{-# LANGUAGE MultiParamTypeClasses #-}

import Data.Sequence
import Data.Monoid
import Data.Monoid.Action
import Data.Group
import Data.Char
import Data.Graph
import Control.Monad.Mersenne.Random

data Z2       = E0 | E1   deriving (Eq, Show)
data Ising    = Up | Down deriving (Eq, Show)

instance Semigroup Z2 where
  -- Z2 is a semigroup
  E0 <> a = a
  E1 <> a | a == E0   = E1
          | otherwise = E0

instance Monoid Z2 where
  -- Z2 is a monoid
  mempty      = E0
  mappend a b = a <> b

instance Group Z2 where
  -- Z2 is a group
  invert = id

instance Action Z2 Ising where
  -- Z2 has an action on Ising spins
  act E0 a = a
  act E1 a | a == Up   = Down
           | otherwise = Up

squareLatticeEdges d l = [(i, (l^j) * quot i (l^j) + mod (l^j + i + s * l^(j-1)) (l^j)) | j <- [1..d], i <- [0..(l^d)-1], s <- [-1, 1]]
ghostEdges n = [(n, i) | i <- [0..n-1]] ++ [(i, n) | i <- [0..n-1]]
squareLattice d l = buildG (0, l^d) ((squareLatticeEdges d l) ++ ghostEdges (l^d))

data State r x = State { ghost :: r, spins :: Seq x }

j :: Ising -> Ising -> Integer
j a b | a == b    =  1
      | otherwise = -1