministic PRNG. In fact, it would be better if your QuickCheck test used the same sequence of "random" numbers each time, to make your tests fully reproducible.

You can do this with the mkStdGen function from System.Random. Adapted from the Haskell wiki:

import System.Random
import Data.List

randomInts :: Int -> [Int]
randomInts n = take n $ unfoldr (Just . random) (mkStdGen 4)

Here, 4 is the seed that you may want to choose by a fair dice roll.

Answer 3

The standard library provides a monad for random-number generation. The monadic stuff is not that hard to learn, but if you want to avoid it, find a pseudo-random function next that takes an Int to an Int in a pseudorandom way, and then just create and pass an infinite list of random numbers:

next :: Int -> Int
randoms :: [Int]
randoms = iterate next 73

You can then pass this list of random numbers wherever you need it.

Here's a linear congruential next from Wikipedia:

next n = (1103515245 * n + 12345) `mod` 1073741824

And here are the first 20 pseudorandom numbers following 73:

Prelude> take 20 $ iterate next 73
[73,25988430,339353199,182384508,910120965,1051209818,737424011,14815080,325218177,1034483750,267480167,394050068,4555453,647786674,916350979,980771712,491556281,584902142,110461279,160249772]