Two.hs

{-# LANGUAGE MultiParamTypeClasses #-}

{-| Module  : FiniteCategories
Description : The __2__ category contains two object `A` and `B` and a morphism @`F` : `A` -> `B`@.
Copyright   : Guillaume Sabbagh 2021
License     : GPL-3
Maintainer  : guillaumesabbagh@protonmail.com
Stability   : experimental
Portability : portable

The __2__ category contains two object `A` and `B` and a morphism @f : `A` -> `B`@ (and of course two identities).
-}

module UsualCategories.Two 
(
    TwoOb(..),
    TwoAr(..),
    Two(..)
)
where
    import          FiniteCategory.FiniteCategory
    import          IO.PrettyPrint
    
    -- | Object of the __2__ category.
    data TwoOb = A | B deriving (Eq, Show)
    
    -- | Morphism of the __2__ category.
    data TwoAr = IdA | IdB | F deriving (Eq,Show)
    
    -- | The __2__ category.
    data Two = Two deriving (Eq,Show)
    
    instance Morphism TwoAr TwoOb where
        source IdA = A
        source IdB = B
        source F = A
        target IdA = A
        target IdB = B
        target F = B
        (@) IdA IdA = IdA
        (@) IdB IdB = IdB
        (@) F IdA = F
        (@) IdB F = F
        (@) x y = error ("Invalid composition of TwoMorph : "++show x++" * "++show y)
    
    instance FiniteCategory Two TwoAr TwoOb where
        ob = const [A,B]
        identity _ A = IdA
        identity _ B = IdB
        ar _ A A = [IdA]
        ar _ A B = [F]
        ar _ B B = [IdB]
        ar _ _ _ = []
        
    instance GeneratedFiniteCategory Two TwoAr TwoOb where
        genAr = defaultGenAr
        decompose = defaultDecompose
        
    instance PrettyPrintable TwoOb where
        pprint = show
        
    instance PrettyPrintable TwoAr where
        pprint = show
        
    instance PrettyPrintable Two where
        pprint = show