Haskell Quiz/Goedel/Solution Dolio

Encoding is quite simple in Haskell, as it's simply combining the stream of characters with a stream of primes in the right way. Extracting a message from the encoded number is somewhat more cumbersome, especially if one wants to implement the somewhat more efficient factoring discussed in the ruby quiz writeup. However, once such operations are defined for a single number, retrieving a stream is just an unfoldr away.

module Main (main) where

import Control.Arrow
import Data.Char
import Data.List
import System.Environment

primes :: [Integer]
primes = 2 : sieve [3,5..]
 where sieve (x:xs) = x : sieve (filter (\n -> n `mod` x /= 0) xs)

goedel :: String -> Integer
goedel = product . zipWith (^) primes . map ord

letter :: ([Integer], Integer) -> Maybe (Char, ([Integer], Integer))
letter (_,   1) = Nothing
letter ([],  _) = Nothing
letter (p:ps,n) = Just (chr k, (ps, n'))
 where (n', k) = extract p n

extract :: Integer -> Integer -> (Integer, Int)
extract p n = foldl' extract' (n,0) eps
 where eps = map (id &&& (p^)) [64,32,16,8,4,2,1]
       extract' (n,s) (k,pp)
            | m /= 0    = (n,s)
            | otherwise = (d,s + k)
        where (d,m) = n `divMod` pp

ungoedel :: Integer -> String
ungoedel = unfoldr letter . (,) primes

main = do (mode:_) <- getArgs
          case mode of
               'e':_ -> interact $ show . goedel
               'd':_ -> interact $ ungoedel . read
               _     -> putStrLn "Unrecognized mode. 'e' for encode, 'd' for decode."