module Equiv where

import Prelude

import Control.Monad.Eff.JQuery (off)
import Data.Array ((:))
import Data.CommutativeRing (class CommutativeRing)
import Data.Enum (class BoundedEnum, class Enum, Cardinality(..), cardinality, toEnum)
import Data.Eq (class Eq)
import Data.EuclideanRing (class EuclideanRing, degree)
import Data.Foldable (all)
import Data.Functor (class Functor, map)
import Data.Generic (class Generic)
import Data.Generic.Rep.Show (genericShow)
import Data.HeytingAlgebra (not, (&&), (||))
import Data.Maybe (Maybe(..))
import Data.Ring (class Ring)
import Data.Semiring (class Semiring)
import Data.Show (class Show)


class Equiv a where
  equiv :: a -> a -> Boolean

infix 5 equiv as ≡

instance equivEq :: Eq a => Equiv a where
  equiv a b = a == b


generateValues :: ∀a. (Int -> Maybe a) -> Int -> Array a -> Array a
generateValues f n acc = case (f n) of
  Just a -> generateValues f (n+1) (a:acc)
  Nothing -> acc

instance equivEnum :: (BoundedEnum a, Equiv b) => Equiv (a -> b) where
  equiv a b = all (\v -> a v ≡ b v) (generateValues toEnum 0 [])

data Values = D1 | D2 | D3 | D4

rotate2 :: Values -> Values
rotate2 D1 = D3
rotate2 D2 = D4
rotate2 D3 = D1
rotate2 D4 = D2