{-# LANGUAGE UndecidableInstances #-}

module Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (..), (:>) (..)) where

import Pandora.Core.Functor (type (~>))
import Pandora.Pattern.Semigroupoid ((.))
import Pandora.Pattern.Category (($))
import Pandora.Pattern.Functor.Covariant (Covariant ((-<$>-)))
import Pandora.Pattern.Functor.Pointable (Pointable (point))
import Pandora.Pattern.Functor.Extractable (Extractable (extract))
import Pandora.Pattern.Functor.Semimonoidal (Semimonoidal (multiply_))
import Pandora.Pattern.Functor.Distributive (Distributive ((-<<)))
import Pandora.Pattern.Functor.Traversable (Traversable ((<<-)))
import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))
import Pandora.Pattern.Functor.Extendable (Extendable ((<<=)))
import Pandora.Pattern.Functor.Monad (Monad)
import Pandora.Pattern.Transformer.Liftable (Liftable (lift))
import Pandora.Pattern.Transformer.Hoistable (Hoistable ((/|\)))
import Pandora.Paradigm.Primary.Algebraic.Product ((:*:)((:*:)))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite))

class Interpreted t => Monadic t where
	{-# MINIMAL wrap #-}
	wrap :: Pointable u (->) => t ~> t :> u

infixr 3 :>
newtype (:>) t u a = TM { (:>) t u a -> Schematic Monad t u a
tm :: Schematic Monad t u a }

instance Covariant (Schematic Monad t u) (->) (->) => Covariant (t :> u) (->) (->) where
	a -> b
f -<$>- :: (a -> b) -> (:>) t u a -> (:>) t u b
-<$>- TM Schematic Monad t u a
x = Schematic Monad t u b -> (:>) t u b
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u b -> (:>) t u b)
-> Schematic Monad t u b -> (:>) t u b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ a -> b
f (a -> b) -> Schematic Monad t u a -> Schematic Monad t u b
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) a b.
Covariant t source target =>
source a b -> target (t a) (t b)
-<$>- Schematic Monad t u a
x

instance Pointable (Schematic Monad t u) (->) => Pointable (t :> u) (->) where
	point :: a -> (:>) t u a
point = Schematic Monad t u a -> (:>) t u a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u a -> (:>) t u a)
-> (a -> Schematic Monad t u a) -> a -> (:>) t u a
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. a -> Schematic Monad t u a
forall (t :: * -> *) (source :: * -> * -> *) a.
Pointable t source =>
source a (t a)
point

instance Extractable (Schematic Monad t u) (->) => Extractable (t :> u) (->) where
	extract :: (:>) t u a -> a
extract = Schematic Monad t u a -> a
forall (t :: * -> *) (source :: * -> * -> *) a.
Extractable t source =>
source (t a) a
extract (Schematic Monad t u a -> a)
-> ((:>) t u a -> Schematic Monad t u a) -> (:>) t u a -> a
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. (:>) t u a -> Schematic Monad t u a
forall (t :: * -> *) (u :: * -> *) a.
(:>) t u a -> Schematic Monad t u a
tm

instance Semimonoidal (Schematic Monad t u) (->) (:*:) (:*:) => Semimonoidal (t :> u) (->) (:*:) (:*:) where
	multiply_ :: ((:>) t u a :*: (:>) t u b) -> (:>) t u (a :*: b)
multiply_ (TM Schematic Monad t u a
f :*: TM Schematic Monad t u b
x) = Schematic Monad t u (a :*: b) -> (:>) t u (a :*: b)
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u (a :*: b) -> (:>) t u (a :*: b))
-> Schematic Monad t u (a :*: b) -> (:>) t u (a :*: b)
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (Schematic Monad t u a :*: Schematic Monad t u b)
-> Schematic Monad t u (a :*: b)
forall k (t :: k -> *) (p :: * -> * -> *) (source :: * -> * -> *)
       (target :: k -> k -> k) (a :: k) (b :: k).
Semimonoidal t p source target =>
p (source (t a) (t b)) (t (target a b))
multiply_ ((Schematic Monad t u a :*: Schematic Monad t u b)
 -> Schematic Monad t u (a :*: b))
-> (Schematic Monad t u a :*: Schematic Monad t u b)
-> Schematic Monad t u (a :*: b)
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ Schematic Monad t u a
f Schematic Monad t u a
-> Schematic Monad t u b
-> Schematic Monad t u a :*: Schematic Monad t u b
forall s a. s -> a -> s :*: a
:*: Schematic Monad t u b
x

instance Traversable (Schematic Monad t u) (->) (->) => Traversable (t :> u) (->) (->) where
	a -> u b
f <<- :: (a -> u b) -> (:>) t u a -> u ((:>) t u b)
<<- TM Schematic Monad t u a
x = Schematic Monad t u b -> (:>) t u b
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u b -> (:>) t u b)
-> u (Schematic Monad t u b) -> u ((:>) t u b)
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) a b.
Covariant t source target =>
source a b -> target (t a) (t b)
-<$>- a -> u b
f (a -> u b) -> Schematic Monad t u a -> u (Schematic Monad t u b)
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) (u :: * -> *) a b.
(Traversable t source target, Covariant u source target,
 Pointable u target, Semimonoidal u target (:*:) (:*:)) =>
source a (u b) -> target (t a) (u (t b))
<<- Schematic Monad t u a
x

