Added a toroidal space

GOL/Space.hs

@@ -1,10 +1,15 @@
 {-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE DeriveFunctor #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE TypeFamilies #-}
 
 module GOL.Space where
 
+import Data.Bifunctor
+import Data.Distributive
 import Data.Functor.Rep
+import Data.Vector (Vector, (!))
+import qualified Data.Vector as V
 
 -- | A space in which a Conway's Game of Life simulation
 -- takes place, with a notion of "neighbors to a cell" defined.
@@ -25,4 +30,39 @@ class Representable f => Space f where
 -- grid. The graphical system requires a displayable space.
 class (Space f, Rep f ~ (Int, Int)) => DisplayableSpace f where
   sizex :: Int
-  sizey :: Int
+  sizey :: Int
+
+-- * Standard spaces
+
+-- Unfortunately, due to the fact that Haskell doesn't have dependent types,
+-- defining a GOL space to have an arbitrary size specified at runtime by
+-- the user is completely impossible. There's simply no way to do it without
+-- features that Haskell doesn't have.
+-- So until we get generalized pi types in GHC, we'll have to make do with
+-- hard-coded space sizes.
+
+-- | A 100x100 2D grid space. This space is _toroidal_, which means that
+-- cells on the opposite edges are considered neighbors of each other.
+newtype ToroidalSpace a = TS (Vector (Vector a))
+  deriving (Show, Functor)
+
+instance Distributive ToroidalSpace where
+  distribute xs = tabulate (\p -> fmap (`index` p) xs)
+
+instance Representable ToroidalSpace where
+  type Rep ToroidalSpace = (Int, Int)
+  index (TS s) (i, j) = s ! j ! i
+  tabulate f = TS $ V.generate 100 (\x -> V.generate 100 $ \y -> f (x, y))
+
+instance Space ToroidalSpace where
+  neighbors (i, j) =
+    bimap ((`mod` 100).(+i)) ((`mod` 100).(+j)) <$>
+    [
+      (-1,-1), (0,-1), (1,-1),
+      (-1, 0),         (1, 0),
+      (-1, 1), (0, 1), (1, 1)
+    ]
+
+instance DisplayableSpace ToroidalSpace where
+  sizex = 100
+  sizey = 100

conways-game-of-life.cabal

@@ -14,4 +14,6 @@ executable main
   build-depends:  base,
                   comonad,
                   Yampa,
-                  adjunctions
+                  distributive,
+                  adjunctions,
+                  vector