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

module Pandora.Paradigm.Structure.Stack where

import Pandora.Core.Functor (type (~>), type (:.), type (:=))
import Pandora.Core.Morphism ((&), (%))
import Pandora.Pattern ((.|..))
import Pandora.Pattern.Category ((.), ($))
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))
import Pandora.Pattern.Functor.Alternative ((<+>))
import Pandora.Pattern.Functor.Pointable (point)
import Pandora.Pattern.Functor.Extractable (extract)
import Pandora.Pattern.Functor.Traversable (Traversable)
import Pandora.Pattern.Functor.Bindable ((>>=))
import Pandora.Pattern.Functor.Extendable (Extendable ((=>>)))
import Pandora.Pattern.Transformer.Liftable (lift)
import Pandora.Pattern.Object.Setoid (Setoid ((==)))
import Pandora.Pattern.Object.Semigroup (Semigroup ((+)))
import Pandora.Pattern.Object.Monoid (Monoid (zero))
import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), (?))
import Pandora.Paradigm.Primary.Functor.Delta (Delta ((:^:)))
import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing))
import Pandora.Paradigm.Primary.Functor.Predicate (Predicate (Predicate))
import Pandora.Paradigm.Primary.Functor.Product (Product ((:*:)))
import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag))
import Pandora.Paradigm.Primary.Functor.Wye (Wye (Left, Right))
import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct, (.-+))
import Pandora.Paradigm.Primary.Transformer.Tap (Tap (Tap))
import Pandora.Paradigm.Inventory.State (State, fold)
import Pandora.Paradigm.Inventory.Store (Store (Store))
import Pandora.Paradigm.Inventory.Optics ((^.))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (run)
import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>))
import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty)
import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null))
import Pandora.Paradigm.Structure.Ability.Zipper (Zipper)
import Pandora.Paradigm.Structure.Ability.Focusable (Focusable (Focusing, focusing), Location (Head), focus)
import Pandora.Paradigm.Structure.Ability.Insertable (Insertable (insert))
import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))
import Pandora.Paradigm.Structure.Ability.Rotatable (Rotatable (Rotational, rotation), rotate)

-- | Linear data structure that serves as a collection of elements
type Stack = Maybe <:.> Construction Maybe

instance Setoid a => Setoid (Stack a) where
	TU (Maybe :. Construction Maybe) := a
ls == :: Stack a -> Stack a -> Boolean
== TU (Maybe :. Construction Maybe) := a
rs = (Maybe :. Construction Maybe) := a
ls ((Maybe :. Construction Maybe) := a)
-> ((Maybe :. Construction Maybe) := a) -> Boolean
forall a. Setoid a => a -> a -> Boolean
== (Maybe :. Construction Maybe) := a
rs

instance Semigroup (Stack a) where
	TU Maybe (Construction Maybe a)
Nothing + :: Stack a -> Stack a -> Stack a
+ TU Maybe (Construction Maybe a)
ys = Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU Maybe (Construction Maybe a)
ys
	TU (Just (Construct a
x Maybe (Construction Maybe a)
xs)) + TU Maybe (Construction Maybe a)
ys = Construction Maybe a -> Stack a
forall (t :: (* -> *) -> * -> *) (u :: * -> *).
(Liftable t, Covariant u) =>
u ~> t u
lift (Construction Maybe a -> Stack a)
-> (Stack a -> Construction Maybe a) -> Stack a -> Stack a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Maybe (Construction Maybe a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct a
x (Maybe (Construction Maybe a) -> Construction Maybe a)
-> (Stack a -> Maybe (Construction Maybe a))
-> Stack a
-> Construction Maybe a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run
		(Stack a -> Stack a) -> Stack a -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU @Covariant @Covariant Maybe (Construction Maybe a)
xs Stack a -> Stack a -> Stack a
forall a. Semigroup a => a -> a -> a
+ Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU @Covariant @Covariant Maybe (Construction Maybe a)
ys

instance Monoid (Stack a) where
	zero :: Stack a
zero = ((Maybe :. Construction Maybe) := a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (Maybe :. Construction Maybe) := a
forall a. Maybe a
Nothing

