module Pandora.Paradigm.Primary.Functor.Wye where

import Pandora.Core.Functor (type (~>))
import Pandora.Pattern.Category ((<--))
import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))
import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (mult))
import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))
import Pandora.Pattern.Object.Monoid (Monoid (zero))
import Pandora.Paradigm.Algebraic.Exponential (type (<--))
-- import Pandora.Paradigm.Algebraic.Product ((:*:) ((:*:)))
import Pandora.Pattern.Morphism.Flip (Flip (Flip))
import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))

data Wye a = End | Left_ a | Right_ a | Both a a

instance Covariant (->) (->) Wye where
	a -> b
_ <-|- :: (a -> b) -> Wye a -> Wye b
<-|- Wye a
End = Wye b
forall a. Wye a
End
	a -> b
f <-|- Left_ a
x = b -> Wye b
forall a. a -> Wye a
Left_ (b -> Wye b) -> b -> Wye b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
x
	a -> b
f <-|- Right_ a
y = b -> Wye b
forall a. a -> Wye a
Right_ (b -> Wye b) -> b -> Wye b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
y
	a -> b
f <-|- Both a
x a
y = b -> b -> Wye b
forall a. a -> a -> Wye a
Both (b -> b -> Wye b) -> b -> b -> Wye b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
x (b -> Wye b) -> b -> Wye b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
y

-- instance Semimonoidal (<--) (:*:) (:*:) Wye where
-- 	mult = Flip <-- \case
-- 		End -> End :*: End
-- 		Left_ (x :*: y) -> Left_ x :*: Left_ y
-- 		Right_ (x :*: y) -> Right_ x :*: Right_ y
-- 		Both (x :*: y) (x' :*: y') -> Both x x' :*: Both y y'

instance Monotonic a (Wye a) where
	reduce :: (a -> r -> r) -> r -> Wye a -> r
reduce a -> r -> r
f r
r (Left_ a
x) = a -> r -> r
f a
x r
r
	reduce a -> r -> r
f r
r (Right_ a
x) = a -> r -> r
f a
x r
r
	reduce a -> r -> r
f r
r (Both a
x a
y) = a -> r -> r
f a
y (r -> r) -> r -> r
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> r -> r
f a
x r
r
	reduce a -> r -> r
_ r
r Wye a
End = r
r

instance Semigroup a => Semigroup (Wye a) where
	Wye a
End + :: Wye a -> Wye a -> Wye a
+ Wye a
x = Wye a
x
	Wye a
x + Wye a
End = Wye a
x
	Left_ a
x + Left_ a
x' = a -> Wye a
forall a. a -> Wye a
Left_ (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
x'
	Left_ a
x + Right_ a
y = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y
	Left_ a
x + Both a
x' a
y = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
x' (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y
	Right_ a
y + Left_ a
x = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y
	Right_ a
y + Right_ a
y' = a -> Wye a
forall a. a -> Wye a
Right_ (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
y'
	Right_ a
y + Both a
x a
y' = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
y'
	Both a
x a
y + Left_ a
x' = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
x' (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y
	Both a
x a
y + Right_ a
y' = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
y'
	Both a
x a
y + Both a
x' a
y' = a -> a -> Wye a
forall a. a -> a -> Wye a
Both (a -> a -> Wye a) -> a -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
x a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
x' (a -> Wye a) -> a -> Wye a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a
y a -> a -> a
forall a. Semigroup a => a -> a -> a
+ a
y'

instance Semigroup a => Monoid (Wye a) where
	zero :: Wye a
zero = Wye a
forall a. Wye a
End

wye :: r -> (a -> r) -> (a -> r) -> (a -> a -> r) -> Wye a -> r
wye :: r -> (a -> r) -> (a -> r) -> (a -> a -> r) -> Wye a -> r
wye r
r a -> r
_ a -> r
_ a -> a -> r
_ Wye a
End = r
r
wye r
_ a -> r
f a -> r
_ a -> a -> r
_ (Left_ a
x) = a -> r
f a
x
wye r
_ a -> r
_ a -> r
g a -> a -> r
_ (Right_ a
y) = a -> r
g a
y
wye r
_ a -> r
_ a -> r
_ a -> a -> r
h (Both a
x a
y) = a -> a -> r
h a
x a
y

swop :: Wye ~> Wye
swop :: Wye a -> Wye a
swop Wye a
End = Wye a
forall a. Wye a
End
swop (Both a
l a
r) = a -> a -> Wye a
forall a. a -> a -> Wye a
Both a
r a
l
swop (Left_ a
l) = a -> Wye a
forall a. a -> Wye a
Right_ a
l
swop (Right_ a
r) = a -> Wye a
forall a. a -> Wye a
Left_ a
r