I've got a pain fetish so I decided to wrestle a program making heavy use of System.Random WITHOUT a State Monad. When I got to the point where I needed to add a mutation rate I decided it works fine enough as it is without one, so here you go! (Technical

Haskell Naturally Selecting Algorithm

module GE where
import System.Random
import Data.List (elemIndex)
import Control.Monad (foldM)

type Aminal = [Int]
type Population = [Aminal]

gen  = 10 {- GENERATIONS -}
pop  = 10  {- POPULATION NUMBER -}
chr  = 10  {- CHROMOSOMAL LENGTH -}
maxi = 9   {- MAXIMUM VALUE OF CHROMOSOME -}

{- GENERATES A LIST OF RANDOM ANIMALS -}
initPop :: (RandomGen g) => Int -> g -> (Population,g)
initPop x rando = foldl (\(l,r) _ -> ( (fst $ randRange (0,maxi) r chr):l, snd $ randRange (0,maxi) r chr) ) ([],rando) [1..x]
  where randRange (x,y) rando range = foldl (\(l,r) _ -> ( (fst $ randomR (x,y) r):l,snd $ randomR (x,y) r ) ) ([],rando) [1..range]

{- Breeds Two Animals Together splitting their genes randomly -}
breed :: StdGen -> Aminal -> Aminal -> (Aminal,StdGen)
breed rando a1 a2 =  foldl (\(l,r) (g1,g2) -> (l++[fst $ randChoice r g1 g2],snd $ randChoice r g1 g2)  ) ([],rando) $ zip a1 a2
 where randChoice r g1 g2 = case random r :: (Bool,StdGen) of
         (True,newRando)  -> (g1,newRando)
         (False,newRando) -> (g2,newRando)

generation :: Population -> StdGen -> IO (Population,StdGen)
generation curPop rando = do
  {- Get Greatest Fit -}
  let fittestIndex = elemIndex (foldl max 0 $ map sum curPop) $ map sum curPop
  case fittestIndex of
    Nothing -> error "There is not a \"most fit\" creature in the population. "
    Just i  -> do
      {- Breed Most Fit with All Others -}
      return $ foldl (\(l,r) aminal -> (l++[fst $ breed r (curPop !! i) aminal],snd $ breed r (curPop !! i) aminal) ) ([],rando) curPop

main :: IO ()
main = do
  rando1 <- getStdGen
  let (initialPop,rando2) = initPop pop rando1
  aminals <- foldM (\(p,r) _ -> generation p r) (initialPop,rando2) [1..gen]
  mapM_  (putStrLn.show) $ fst aminals                          

HaskellNaturallySelectingAlgorithm

module GE where
import System.Random
import Data.List (elemIndex)
import Control.Monad (foldM)

type Aminal = [Int]
type Population = [Aminal]

gen  = 10 {- GENERATIONS -}
pop  = 10  {- POPULATION NUMBER -}
chr  = 10  {- CHROMOSOMAL LENGTH -}
maxi = 9   {- MAXIMUM VALUE OF CHROMOSOME -}

{- GENERATES A LIST OF RANDOM ANIMALS -}
initPop :: (RandomGen g) => Int -> g -> (Population,g)
initPop x rando = foldl (\(l,r) _ -> ( (fst $ randRange (0,maxi) r chr):l, snd $ randRange (0,maxi) r chr) ) ([],rando) [1..x]
  where randRange (x,y) rando range = foldl (\(l,r) _ -> ( (fst $ randomR (x,y) r):l,snd $ randomR (x,y) r ) ) ([],rando) [1..range]

{- Breeds Two Animals Together splitting their genes randomly -}
breed :: StdGen -> Aminal -> Aminal -> (Aminal,StdGen)
breed rando a1 a2 =  foldl (\(l,r) (g1,g2) -> (l++[fst $ randChoice r g1 g2],snd $ randChoice r g1 g2)  ) ([],rando) $ zip a1 a2
 where randChoice r g1 g2 = case random r of
         (True,newRando)  -> (g1,newRando)
         (False,newRando) -> (g2,newRando)

generation :: Population -> StdGen -> IO (Population,StdGen)
generation curPop rando = do
  {- Get Greatest Fit -}
  let fittestIndex = elemIndex (foldl max 0 $ map sum curPop) $ map sum curPop
  case fittestIndex of
    Nothing -> error "There is not a \"most fit\" creature in the population. "
    Just i  -> do
      {- Breed Most Fit with All Others -}
      return $ foldl (\(l,r) aminal -> (l++[fst $ breed r (curPop !! i) aminal],snd $ breed r (curPop !! i) aminal) ) ([],rando) curPop

main :: IO ()
main = do
  rando1 <- getStdGen
  let (initialPop,rando2) = initPop pop rando1
  aminals <- foldM (\(p,r) _ -> generation p r) (initialPop,rando2) [1..gen]
  mapM_  (putStrLn.show) $ fst aminals