Haskell Quiz/SimFrost/Solution Dolio

This solution is based solely on list processing. The main datatype, Region a, is simply an alias for a. At each step, the region is broken into sub-regions (the 2x2 squares), each is rotated or frozen appropriately, and then the sub-regions are combined back into a single region.

The text output follows the Ruby Quiz convention of ' ' for vacuum, '.' for vapor and '*' for ice. A '|' is added on the left side of each line of the grid to distinguish them from separator lines.

The default output of this program is a number of PPM images of each step in the process. They are called frostNNN.ppm, where NNN starts from 100.

This code makes use of the random monad.

{-# OPTIONS -fno-monomorphism-restriction -fglasgow-exts #-}

module Main where

import Data.List

import Control.Arrow
import Control.Monad
import Control.Monad.Instances

import System
import System.Random

import MonadRandom
import PPImage

data Content = Frost | Vapor | Vacuum deriving (Eq, Bounded, Enum)
data Direction = L | R deriving (Eq, Bounded, Enum, Show)

instance Random Direction where
    random = randomR (minBound, maxBound)
    randomR = (first toEnum .) . randomR . (fromEnum *** fromEnum)

instance Random Content where
    random = randomR (minBound, maxBound)
    randomR = (first toEnum .) . randomR . (fromEnum *** fromEnum)

instance Show Content where
    show Frost = "*"
    show Vapor = "."
    show Vacuum = " "

type Region a = [[a]]

shift, unshift :: [a] -> [a]
shift   = liftM2 (:) last init
unshift = liftM2 (++) tail (return . head)

rotateR :: (MonadRandom m) => Region a -> m (Region a)
rotateR = flip liftM getRandom . flip r
 where r R = transpose . reverse
       r L = reverse . transpose

splitAtM :: (MonadPlus m) => Int -> [a] -> m ([a], [a])
splitAtM _ [] = mzero
splitAtM n xs = return $ splitAt n xs

part :: Region a -> [[Region a]]
part = unfoldr (fmap (first z) . splitAtM 2) . map (unfoldr $ splitAtM 2)
 where
 z [x, y] = zipWith (\a b -> [a, b]) x y

unpart :: [[Region a]] -> [[a]]
unpart = join . (map $ foldr1 (zipWith (++)))

freeze :: Region Content -> Region Content
freeze = map (map f)
 where f Vacuum = Vacuum ; f _ = Frost

anyR :: (a -> Bool) -> Region a -> Bool
anyR = (or .) . map . any

vaporous, frosty :: Region Content -> Bool
vaporous = anyR (== Vapor)
frosty = anyR (== Frost)

randomRegion :: (MonadRandom m) => Int -> Int -> m (Region Content)
randomRegion n m = do r <- replicateM (n - 1) rv
                      rs <- replicateM (m - 1) (replicateM n rv)
                      return $ insert (div m 2) (insert (div n 2) Frost r) rs
 where
 insert n e l = let (h, t) = splitAt n l in h ++ e : t
 rv = getRandomR (Vapor, Vacuum)

update, update' :: (MonadRandom m) => Region Content -> m (Region Content)
update = liftM unpart . mapM (mapM op) . part
 where op r = if frosty r then return $ freeze r else rotateR r

update' = liftM unodd . update . odd
 where
 odd = shift . map (shift)
 unodd = unshift . map (unshift)

process :: (MonadRandom m) => Region Content -> m [Region Content]
process r = liftM (r:) $ step r
 where
 stepper g f r
    | not (vaporous r) = return []
    | otherwise        = do r' <- g r
                            rs <- f r'
                            return (r':rs)
 step  = stepper update step'
 step' = stepper update' step

main = do [n, m] <- fmap (map read) getArgs
          if odd n || odd m
             then putStrLn "Dimensions must be even."
             else randomRegion n m >>= process
                                   >>= mapM_ output . zip [100..]
                                                    . map ppmRegion

output :: (Integer, PPM) -> IO ()
output (n, ppm) = writeFile ("frost" ++ show n ++ ".ppm") (show ppm)

showRegion :: Region Content -> String
showRegion = unlines . map ('|':) . map join . map (map show)

ppmRegion :: Region Content -> PPM
ppmRegion r = PPM pix h w 255
 where
 pix = map (map f) r
 h   = length r
 w   = head . map length $ r
 f Vacuum = black
 f Frost  = white
 f Vapor  = blue

The following is some auxiliary code to output PPM images of the results:

module PPImage ( Point
               , Image
               , Color(..)
               , PPM(..)
               , red
               , yellow
               , green
               , cyan
               , blue
               , magenta
               , black
               , white
               , pixelate )
    where

type Point = (Double, Double)
type Image a = Point -> a

data Color = Color { r :: Int, g :: Int, b :: Int }

data PPM = PPM {
                pixels :: [[Color]],
                height :: Int,
                width :: Int,
                depth :: Int
               }

instance Show Color where
    show (Color r g b) = unwords [show r, show g, show b]

instance Show PPM where
    show pg =  "P3\n"
            ++ show h ++ " " ++ show w ++ "\n"
            ++ show d ++ "\n"
            ++ (unlines . map unlines . map (map show) . pixels $ pg) ++ "\n"
     where h = height pg
           w = width pg
           d = depth pg

black   = Color   0   0   0
red     = Color 255   0   0
yellow  = Color 255 255   0
green   = Color   0 255   0
cyan    = Color   0 255 255
blue    = Color   0   0 255
magenta = Color 255   0 255
white   = Color 255 255 255

pixelate n m d (x0, x1) (y0, y1) i = PPM pixels m n d
 where
 pixels = [ i (x, y) | x <- px, y <- py ]
 dx = (x1 - x0) / fromIntegral n
 dy = (y0 - y1) / fromIntegral m
 px = take n $ iterate (+dx) x0
 py = take m $ iterate (+dy) y1