instance Focusable Head Stack where
	type Focusing Head Stack a = Maybe a
	focusing :: Tagged 'Head (Stack a) :-. Focusing 'Head Stack a
focusing (Tag Stack a
stack) = (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Head (Stack a))
-> Store (Maybe a) (Tagged 'Head (Stack a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Head (Stack a))
 -> Store (Maybe a) (Tagged 'Head (Stack a)))
-> (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Head (Stack a))
-> Store (Maybe a) (Tagged 'Head (Stack a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a <-| Construction Maybe
forall (t :: * -> *) a. Extractable t => a <-| t
extract (a <-| Construction Maybe)
-> Maybe (Construction Maybe a) -> Maybe a
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> Stack a -> Primary Stack a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run Stack a
stack Maybe a
-> (Maybe a -> Tagged 'Head (Stack a))
-> ((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Head (Stack a)
forall s a. s -> a -> Product s a
:*: \case
		Just a
x -> Stack a
stack Stack a -> (Stack a -> Stack a) -> Stack a
forall a b. a -> (a -> b) -> b
& Stack a -> Stack a
Stack ~> Stack
pop Stack a -> (Stack a -> Stack a) -> Stack a
forall a b. a -> (a -> b) -> b
& a -> Stack a -> Stack a
forall (t :: * -> *) a. Insertable t => a -> t a -> t a
insert a
x Stack a
-> (Stack a -> Tagged 'Head (Stack a)) -> Tagged 'Head (Stack a)
forall a b. a -> (a -> b) -> b
& Stack a -> Tagged 'Head (Stack a)
forall k (tag :: k) a. a -> Tagged tag a
Tag
		Maybe a
Nothing -> Stack a -> Tagged 'Head (Stack a)
forall k (tag :: k) a. a -> Tagged tag a
Tag (Stack a -> Tagged 'Head (Stack a))
-> Stack a -> Tagged 'Head (Stack a)
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Stack a -> Stack a
Stack ~> Stack
pop Stack a
stack

instance Insertable Stack where
	insert :: a -> Stack a -> Stack a
insert a
x (TU (Maybe :. Construction Maybe) := a
stack) = ((Maybe :. Construction Maybe) := a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Maybe :. Construction Maybe) := a) -> Stack a)
-> ((Maybe :. Construction Maybe) := a) -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ (a -> ((Maybe :. Construction Maybe) := a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct a
x (((Maybe :. Construction Maybe) := a) -> Construction Maybe a)
-> (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> Construction Maybe a
-> Construction Maybe a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall a. a -> Maybe a
Just (Construction Maybe a -> Construction Maybe a)
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> (Maybe :. Construction Maybe) := a
stack) ((Maybe :. Construction Maybe) := a)
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Alternative t => t a -> t a -> t a
<+> (Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Pointable t => a |-> t
point (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> (a -> Construction Maybe a)
-> a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Construction Maybe a
forall (t :: * -> *) a. Pointable t => a |-> t
point) a
x

instance Nullable Stack where
	null :: (Predicate :. Stack) := a
null = (Stack a -> Boolean) -> (Predicate :. Stack) := a
forall a. (a -> Boolean) -> Predicate a
Predicate ((Stack a -> Boolean) -> (Predicate :. Stack) := a)
-> (Stack a -> Boolean) -> (Predicate :. Stack) := a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ \case { TU Maybe (Construction Maybe a)
Nothing -> Boolean
True ; Stack a
_ -> Boolean
False }

pop :: Stack ~> Stack
pop :: Stack a -> Stack a
pop (TU (Maybe :. Construction Maybe) := a
stack) = ((Maybe :. Construction Maybe) := a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Maybe :. Construction Maybe) := a) -> Stack a)
-> ((Maybe :. Construction Maybe) := a) -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ (Maybe :. Construction Maybe) := a
stack ((Maybe :. Construction Maybe) := a)
-> (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b
>>= Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct

delete :: Setoid a => a -> Stack a -> Stack a
delete :: a -> Stack a -> Stack a
delete a
_ (TU Maybe (Construction Maybe a)
Nothing) = Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU Maybe (Construction Maybe a)
forall a. Maybe a
Nothing
delete a
x (TU (Just (Construct a
y Maybe (Construction Maybe a)
ys))) = a
x a -> a -> Boolean
forall a. Setoid a => a -> a -> Boolean
== a
y Boolean -> Stack a -> Stack a -> Stack a
forall a. Boolean -> a -> a -> a
? Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU Maybe (Construction Maybe a)
ys
	(Stack a -> Stack a) -> Stack a -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Construction Maybe a -> Stack a
forall (t :: (* -> *) -> * -> *) (u :: * -> *).
(Liftable t, Covariant u) =>
u ~> t u
lift (Construction Maybe a -> Stack a)
-> (Stack a -> Construction Maybe a) -> Stack a -> Stack a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Maybe (Construction Maybe a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct a
y (Maybe (Construction Maybe a) -> Construction Maybe a)
-> (Stack a -> Maybe (Construction Maybe a))
-> Stack a
-> Construction Maybe a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> Maybe (Construction Maybe a))
-> (Stack a -> Stack a) -> Stack a -> Maybe (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Stack a -> Stack a
forall a. Setoid a => a -> Stack a -> Stack a
delete a
x (Stack a -> Stack a) -> Stack a -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Maybe (Construction Maybe a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU Maybe (Construction Maybe a)
ys

