gistfile1.hs

import Control.Arrow
import Control.Monad
import Control.Monad.Random
import Data.List
import Data.Map
import Data.Maybe

-- A monad which represents a random integer from 1-6
die :: (RandomGen g) => Rand g Int
die = getRandomR (1,6)

-- A monad which represents our infinite list of summed paired die
dice :: (RandomGen g) => Rand g [Int]
dice = sequence . repeat . summedTuple $ pair
  where summedTuple = liftM (\(a, b) -> a + b)

-- A roll of 2 dice
pair :: (RandomGen g) => Rand g (Int, Int)
pair = do
  r1 <- die
  r2 <- die
  return (r1, r2)

-- Build a histogram of a list of objects
hist :: (Ord a) => [a] -> [(a, Int)]
hist = map (head &&& length) . group . sort

-- Take stuff from a list in a monad
takeM n = liftM (take n)

-- Build a histogram of our random list
randHist n = (liftM hist) . takeM n
diceHist n = randHist n dice

-- The probability distribution of a paired dice roll
diceDist :: [(Int, Rational)]
diceDist = [(2, 1/36), (3, 2/36), (4, 3/36), (5, 4/36), (6, 5/36), (7, 6/36),
  (8, 5/36), (9, 4/36), (10, 3/36), (11, 2/36), (12, 1/36)]

initFreqs :: [(Int, Int)]
initFreqs = [ (x, 0) | x <- [2..12] ]

main = do
  print =<< (evalRandIO $ diceHist 100000)