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
	(!=) a
x a
y = a
x a -> a -> Boolean
forall a. Setoid a => a -> a -> Boolean
== a
y Boolean -> Boolean -> Boolean -> Boolean
forall a. Boolean -> a -> a -> a
? Boolean
False (Boolean -> Boolean) -> Boolean -> Boolean
forall (m :: * -> * -> *). Category m => m ~~> m
$ Boolean
True