filter :: forall a . Predicate a -> Stack a -> Stack a
filter :: Predicate a -> Stack a -> Stack a
filter (Predicate a -> Boolean
p) = ((Maybe :. Construction Maybe) := a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Maybe :. Construction Maybe) := a) -> Stack a)
-> (Stack a -> (Maybe :. Construction Maybe) := a)
-> Stack a
-> Stack a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. ((Maybe :. Construction Maybe) := a)
<-| Product ((Maybe :. Construction Maybe) := a)
forall (t :: * -> *) a. Extractable t => a <-| t
extract
	(((Maybe :. Construction Maybe) := a)
 <-| Product ((Maybe :. Construction Maybe) := a))
-> (Stack a
    -> Product
         ((Maybe :. Construction Maybe) := a)
         ((Maybe :. Construction Maybe) := a))
-> Stack a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. forall a.
Interpreted (State ((Maybe :. Nonempty Stack) := a)) =>
State ((Maybe :. Nonempty Stack) := a) a
-> Primary (State ((Maybe :. Nonempty Stack) := a)) a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run @(State (Maybe :. Nonempty Stack := a)) (State
   ((Maybe :. Construction Maybe) := a)
   ((Maybe :. Construction Maybe) := a)
 -> ((Maybe :. Construction Maybe) := a)
 -> Product
      ((Maybe :. Construction Maybe) := a)
      ((Maybe :. Construction Maybe) := a))
-> ((Maybe :. Construction Maybe) := a)
-> State
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
-> Product
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall a b c. (a -> b -> c) -> b -> a -> c
% (Maybe :. Construction Maybe) := a
forall a. Maybe a
Nothing
	(State
   ((Maybe :. Construction Maybe) := a)
   ((Maybe :. Construction Maybe) := a)
 -> Product
      ((Maybe :. Construction Maybe) := a)
      ((Maybe :. Construction Maybe) := a))
-> (Stack a
    -> State
         ((Maybe :. Construction Maybe) := a)
         ((Maybe :. Construction Maybe) := a))
-> Stack a
-> Product
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (a
 -> ((Maybe :. Construction Maybe) := a)
 -> (Maybe :. Construction Maybe) := a)
-> Stack a
-> State
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall (t :: * -> *) s (u :: * -> *) a.
(Traversable t, Memorable s u) =>
(a -> s -> s) -> t a -> u s
fold (\a
now (Maybe :. Construction Maybe) := a
new -> a -> Boolean
p a
now Boolean
-> ((Maybe :. Construction Maybe) := a)
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall a. Boolean -> a -> a -> a
? Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall a. a -> Maybe a
Just (a -> ((Maybe :. Construction Maybe) := a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct a
now (Maybe :. Construction Maybe) := a
new) (((Maybe :. Construction Maybe) := a)
 -> (Maybe :. Construction Maybe) := a)
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ (Maybe :. Construction Maybe) := a
new)