instance Distributive (Schematic Monad t u) (->) (->) => Distributive (t :> u) (->) (->) where
	a -> (:>) t u b
f -<< :: (a -> (:>) t u b) -> u a -> (:>) t u (u b)
-<< u a
x = Schematic Monad t u (u b) -> (:>) t u (u b)
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u (u b) -> (:>) t u (u b))
-> Schematic Monad t u (u b) -> (:>) t u (u b)
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (:>) t u b -> Schematic Monad t u b
forall (t :: * -> *) (u :: * -> *) a.
(:>) t u a -> Schematic Monad t u a
tm ((:>) t u b -> Schematic Monad t u b)
-> (a -> (:>) t u b) -> a -> Schematic Monad t u b
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. a -> (:>) t u b
f (a -> Schematic Monad t u b) -> u a -> Schematic Monad t u (u b)
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) (u :: * -> *) a b.
(Distributive t source target, Covariant u source target) =>
source a (t b) -> target (u a) (t (u b))
-<< u a
x

instance Bindable (Schematic Monad t u) (->) => Bindable (t :> u) (->) where
	a -> (:>) t u b
f =<< :: (a -> (:>) t u b) -> (:>) t u a -> (:>) t u b
=<< TM Schematic Monad t u a
x = Schematic Monad t u b -> (:>) t u b
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u b -> (:>) t u b)
-> Schematic Monad t u b -> (:>) t u b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (:>) t u b -> Schematic Monad t u b
forall (t :: * -> *) (u :: * -> *) a.
(:>) t u a -> Schematic Monad t u a
tm ((:>) t u b -> Schematic Monad t u b)
-> (a -> (:>) t u b) -> a -> Schematic Monad t u b
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. a -> (:>) t u b
f (a -> Schematic Monad t u b)
-> Schematic Monad t u a -> Schematic Monad t u b
forall (t :: * -> *) (source :: * -> * -> *) a b.
Bindable t source =>
source a (t b) -> source (t a) (t b)
=<< Schematic Monad t u a
x

instance Extendable (Schematic Monad t u) (->) => Extendable (t :> u) (->) where
	(:>) t u a -> b
f <<= :: ((:>) t u a -> b) -> (:>) t u a -> (:>) t u b
<<= TM Schematic Monad t u a
x = Schematic Monad t u b -> (:>) t u b
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u b -> (:>) t u b)
-> Schematic Monad t u b -> (:>) t u b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (:>) t u a -> b
f ((:>) t u a -> b)
-> (Schematic Monad t u a -> (:>) t u a)
-> Schematic Monad t u a
-> b
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. Schematic Monad t u a -> (:>) t u a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u a -> b)
-> Schematic Monad t u a -> Schematic Monad t u b
forall (t :: * -> *) (source :: * -> * -> *) a b.
Extendable t source =>
source (t a) b -> source (t a) (t b)
<<= Schematic Monad t u a
x

instance (Covariant (Schematic Monad t u) (->) (->), Pointable (t :> u) (->), Bindable (t :> u) (->)) => Monad (t :> u) where

instance Liftable (Schematic Monad t) => Liftable ((:>) t) where
	lift :: u ~> (t :> u)
lift = Schematic Monad t u a -> (:>) t u a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u a -> (:>) t u a)
-> (u a -> Schematic Monad t u a) -> u a -> (:>) t u a
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. u a -> Schematic Monad t u a
forall (t :: (* -> *) -> * -> *) (u :: * -> *).
(Liftable t, Covariant u (->) (->)) =>
u ~> t u
lift

instance Hoistable (Schematic Monad t) => Hoistable ((:>) t) where
	u ~> v
f /|\ :: (u ~> v) -> (t :> u) ~> (t :> v)
/|\ TM Schematic Monad t u a
x = Schematic Monad t v a -> (:>) t v a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t v a -> (:>) t v a)
-> Schematic Monad t v a -> (:>) t v a
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ u ~> v
f (u ~> v) -> Schematic Monad t u a -> Schematic Monad t v a
forall k (t :: (* -> *) -> k -> *) (u :: * -> *) (v :: * -> *).
(Hoistable t, Covariant u (->) (->)) =>
(u ~> v) -> t u ~> t v
/|\ Schematic Monad t u a
x

instance (Interpreted (Schematic Monad t u)) => Interpreted (t :> u) where
	type Primary (t :> u) a = Primary (Schematic Monad t u) a
	run :: (:>) t u a -> Primary (t :> u) a
run ~(TM Schematic Monad t u a
x) = Schematic Monad t u a -> Primary (Schematic Monad t u) a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run Schematic Monad t u a
x
	unite :: Primary (t :> u) a -> (:>) t u a
unite = Schematic Monad t u a -> (:>) t u a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM (Schematic Monad t u a -> (:>) t u a)
-> (Primary (Schematic Monad t u) a -> Schematic Monad t u a)
-> Primary (Schematic Monad t u) a
-> (:>) t u a
forall (m :: * -> * -> *) b c a.
Semigroupoid m =>
m b c -> m a b -> m a c
. Primary (Schematic Monad t u) a -> Schematic Monad t u a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite