{-# LANGUAGE MultiParamTypeClasses #-}

{-| Module  : FiniteCategories
Description : The __'Parallel'__ category contains two parallel arrows.
Copyright   : Guillaume Sabbagh 2022
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 Math.FiniteCategories.Parallel 
(
    ParallelOb(..),
    ParallelAr(..),
    Parallel(..)
)
where
    import          Math.FiniteCategory
    import          Math.IO.PrettyPrint
    
    import          Data.WeakSet.Safe
    
    -- | Objects of the __'Parallel'__ category.

    data ParallelOb = ParallelA | ParallelB deriving (ParallelOb -> ParallelOb -> Bool
(ParallelOb -> ParallelOb -> Bool)
-> (ParallelOb -> ParallelOb -> Bool) -> Eq ParallelOb
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: ParallelOb -> ParallelOb -> Bool
== :: ParallelOb -> ParallelOb -> Bool
$c/= :: ParallelOb -> ParallelOb -> Bool
/= :: ParallelOb -> ParallelOb -> Bool
Eq, Int -> ParallelOb -> ShowS
[ParallelOb] -> ShowS
ParallelOb -> String
(Int -> ParallelOb -> ShowS)
-> (ParallelOb -> String)
-> ([ParallelOb] -> ShowS)
-> Show ParallelOb
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> ParallelOb -> ShowS
showsPrec :: Int -> ParallelOb -> ShowS
$cshow :: ParallelOb -> String
show :: ParallelOb -> String
$cshowList :: [ParallelOb] -> ShowS
showList :: [ParallelOb] -> ShowS
Show)
    
    -- | Morphisms of the __'Parallel'__ category.

    data ParallelAr = ParallelIdA | ParallelIdB | ParallelF | ParallelG deriving (ParallelAr -> ParallelAr -> Bool
(ParallelAr -> ParallelAr -> Bool)
-> (ParallelAr -> ParallelAr -> Bool) -> Eq ParallelAr
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: ParallelAr -> ParallelAr -> Bool
== :: ParallelAr -> ParallelAr -> Bool
$c/= :: ParallelAr -> ParallelAr -> Bool
/= :: ParallelAr -> ParallelAr -> Bool
Eq, Int -> ParallelAr -> ShowS
[ParallelAr] -> ShowS
ParallelAr -> String
(Int -> ParallelAr -> ShowS)
-> (ParallelAr -> String)
-> ([ParallelAr] -> ShowS)
-> Show ParallelAr
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> ParallelAr -> ShowS
showsPrec :: Int -> ParallelAr -> ShowS
$cshow :: ParallelAr -> String
show :: ParallelAr -> String
$cshowList :: [ParallelAr] -> ShowS
showList :: [ParallelAr] -> ShowS
Show)
    
    -- | The __'Parallel'__ category.

    data Parallel = Parallel deriving (Parallel -> Parallel -> Bool
(Parallel -> Parallel -> Bool)
-> (Parallel -> Parallel -> Bool) -> Eq Parallel
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: Parallel -> Parallel -> Bool
== :: Parallel -> Parallel -> Bool
$c/= :: Parallel -> Parallel -> Bool
/= :: Parallel -> Parallel -> Bool
Eq, Int -> Parallel -> ShowS
[Parallel] -> ShowS
Parallel -> String
(Int -> Parallel -> ShowS)
-> (Parallel -> String) -> ([Parallel] -> ShowS) -> Show Parallel
forall a.
(Int -> a -> ShowS) -> (a -> String) -> ([a] -> ShowS) -> Show a
$cshowsPrec :: Int -> Parallel -> ShowS
showsPrec :: Int -> Parallel -> ShowS
$cshow :: Parallel -> String
show :: Parallel -> String
$cshowList :: [Parallel] -> ShowS
showList :: [Parallel] -> ShowS
Show)
    
    instance Morphism ParallelAr ParallelOb where
        source :: ParallelAr -> ParallelOb
source ParallelAr
ParallelIdA = ParallelOb
ParallelA
        source ParallelAr
ParallelIdB = ParallelOb
ParallelB
        source ParallelAr
_ = ParallelOb
ParallelA
        target :: ParallelAr -> ParallelOb
target ParallelAr
ParallelIdA = ParallelOb
ParallelA
        target ParallelAr
ParallelIdB = ParallelOb
ParallelB
        target ParallelAr
_ = ParallelOb
ParallelB
        @? :: ParallelAr -> ParallelAr -> Maybe ParallelAr
(@?) ParallelAr
ParallelIdA ParallelAr
ParallelIdA = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelIdA
        (@?) ParallelAr
ParallelF ParallelAr
ParallelIdA = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelF
        (@?) ParallelAr
ParallelG ParallelAr
ParallelIdA = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelG
        (@?) ParallelAr
ParallelIdB ParallelAr
ParallelIdB = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelIdB
        (@?) ParallelAr
ParallelIdB ParallelAr
ParallelF = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelF
        (@?) ParallelAr
ParallelIdB ParallelAr
ParallelG = ParallelAr -> Maybe ParallelAr
forall a. a -> Maybe a
Just ParallelAr
ParallelG
        (@?) ParallelAr
_ ParallelAr
_ = Maybe ParallelAr
forall a. Maybe a
Nothing
        
    instance Category Parallel ParallelAr ParallelOb where
        identity :: Morphism ParallelAr ParallelOb =>
Parallel -> ParallelOb -> ParallelAr
identity Parallel
_ ParallelOb
ParallelA = ParallelAr
ParallelIdA
        identity Parallel
_ ParallelOb
ParallelB = ParallelAr
ParallelIdB
        ar :: Morphism ParallelAr ParallelOb =>
Parallel -> ParallelOb -> ParallelOb -> Set ParallelAr
ar Parallel
_ ParallelOb
ParallelA ParallelOb
ParallelA = [ParallelAr] -> Set ParallelAr
forall a. [a] -> Set a
set [ParallelAr
ParallelIdA]
        ar Parallel
_ ParallelOb
ParallelA ParallelOb
ParallelB = [ParallelAr] -> Set ParallelAr
forall a. [a] -> Set a
set [ParallelAr
ParallelF,ParallelAr
ParallelG]
        ar Parallel
_ ParallelOb
ParallelB ParallelOb
ParallelB = [ParallelAr] -> Set ParallelAr
forall a. [a] -> Set a
set [ParallelAr
ParallelIdB]
        ar Parallel
_ ParallelOb
_ ParallelOb
_ = [ParallelAr] -> Set ParallelAr
forall a. [a] -> Set a
set []
        
    
    instance FiniteCategory Parallel ParallelAr ParallelOb where
        ob :: Parallel -> Set ParallelOb
ob Parallel
_ = [ParallelOb] -> Set ParallelOb
forall a. [a] -> Set a
set [ParallelOb
ParallelA,ParallelOb
ParallelB]
        
    instance PrettyPrint ParallelOb where
        pprint :: ParallelOb -> String
pprint ParallelOb
ParallelA = String
"A"
        pprint ParallelOb
ParallelB = String
"B"
        
    instance PrettyPrint ParallelAr where
        pprint :: ParallelAr -> String
pprint ParallelAr
ParallelIdA = String
"IdA"
        pprint ParallelAr
ParallelIdB = String
"IdB"
        pprint ParallelAr
ParallelF = String
"f"
        pprint ParallelAr
ParallelG = String
"g"
        
    instance PrettyPrint Parallel where
        pprint :: Parallel -> String
pprint Parallel
Parallel = String
"Parallel"