Examples/Random list

Create a random list

Generate a random list of numbers, without using the System.Random.randoms method:

import System.Random
import Data.List

main = do
seed  <- newStdGen
let rs = randomlist 10 seed
print rs

randomlist :: Int -> StdGen -> [Int]
randomlist n = take n . unfoldr (Just . random)

Delete an element at random

unpick and unpick' are by osfameron and are from http://osfameron.vox.com/library/post/more-random-fun.html (no explicit license)
removeOne is by Chris Kuklewicz (BSD3 licence, 2007)

> import System.Random
> import Debug.Trace -- for removeOne' demonstration

The unpick function and its helper unpick' are strict in the entire
list being operated on (forcing it all into memory at once).  And IO
[a] cannot lazily return any initial values.

> unpick :: [a] -> IO [a]
> unpick []     = undefined
> unpick [x]    = do return []
> unpick (x:xs) = do zs <- unpick' [] [x] xs 2
>                    return (reverse zs)
>
> unpick' :: (Num p, Random p) => [t] -> [t] -> [t] -> p -> IO [t]
> unpick' curr orig [] _
>     = do return curr
> unpick' curr orig (next:rest) prob
>     = do r <- getStdRandom (randomR (1,prob))
>          let curr' = if r == 1 then orig else (next:curr)
>          unpick' curr' (next:orig) rest (prob+1)

To run in the IO Monad just use (getStdRandom . removeOne) :: [a] -> IO [a].

removeOne returns the output list lazily as soon as it has decided
not to delete any element in a prefix of the input list.
The resulting list is constructed efficiently, with no wasted
intermediate list construction.  removeOne allows any output it
generates to be garbage collected, it holds no references to it.

"removeOne" is presented in curried form, without a binding for the
RandomGen g.  The StdGen is hidden inside a State
monad. removeOne is designed for use with Strict.Lazy.  It may not be
optimal to use with Strict.Strict.

Like "tail" this function is partial and will produce an error if
given the empty list.

> removeOne :: (RandomGen g) => [a] -> g -> ([a],g)
> removeOne [] = error "Cannot removeOne from empty list"
> removeOne whole@(_:xs) = runState (helper whole xs 0 1) where

The laziness is needed in helper to make "rest" a lazy thunk.  The
"start" list parameter to helper is a suffix of "whole" that has the
current candidate for deletion as its head.  "oldIndex" is the index
of the current candidate for deletion in the "whole" list. "here" is a
suffix of "whole" with the "index" element of whole as its head.  The
randomR decides if the head of "here" replaces the head of "start" as
the candidate to remove.  If it does replace the old candidate then
a prefix of "start" of length "(index-oldIndex)" is immediately
output, counted off by prependSome.

Assert "start" is never [].
Assert 0 <= oldIndex < index.

>   helper start [] oldIndex index = return (tail start)
>   helper start here@(_:ys) oldIndex index = do
>     r <- State (randomR (0,index))
>     if r==0 then do rest <- helper here ys index \$! succ index
>                     return (prependSome (index-oldIndex) start rest)
>             else helper start ys oldIndex \$! succ index

I assert that "prependSome n xs ys == take n xs ++ ys" but slightly
optimized (without depending on the compiler).  Assert n >= length xs.

> prependSome :: Int -> [a] -> [a] -> [a]
> prependSome 0 _ rest = rest
> prependSome n (x:xs) rest = x : prependSome (pred n) xs rest
> prependSome _ [] _ = error "impossible error in removeOne.prependSome"

"removeOne'" is a tracing version for demonstration below:

> removeOne' :: (Show a,RandomGen g) => [a] -> g -> ([a],g)
> removeOne' [] _ = error "Cannot removeOne from empty list"
> removeOne' whole@(x:xs) g = runState (helper whole xs 0 1) g where
>   helper start [] oldIndex index = return (tail start)
>   helper start here@(_:ys) oldIndex index = do
>     r <- State (randomR (0,index))
>     if r==0 then do rest <- helper here ys index \$! succ index
>                     let rest' = trace "." rest
>                     return (prependSome (index-oldIndex) start rest')
>             else do let ys' = trace "_" ys
>                     helper start ys' oldIndex \$! succ index

Use "removeOne'" to demonstrate when random decisions to drop
elements are made.  This also demonstrates that removeOne is lazy,
returning elements as soon as the removal decision has moved on to a
later element (the "." is output instead of "_").

The element after the last "." is the one actually removed,
defaulting to the first element.

Since the probability of "." decreases, the average length of the
run of output produced by appendSome increases as the list is
processed.

*Main> getStdRandom (removeOne' [1..10])
[1.
_
_
,2,3,4.
_
_
_
_
,5,6,7,8,9.
]
*Main> getStdRandom (removeOne' [1..10])
_
_
[1,2,3.
_
_
_
_
_
_
,5,6,7,8,9,10]
*Main> getStdRandom (removeOne' [1..10])
_
_
_
_
_
_
_
_
_
[2,3,4,5,6,7,8,9,10]
*Main> getStdRandom (removeOne' [1..10])
[1.
_
_
_
_
_
_
_
_
,3,4,5,6,7,8,9,10]
*Main> getStdRandom (removeOne' [1..10])
[1.
,2.
_
_
_
_
_
_
_
,4,5,6,7,8,9,10]
*Main> getStdRandom (removeOne' [1..10])
[1.
_
_
_
_
,2,3,4,5,6.
_
_
,7,8,9.
]

If I use ":m + Data.List" then I can demonstrate how fair the removal is:

*Main Data.List> sequence (replicate 1000 \$ getStdRandom (removeOne [1..4])) >>= return . map length . group . sort
[241,255,239,265]

where a perfect balance would be [250,250,250,250]