{-# LANGUAGE MultiParamTypeClasses #-}

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

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

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

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

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

instance Group Z2 where
  invert = id

instance Action Z2 Ising where
  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