{-# LANGUAGE NoImplicitPrelude #-}

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DataKinds #-}

-- |
-- Module      : OAlg.Limes.Perspective
-- Description : concept of perspective
-- Copyright   : (c) Erich Gut
-- License     : BSD3
-- Maintainer  : zerich.gut@gmail.com
--
-- concept of 'Projective' and 'Injective'.
module OAlg.Limes.Perspective
  ( Perspective(..)
  ) where

import OAlg.Prelude

--------------------------------------------------------------------------------
-- Perspective -

-- | concept of 'Projective' and 'Injective'.
data Perspective = Projective | Injective deriving (Int -> Perspective -> ShowS
[Perspective] -> ShowS
Perspective -> String
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
showList :: [Perspective] -> ShowS
$cshowList :: [Perspective] -> ShowS
show :: Perspective -> String
$cshow :: Perspective -> String
showsPrec :: Int -> Perspective -> ShowS
$cshowsPrec :: Int -> Perspective -> ShowS
Show,Perspective -> Perspective -> Bool
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
/= :: Perspective -> Perspective -> Bool
$c/= :: Perspective -> Perspective -> Bool
== :: Perspective -> Perspective -> Bool
$c== :: Perspective -> Perspective -> Bool
Eq,Eq Perspective
Perspective -> Perspective -> Bool
Perspective -> Perspective -> Ordering
Perspective -> Perspective -> Perspective
forall a.
Eq a
-> (a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
min :: Perspective -> Perspective -> Perspective
$cmin :: Perspective -> Perspective -> Perspective
max :: Perspective -> Perspective -> Perspective
$cmax :: Perspective -> Perspective -> Perspective
>= :: Perspective -> Perspective -> Bool
$c>= :: Perspective -> Perspective -> Bool
> :: Perspective -> Perspective -> Bool
$c> :: Perspective -> Perspective -> Bool
<= :: Perspective -> Perspective -> Bool
$c<= :: Perspective -> Perspective -> Bool
< :: Perspective -> Perspective -> Bool
$c< :: Perspective -> Perspective -> Bool
compare :: Perspective -> Perspective -> Ordering
$ccompare :: Perspective -> Perspective -> Ordering
Ord,Int -> Perspective
Perspective -> Int
Perspective -> [Perspective]
Perspective -> Perspective
Perspective -> Perspective -> [Perspective]
Perspective -> Perspective -> Perspective -> [Perspective]
forall a.
(a -> a)
-> (a -> a)
-> (Int -> a)
-> (a -> Int)
-> (a -> [a])
-> (a -> a -> [a])
-> (a -> a -> [a])
-> (a -> a -> a -> [a])
-> Enum a
enumFromThenTo :: Perspective -> Perspective -> Perspective -> [Perspective]
$cenumFromThenTo :: Perspective -> Perspective -> Perspective -> [Perspective]
enumFromTo :: Perspective -> Perspective -> [Perspective]
$cenumFromTo :: Perspective -> Perspective -> [Perspective]
enumFromThen :: Perspective -> Perspective -> [Perspective]
$cenumFromThen :: Perspective -> Perspective -> [Perspective]
enumFrom :: Perspective -> [Perspective]
$cenumFrom :: Perspective -> [Perspective]
fromEnum :: Perspective -> Int
$cfromEnum :: Perspective -> Int
toEnum :: Int -> Perspective
$ctoEnum :: Int -> Perspective
pred :: Perspective -> Perspective
$cpred :: Perspective -> Perspective
succ :: Perspective -> Perspective
$csucc :: Perspective -> Perspective
Enum,Perspective
forall a. a -> a -> Bounded a
maxBound :: Perspective
$cmaxBound :: Perspective
minBound :: Perspective
$cminBound :: Perspective
Bounded)

type instance Dual Projective = Injective
type instance Dual Injective = Projective