From 12c28cd733ab10058b2aee6e44ab25ffb4bebe31 Mon Sep 17 00:00:00 2001
From: kiana-S <kiana.a.sheibani@gmail.com>
Date: Tue, 21 Dec 2021 21:36:59 -0500
Subject: [PATCH] Added a toroidal space

---
 GOL/Space.hs               | 42 +++++++++++++++++++++++++++++++++++++-
 conways-game-of-life.cabal |  4 +++-
 2 files changed, 44 insertions(+), 2 deletions(-)

diff --git a/GOL/Space.hs b/GOL/Space.hs
index 890e9b3..3d0526a 100644
--- a/GOL/Space.hs
+++ b/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
\ No newline at end of file
+  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
\ No newline at end of file
diff --git a/conways-game-of-life.cabal b/conways-game-of-life.cabal
index 00ee47e..a16603d 100644
--- a/conways-game-of-life.cabal
+++ b/conways-game-of-life.cabal
@@ -14,4 +14,6 @@ executable main
   build-depends:  base,
                   comonad,
                   Yampa,
-                  adjunctions
\ No newline at end of file
+                  distributive,
+                  adjunctions,
+                  vector
\ No newline at end of file