{-# OPTIONS_GHC -fno-warn-orphans #-}

module Pandora.Paradigm.Inventory.Accumulator (Accumulator (..), Accumulated, gather) where

import Pandora.Pattern.Category ((.), ($), (#))
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)), Covariant_ ((-<$>-)))
import Pandora.Pattern.Functor.Pointable (Pointable (point))
import Pandora.Pattern.Functor.Applicative (Applicative ((<*>)))
import Pandora.Pattern.Functor.Bindable (Bindable ((=<<)))
import Pandora.Pattern.Functor.Monad (Monad)
import Pandora.Pattern.Object.Monoid (Monoid (zero))
import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))
import Pandora.Paradigm.Primary.Algebraic.Product ((:*:) ((:*:)))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (Schematic, Interpreted (Primary, run, unite))
import Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic (Monadic (wrap), (:>) (TM))
import Pandora.Paradigm.Controlflow.Effect.Adaptable (Adaptable (adapt))
import Pandora.Paradigm.Schemes.UT (UT (UT), type (<.:>))

newtype Accumulator e a = Accumulator (e :*: a)

instance Covariant (Accumulator e) where
	a -> b
f <$> :: (a -> b) -> Accumulator e a -> Accumulator e b
<$> Accumulator e :*: a
x = (e :*: b) -> Accumulator e b
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: b) -> Accumulator e b) -> (e :*: b) -> Accumulator e b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ a -> b
f (a -> b) -> (e :*: a) -> e :*: b
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> e :*: a
x

instance Covariant_ (Accumulator e) (->) (->) where
	a -> b
f -<$>- :: (a -> b) -> Accumulator e a -> Accumulator e b
-<$>- Accumulator e :*: a
x = (e :*: b) -> Accumulator e b
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: b) -> Accumulator e b) -> (e :*: b) -> Accumulator e b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ a -> b
f (a -> b) -> (e :*: a) -> e :*: b
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) a b.
Covariant_ t source target =>
source a b -> target (t a) (t b)
-<$>- e :*: a
x

instance Semigroup e => Applicative (Accumulator e) where
	Accumulator e (a -> b)
f <*> :: Accumulator e (a -> b) -> Accumulator e a -> Accumulator e b
<*> Accumulator e a
v = (e :*: b) -> Accumulator e b
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: b) -> Accumulator e b) -> (e :*: b) -> Accumulator e b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (e :*: (a -> b)) -> (e :*: a) -> e :*: b
forall s t a.
Semigroup s =>
(s :*: (t -> a)) -> (s :*: t) -> s :*: a
k ((e :*: (a -> b)) -> (e :*: a) -> e :*: b)
-> (e :*: (a -> b)) -> (e :*: a) -> e :*: b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
# Accumulator e (a -> b) -> Primary (Accumulator e) (a -> b)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run Accumulator e (a -> b)
f ((e :*: a) -> e :*: b) -> (e :*: a) -> e :*: b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
# Accumulator e a -> Primary (Accumulator e) a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run Accumulator e a
v where
		k :: (s :*: (t -> a)) -> (s :*: t) -> s :*: a
k ~(s
e :*: t -> a
g) ~(s
e' :*: t
w) = s
e s -> s -> s
forall a. Semigroup a => a -> a -> a
+ s
e' s -> a -> s :*: a
forall s a. s -> a -> s :*: a
:*: t -> a
g t
w

instance Monoid e => Pointable (Accumulator e) (->) where
	point :: a -> Accumulator e a
point = (e :*: a) -> Accumulator e a
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: a) -> Accumulator e a)
-> (a -> e :*: a) -> a -> Accumulator e a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (e
forall a. Monoid a => a
zero e -> a -> e :*: a
forall s a. s -> a -> s :*: a
:*:)

instance Semigroup e => Bindable (Accumulator e) (->) where
	a -> Accumulator e b
f =<< :: (a -> Accumulator e b) -> Accumulator e a -> Accumulator e b
=<< Accumulator (e
e :*: a
x) = let e
e' :*: b
b = Accumulator e b -> e :*: b
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Accumulator e b -> e :*: b) -> Accumulator e b -> e :*: b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ a -> Accumulator e b
f a
x in
		(e :*: b) -> Accumulator e b
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: b) -> Accumulator e b) -> (e :*: b) -> Accumulator e b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ e
e e -> e -> e
forall a. Semigroup a => a -> a -> a
+ e
e'e -> b -> e :*: b
forall s a. s -> a -> s :*: a
:*: b
b

type instance Schematic Monad (Accumulator e) = (<.:>) ((:*:) e)

instance Interpreted (Accumulator e) where
	type Primary (Accumulator e) a = e :*: a
	run :: Accumulator e a -> Primary (Accumulator e) a
run ~(Accumulator e :*: a
x) = Primary (Accumulator e) a
e :*: a
x
	unite :: Primary (Accumulator e) a -> Accumulator e a
unite = Primary (Accumulator e) a -> Accumulator e a
forall e a. (e :*: a) -> Accumulator e a
Accumulator

instance Monoid e => Monadic (Accumulator e) where
	wrap :: Accumulator e ~> (Accumulator e :> u)
wrap = (<.:>) ((:*:) e) u a -> (:>) (Accumulator e) u a
forall (t :: * -> *) (u :: * -> *) a.
Schematic Monad t u a -> (:>) t u a
TM ((<.:>) ((:*:) e) u a -> (:>) (Accumulator e) u a)
-> (Accumulator e a -> (<.:>) ((:*:) e) u a)
-> Accumulator e a
-> (:>) (Accumulator e) u a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. ((u :. (:*:) e) := a) -> (<.:>) ((:*:) e) u a
forall k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *)
       (a :: k).
((u :. t) := a) -> UT ct cu t u a
UT (((u :. (:*:) e) := a) -> (<.:>) ((:*:) e) u a)
-> (Accumulator e a -> (u :. (:*:) e) := a)
-> Accumulator e a
-> (<.:>) ((:*:) e) u a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (e :*: a) -> (u :. (:*:) e) := a
forall (t :: * -> *) (source :: * -> * -> *) a.
Pointable t source =>
source a (t a)
point ((e :*: a) -> (u :. (:*:) e) := a)
-> (Accumulator e a -> e :*: a)
-> Accumulator e a
-> (u :. (:*:) e) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Accumulator e a -> e :*: a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run

