module Pandora.Paradigm.Primary.Functor.Edges where

import Pandora.Pattern.Category ((<--))
import Pandora.Pattern.Functor.Covariant (Covariant ((<-|-)))
import Pandora.Pattern.Functor.Traversable (Traversable ((<-/-)))
import Pandora.Paradigm.Algebraic.Exponential ()
import Pandora.Paradigm.Algebraic (point)

data Edges a = Empty | Leap a | Connect a | Overlay a

instance Covariant (->) (->) Edges where
	a -> b
_ <-|- :: (a -> b) -> Edges a -> Edges b
<-|- Edges a
Empty = Edges b
forall a. Edges a
Empty
	a -> b
f <-|- Connect a
x = b -> Edges b
forall a. a -> Edges a
Connect (b -> Edges b) -> b -> Edges b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
x
	a -> b
f <-|- Overlay a
x = b -> Edges b
forall a. a -> Edges a
Overlay (b -> Edges b) -> b -> Edges b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
x
	a -> b
f <-|- Leap a
x = b -> Edges b
forall a. a -> Edges a
Leap (b -> Edges b) -> b -> Edges b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
<-- a -> b
f a
x

instance Traversable (->) (->) Edges where
	a -> u b
_ <-/- :: (a -> u b) -> Edges a -> u (Edges b)
<-/- Edges a
Empty = Edges b -> u (Edges b)
forall (t :: * -> *) a. Pointable t => a -> t a
point Edges b
forall a. Edges a
Empty
	a -> u b
f <-/- Connect a
x = b -> Edges b
forall a. a -> Edges a
Connect (b -> Edges b) -> u b -> u (Edges b)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
<-|- a -> u b
f a
x
	a -> u b
f <-/- Overlay a
x = b -> Edges b
forall a. a -> Edges a
Overlay (b -> Edges b) -> u b -> u (Edges b)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
<-|- a -> u b
f a
x
	a -> u b
f <-/- Leap a
x = b -> Edges b
forall a. a -> Edges a
Leap (b -> Edges b) -> u b -> u (Edges b)
forall (source :: * -> * -> *) (target :: * -> * -> *)
       (t :: * -> *) a b.
Covariant source target t =>
source a b -> target (t a) (t b)
<-|- a -> u b
f a
x

edges :: r -> (a -> r) -> (a -> r) -> (a -> r) -> Edges a -> r
edges :: r -> (a -> r) -> (a -> r) -> (a -> r) -> Edges a -> r
edges r
r a -> r
_ a -> r
_ a -> r
_ Edges a
Empty = r
r
edges r
_ a -> r
f a -> r
_ a -> r
_ (Connect a
x) = a -> r
f a
x
edges r
_ a -> r
_ a -> r
g a -> r
_ (Overlay a
y) = a -> r
g a
y
edges r
_ a -> r
_ a -> r
_ a -> r
h (Leap a
z) = a -> r
h a
z