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Lazy list calculated using mutable state?

I would like to figure out how to use mutable state when calculating lazy lists.

For example, this is a naive sieve of Eratosthenes, implemented using a variable array ( source ):

import Control.Monad.ST
import Data.Array.ST
import Data.Array.Unboxed
import Control.Monad
import Data.List

prime :: Int -> UArray Int Bool
prime n = runSTUArray $ do
    arr <- newArray ( 2 , n ) True :: ST s ( STUArray s Int Bool )
    forM_ ( takeWhile ( \x -> x*x <= n ) [ 2 .. n ] ) $ \i -> do
        ai <- readArray arr i
        when ( ai  ) $ forM_ [ i^2 , i^2 + i .. n ] $ \j -> do
            writeArray arr j False
            -- yield i ???

prime n returns an array of logical numbers that indicate which numbers are the first.

Is there a way to use this approach to create a lazy list of these primes? This would be like adding yield iright after the statement writeArray.

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1 answer

- , , ST (http://hackage.haskell.org/packages/archive/base/latest/doc/html/Control-Monad-ST-Lazy.html), :

import Control.Monad.ST.Lazy
import Data.Array.ST
import Data.Array.Unboxed
import Control.Monad
import Data.List
import Data.Maybe

prime :: Int -> [Int]
prime n = catMaybes $ runST $ do
    arr <- strictToLazyST $ newArray ( 2 , n ) True :: ST s ( STUArray s Int Bool )
    forM ( takeWhile ( \x -> x <= n ) [ 2 .. n ] ) $ \i -> do
        if i == 83 then error "Reached 83" else return ()
        ai <- strictToLazyST $ readArray arr i
        if ai
          then do
            strictToLazyST $ forM_ [ i^2 , i^2 + i .. n ] $
                 \j -> writeArray arr j False
            return (Just i)
          else return Nothing

- :

*Main> prime 10000
[2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79*** Exception: Reached 83

Maybes, , , :

import Control.Monad.ST.Lazy
import Data.Array.ST
import Data.Array.Unboxed
import Control.Monad
import Data.List
import Data.Functor

prime :: Int -> [Int]
prime n = runST $ do
    arr <- strictToLazyST $ newArray ( 2 , n ) True :: ST s ( STUArray s Int Bool )
    let primesFrom i | i > n = return []
                     | otherwise = do
            ai <- strictToLazyST $ readArray arr i
            if ai then do
                strictToLazyST $ forM_ [ i^2 , i^2 + i .. n ] $
                   \j -> writeArray arr j False
                (i:) <$> primesFrom (i + 1)
              else primesFrom (i + 1)
    primesFrom 2
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