-- | Transform any traversable structure into a stack
linearize :: forall t a . Traversable t => t a -> Stack a
linearize :: t a -> Stack a
linearize = ((Maybe :. Construction Maybe) := a) -> Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Maybe :. Construction Maybe) := a) -> Stack a)
-> (t a -> (Maybe :. Construction Maybe) := a) -> t a -> Stack a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. ((Maybe :. Construction Maybe) := a)
<-| Product ((Maybe :. Construction Maybe) := a)
forall (t :: * -> *) a. Extractable t => a <-| t
extract (((Maybe :. Construction Maybe) := a)
 <-| Product ((Maybe :. Construction Maybe) := a))
-> (t a
    -> Product
         ((Maybe :. Construction Maybe) := a)
         ((Maybe :. Construction Maybe) := a))
-> t a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. forall a.
Interpreted (State ((Maybe :. Nonempty Stack) := a)) =>
State ((Maybe :. Nonempty Stack) := a) a
-> Primary (State ((Maybe :. Nonempty Stack) := a)) a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run @(State (Maybe :. Nonempty Stack := a)) (State
   ((Maybe :. Construction Maybe) := a)
   ((Maybe :. Construction Maybe) := a)
 -> ((Maybe :. Construction Maybe) := a)
 -> Product
      ((Maybe :. Construction Maybe) := a)
      ((Maybe :. Construction Maybe) := a))
-> ((Maybe :. Construction Maybe) := a)
-> State
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
-> Product
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall a b c. (a -> b -> c) -> b -> a -> c
% (Maybe :. Construction Maybe) := a
forall a. Maybe a
Nothing (State
   ((Maybe :. Construction Maybe) := a)
   ((Maybe :. Construction Maybe) := a)
 -> Product
      ((Maybe :. Construction Maybe) := a)
      ((Maybe :. Construction Maybe) := a))
-> (t a
    -> State
         ((Maybe :. Construction Maybe) := a)
         ((Maybe :. Construction Maybe) := a))
-> t a
-> Product
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (a
 -> ((Maybe :. Construction Maybe) := a)
 -> (Maybe :. Construction Maybe) := a)
-> t a
-> State
     ((Maybe :. Construction Maybe) := a)
     ((Maybe :. Construction Maybe) := a)
forall (t :: * -> *) s (u :: * -> *) a.
(Traversable t, Memorable s u) =>
(a -> s -> s) -> t a -> u s
fold (Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall a. a -> Maybe a
Just (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> (((->) a :. (->) ((Maybe :. Construction Maybe) := a))
    := Construction Maybe a)
-> a
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Construction Maybe) := a
forall (v :: * -> * -> *) a c d b.
(Category v, Covariant (v a)) =>
v c d -> ((v a :. v b) := c) -> (v a :. v b) := d
.|.. ((->) a :. (->) ((Maybe :. Construction Maybe) := a))
:= Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct)

type instance Nonempty Stack = Construction Maybe

instance Focusable Head (Construction Maybe) where
	type Focusing Head (Construction Maybe) a = a
	focusing :: Tagged 'Head (Construction Maybe a)
:-. Focusing 'Head (Construction Maybe) a
focusing (Tag Construction Maybe a
stack) = (((:*:) a :. (->) a) := Tagged 'Head (Construction Maybe a))
-> Store a (Tagged 'Head (Construction Maybe a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) a :. (->) a) := Tagged 'Head (Construction Maybe a))
 -> Store a (Tagged 'Head (Construction Maybe a)))
-> (((:*:) a :. (->) a) := Tagged 'Head (Construction Maybe a))
-> Store a (Tagged 'Head (Construction Maybe a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a <-| Construction Maybe
forall (t :: * -> *) a. Extractable t => a <-| t
extract Construction Maybe a
stack a
-> (a -> Tagged 'Head (Construction Maybe a))
-> ((:*:) a :. (->) a) := Tagged 'Head (Construction Maybe a)
forall s a. s -> a -> Product s a
:*: Construction Maybe a -> Tagged 'Head (Construction Maybe a)
forall k (tag :: k) a. a -> Tagged tag a
Tag (Construction Maybe a -> Tagged 'Head (Construction Maybe a))
-> (a -> Construction Maybe a)
-> a
-> Tagged 'Head (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> ((Maybe :. Construction Maybe) := a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct (a -> ((Maybe :. Construction Maybe) := a) -> Construction Maybe a)
-> ((Maybe :. Construction Maybe) := a)
-> a
-> Construction Maybe a
forall a b c. (a -> b -> c) -> b -> a -> c
% Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct Construction Maybe a
stack

instance Insertable (Construction Maybe) where
	insert :: a -> Construction Maybe a -> Construction Maybe a
insert a
x = a -> ((Maybe :. Construction Maybe) := a) -> Construction Maybe a
forall (t :: * -> *) a.
a -> ((t :. Construction t) := a) -> Construction t a
Construct a
x (((Maybe :. Construction Maybe) := a) -> Construction Maybe a)
-> (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> Construction Maybe a
-> Construction Maybe a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall a. a -> Maybe a
Just

instance Monotonic a (Construction Maybe a) where
	reduce :: (a -> r -> r) -> r -> Construction Maybe a -> r
reduce a -> r -> r
f r
r ~(Construct a
x (Maybe :. Construction Maybe) := a
xs) = a -> r -> r
f a
x (r -> r) -> r -> r
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ (a -> r -> r) -> r -> ((Maybe :. Construction Maybe) := a) -> r
forall a e r. Monotonic a e => (a -> r -> r) -> r -> e -> r
reduce a -> r -> r
f r
r (Maybe :. Construction Maybe) := a
xs

type instance Zipper Stack = Tap (Delta <:.> Stack)

