.

.gitignore

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+dist
+dist-*
+cabal-dev
+*.o
+*.hi
+*.chi
+*.chs.h
+*.dyn_o
+*.dyn_hi
+.hpc
+.hsenv
+.cabal-sandbox/
+cabal.sandbox.config
+*.prof
+*.aux
+*.hp
+*.eventlog
+.stack-work/
+cabal.project.local
+.HTF/
+*~

LICENSE

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+Copyright (c) 2017, Runar Bjarnason
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Runar Bjarnason nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Life.cabal

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+-- Initial Life.cabal generated by cabal init.  For further documentation, 
+-- see http://haskell.org/cabal/users-guide/
+
+-- The name of the package.
+name:                Life
+
+-- The package version.  See the Haskell package versioning policy (PVP) 
+-- for standards guiding when and how versions should be incremented.
+-- https://wiki.haskell.org/Package_versioning_policy
+-- PVP summary:      +-+------- breaking API changes
+--                   | | +----- non-breaking API additions
+--                   | | | +--- code changes with no API change
+version:             0.1.0.0
+
+-- A short (one-line) description of the package.
+-- synopsis:            
+
+-- A longer description of the package.
+-- description:         
+
+-- The license under which the package is released.
+license:             BSD3
+
+-- The file containing the license text.
+license-file:        LICENSE
+
+-- The package author(s).
+author:              Runar Bjarnason
+
+-- An email address to which users can send suggestions, bug reports, and 
+-- patches.
+maintainer:          [email protected]
+
+-- A copyright notice.
+-- copyright:           
+
+-- category:            
+
+build-type:          Simple
+
+-- Extra files to be distributed with the package, such as examples or a 
+-- README.
+extra-source-files:  ChangeLog.md
+
+-- Constraint on the version of Cabal needed to build this package.
+cabal-version:       >=1.10
+
+
+executable Life
+  -- .hs or .lhs file containing the Main module.
+  main-is:             Main.hs
+
+  -- Modules included in this executable, other than Main.
+  -- other-modules:       
+
+  -- LANGUAGE extensions used by modules in this package.
+  -- other-extensions:    
+
+  -- Other library packages from which modules are imported.
+  build-depends:       base >=4.9 && <4.10, adjunctions >=4.3 && <4.4, 
+                       containers >=0.5 && <0.6, comonad >3, random,
+                       MemoTrie, distributive
+
+  -- Directories containing source files.
+  hs-source-dirs:      src
+
+  -- Base language which the package is written in.
+  default-language:    Haskell2010
+
+  ghc-options:         -threaded -O2

Setup.hs

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+import Distribution.Simple
+main = defaultMain

src/Main.hs

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+{-# LANGUAGE TypeFamilies #-}
+
+module Main where
+
+import Control.Arrow ((&&&))
+import Control.Comonad.Representable.Store
+import Control.Comonad
+import Control.Monad
+import Data.Bifunctor
+import Data.Distributive
+import Data.Foldable
+import Data.Functor.Rep
+import Data.Maybe (fromMaybe)
+import qualified Data.Map.Lazy as M
+import Data.Map.Lazy (Map(..))
+import Data.MemoTrie
+import System.Random
+
+boardSize :: Int
+boardSize = 50
+
+wrap :: Int -> ((Int, Int) -> a) -> (Int, Int) -> a
+wrap n f p =
+  f $ (join bimap) (\x -> if x < 0 then n - (x `mod` n) else x `mod` n) p
+
+newtype Mem a = Mem { unMem :: (Int, Int) -> a }
+
+mem = Mem . wrap boardSize
+
+instance Functor Mem where
+  fmap f (Mem g) = mem . memo $ f . g
+
+instance Distributive Mem where
+  distribute x = Mem . distribute $ fmap (\m -> unMem m) x
+
+instance Representable Mem where
+  type Rep Mem = (Int,Int)
+  tabulate = mem . tabulate . memo
+  index (Mem f) k = f k
+
+type Board = Store Mem Bool
+
+alive :: Board -> Bool
+alive b = c && n > 1 && n < 4 || not c && n == 3
+  where
+    (c,n) = (extract &&& liveNeighbors) b
+
+liveNeighbors :: Board -> Int
+liveNeighbors b = length . filter id $ do
+  x <- [-1..1]
+  y <- [-1..1]
+  if x == 0 && y == 0
+    then []
+    else
+      return $ let (cx,cy) = pos b in peek (cx + x, cy + y) b
+
+blankBoard :: Board
+blankBoard = store (const False) (0,0)
+
+randomBoard :: Int -> IO Board
+randomBoard n = do
+  rs <- replicateM n $ randoms <$> mkStdGen <$> randomIO
+  return . mkBoard . M.fromList $ do
+    (x, row) <- zip [1..n] rs
+    (y, c)   <- zip [1..n] row
+    return ((x,y), c)
+
+mkBoard :: Map (Int, Int) Bool -> Board
+mkBoard m = store (fromMaybe False . flip M.lookup m) (0,0)
+
+lifeStep = extend alive
+
+printBoard :: Int -> Int -> Board -> IO ()
+printBoard x y b = do
+  for_ [1..y] $ \y -> do
+    for_ [1..x] $ \x ->
+      putStr (if peek (x,y) b then "x" else ".")
+    putStrLn ""
+  putStrLn ""
+
+main :: IO ()
+main = randomBoard 50 >>= go
+  where
+    go b = do
+      printBoard 100 50 b
+      go $ lifeStep b
+