pandora-0.3.7: Pandora/Pattern/Object/Setoid.hs

module Pandora.Pattern.Object.Setoid (Setoid (..)) where

import Pandora.Pattern.Category (($))
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (False, True), (?))

infix 4 ==, !=

{- |
> When providing a new instance, you should ensure it satisfies the four laws:
> * Reflexivity: x == x ≡ True
> * Symmetry: x == y ≡ y == x
> * Transitivity: x == y * y == z ≡ True ===> x == z ≡ True
> * Negation: x != y ≡ invert (x == y)
-}

class Setoid a where
	{-# MINIMAL (==) #-}
	(==) :: a -> a -> Boolean

	(!=) :: a -> a -> Boolean
	(!=) x y = x == y ? False $ True