Parallel.hs

{-# LANGUAGE MultiParamTypeClasses #-}

{-| Module  : FiniteCategories
Description : The parallel category contains two parallel arrows.
Copyright   : Guillaume Sabbagh 2021
License     : GPL-3
Maintainer  : guillaumesabbagh@protonmail.com
Stability   : experimental
Portability : portable

The parallel category contains two objects `A` and `B` and two morphisms @`F` : `A` -> `B`@ and @`G` : `A` -> `B`@.
-}

module UsualCategories.Parallel 
(
    ParallelOb(..),
    ParallelAr(..),
    Parallel(..)
)
where
    import          FiniteCategory.FiniteCategory
    import          IO.PrettyPrint
    
    -- | Object of the parallel category.
    data ParallelOb = A | B deriving (Eq, Show)
    
    -- | Morphism of the parallel category.
    data ParallelAr = IdA | IdB | F | G deriving (Eq, Show)
    
    -- | The parallel category.
    data Parallel = Parallel deriving (Eq, Show)
    
    instance Morphism ParallelAr ParallelOb where
        source IdA = A
        source IdB = B
        source _ = A
        target IdA = A
        target IdB = B
        target _ = B
        (@) IdA IdA = IdA
        (@) F IdA = F
        (@) G IdA = G
        (@) IdB IdB = IdB
        (@) IdB F = F
        (@) IdB G = G
    
    instance FiniteCategory Parallel ParallelAr ParallelOb where
        ob = const [A,B]
        identity _ A = IdA
        identity _ B = IdB
        ar _ A A = [IdA]
        ar _ A B = [F,G]
        ar _ B B = [IdB]
        ar _ _ _ = []
        
    instance GeneratedFiniteCategory Parallel ParallelAr ParallelOb where
        genAr = defaultGenAr
        decompose = defaultDecompose
        
    instance PrettyPrintable ParallelOb where
        pprint = show
        
    instance PrettyPrintable ParallelAr where
        pprint = show
    
    instance PrettyPrintable Parallel where
        pprint = show