type Accumulated e t = Adaptable (Accumulator e) t

instance {-# OVERLAPS #-} (Semigroup e, Applicative u) => Applicative ((:*:) e <.:> u) where
	UT (u :. (:*:) e) := (a -> b)
f <*> :: (<.:>) ((:*:) e) u (a -> b)
-> (<.:>) ((:*:) e) u a -> (<.:>) ((:*:) e) u b
<*> UT (u :. (:*:) e) := a
x = ((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b
forall k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *)
       (a :: k).
((u :. t) := a) -> UT ct cu t u a
UT (((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b)
-> ((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (e :*: (a -> b)) -> (e :*: a) -> e :*: b
forall s t a.
Semigroup s =>
(s :*: (t -> a)) -> (s :*: t) -> s :*: a
k ((e :*: (a -> b)) -> (e :*: a) -> e :*: b)
-> ((u :. (:*:) e) := (a -> b)) -> u ((e :*: a) -> e :*: b)
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> (u :. (:*:) e) := (a -> b)
f u ((e :*: a) -> e :*: b)
-> ((u :. (:*:) e) := a) -> (u :. (:*:) e) := b
forall (t :: * -> *) a b. Applicative t => t (a -> b) -> t a -> t b
<*> (u :. (:*:) e) := a
x where
		k :: (s :*: (t -> a)) -> (s :*: t) -> s :*: a
k ~(s
u :*: t -> a
g) ~(s
v :*: t
y) = s
u s -> s -> s
forall a. Semigroup a => a -> a -> a
+ s
v s -> a -> s :*: a
forall s a. s -> a -> s :*: a
:*: t -> a
g t
y

instance {-# OVERLAPS #-} (Pointable u (->), Monoid e) => Pointable ((:*:) e <.:> u) (->) where
	point :: a -> (<.:>) ((:*:) e) u a
point = ((u :. (:*:) e) := a) -> (<.:>) ((:*:) e) u a
forall k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *)
       (a :: k).
((u :. t) := a) -> UT ct cu t u a
UT (((u :. (:*:) e) := a) -> (<.:>) ((:*:) e) u a)
-> (a -> (u :. (:*:) e) := a) -> a -> (<.:>) ((:*:) e) u a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (e :*: a) -> (u :. (:*:) e) := a
forall (t :: * -> *) (source :: * -> * -> *) a.
Pointable t source =>
source a (t a)
point ((e :*: a) -> (u :. (:*:) e) := a)
-> (a -> e :*: a) -> a -> (u :. (:*:) e) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (e
forall a. Monoid a => a
zero e -> a -> e :*: a
forall s a. s -> a -> s :*: a
:*:)

instance {-# OVERLAPS #-} (Semigroup e, Pointable u (->), Bindable u (->)) => Bindable ((:*:) e <.:> u) (->) where
	a -> (<.:>) ((:*:) e) u b
f =<< :: (a -> (<.:>) ((:*:) e) u b)
-> (<.:>) ((:*:) e) u a -> (<.:>) ((:*:) e) u b
=<< UT (u :. (:*:) e) := a
x = ((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b
forall k k k k (ct :: k) (cu :: k) (t :: k -> k) (u :: k -> *)
       (a :: k).
((u :. t) := a) -> UT ct cu t u a
UT (((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b)
-> ((u :. (:*:) e) := b) -> (<.:>) ((:*:) e) u b
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ (\(e
acc :*: a
v) -> (\(e
acc' :*: b
y) -> (e
acc e -> e -> e
forall a. Semigroup a => a -> a -> a
+ e
acc' e -> b -> e :*: b
forall s a. s -> a -> s :*: a
:*: b
y)) ((e :*: b) -> e :*: b)
-> ((u :. (:*:) e) := b) -> (u :. (:*:) e) := b
forall (t :: * -> *) (source :: * -> * -> *)
       (target :: * -> * -> *) a b.
Covariant_ t source target =>
source a b -> target (t a) (t b)
-<$>- (<.:>) ((:*:) e) u b -> Primary ((:*:) e <.:> u) b
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (a -> (<.:>) ((:*:) e) u b
f a
v)) ((e :*: a) -> (u :. (:*:) e) := b)
-> ((u :. (:*:) e) := a) -> (u :. (:*:) e) := b
forall (t :: * -> *) (source :: * -> * -> *) a b.
Bindable t source =>
source a (t b) -> source (t a) (t b)
=<< (u :. (:*:) e) := a
x

gather :: Accumulated e t => e -> t ()
gather :: e -> t ()
gather e
x = Accumulator e () -> t ()
forall k (t :: k -> *) (u :: k -> *). Adaptable t u => t ~> u
adapt (Accumulator e () -> t ())
-> ((e :*: ()) -> Accumulator e ()) -> (e :*: ()) -> t ()
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (e :*: ()) -> Accumulator e ()
forall e a. (e :*: a) -> Accumulator e a
Accumulator ((e :*: ()) -> t ()) -> (e :*: ()) -> t ()
forall (m :: * -> * -> *) a b. Category m => m (m a b) (m a b)
$ e
x e -> () -> e :*: ()
forall s a. s -> a -> s :*: a
:*: ()