instance {-# OVERLAPS #-} Extendable (Tap (Delta <:.> Stack)) where
	Tap (Delta <:.> Stack) a
z =>> :: Tap (Delta <:.> Stack) a
-> (Tap (Delta <:.> Stack) a -> b) -> Tap (Delta <:.> Stack) b
=>> Tap (Delta <:.> Stack) a -> b
f = let move :: (Tap (Delta <:.> Stack) a |-> Maybe)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
move Tap (Delta <:.> Stack) a |-> Maybe
rtt = ((Maybe :. Construction Maybe) := Tap (Delta <:.> Stack) a)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Maybe :. Construction Maybe) := Tap (Delta <:.> Stack) a)
 -> TU
      Covariant
      Covariant
      Maybe
      (Construction Maybe)
      (Tap (Delta <:.> Stack) a))
-> (Construction Maybe (Tap (Delta <:.> Stack) a)
    -> (Maybe :. Construction Maybe) := Tap (Delta <:.> Stack) a)
-> Construction Maybe (Tap (Delta <:.> Stack) a)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Construction Maybe (Tap (Delta <:.> Stack) a)
-> (Maybe :. Construction Maybe) := Tap (Delta <:.> Stack) a
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct (Construction Maybe (Tap (Delta <:.> Stack) a)
 -> TU
      Covariant
      Covariant
      Maybe
      (Construction Maybe)
      (Tap (Delta <:.> Stack) a))
-> Construction Maybe (Tap (Delta <:.> Stack) a)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Tap (Delta <:.> Stack) a |-> Maybe
rtt (Tap (Delta <:.> Stack) a |-> Maybe)
-> Tap (Delta <:.> Stack) a |-> Construction Maybe
forall (t :: * -> *) a.
Covariant t =>
(a |-> t) -> a |-> Construction t
.-+ Tap (Delta <:.> Stack) a
z
		in Tap (Delta <:.> Stack) a -> b
f (Tap (Delta <:.> Stack) a -> b)
-> Tap (Delta <:.> Stack) (Tap (Delta <:.> Stack) a)
-> Tap (Delta <:.> Stack) b
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> Tap (Delta <:.> Stack) a
-> (<:.>) Delta Stack (Tap (Delta <:.> Stack) a)
-> Tap (Delta <:.> Stack) (Tap (Delta <:.> Stack) a)
forall (t :: * -> *) a. a -> t a -> Tap t a
Tap Tap (Delta <:.> Stack) a
z (((Delta :. Stack) := Tap (Delta <:.> Stack) a)
-> (<:.>) Delta Stack (Tap (Delta <:.> Stack) a)
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (((Delta :. Stack) := Tap (Delta <:.> Stack) a)
 -> (<:.>) Delta Stack (Tap (Delta <:.> Stack) a))
-> ((Delta :. Stack) := Tap (Delta <:.> Stack) a)
-> (<:.>) Delta Stack (Tap (Delta <:.> Stack) a)
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ (Tap (Delta <:.> Stack) a |-> Maybe)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
move (forall k (f :: k) (t :: * -> *) a.
Rotatable f t =>
t a -> Rotational f t a
forall (t :: * -> *) a.
Rotatable 'Left t =>
t a -> Rotational 'Left t a
rotate @Left) TU
  Covariant
  Covariant
  Maybe
  (Construction Maybe)
  (Tap (Delta <:.> Stack) a)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
-> (Delta :. Stack) := Tap (Delta <:.> Stack) a
forall a. a -> a -> Delta a
:^: (Tap (Delta <:.> Stack) a |-> Maybe)
-> TU
     Covariant
     Covariant
     Maybe
     (Construction Maybe)
     (Tap (Delta <:.> Stack) a)
move (forall k (f :: k) (t :: * -> *) a.
Rotatable f t =>
t a -> Rotational f t a
forall (t :: * -> *) a.
Rotatable 'Right t =>
t a -> Rotational 'Right t a
rotate @Right))

instance Rotatable Left (Tap (Delta <:.> Stack)) where
	type Rotational Left (Tap (Delta <:.> Stack)) a = Maybe :. Zipper Stack := a
	rotation :: Tagged 'Left (Tap (Delta <:.> Stack) a)
-> Rotational 'Left (Tap (Delta <:.> Stack)) a
rotation (Tap (Delta <:.> Stack) a <-| Tagged 'Left
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Tap a
x (TU (Stack a
bs :^: Stack a
fs))) = a
-> TU Covariant Covariant Delta Stack a -> Tap (Delta <:.> Stack) a
forall (t :: * -> *) a. a -> t a -> Tap t a
Tap (a
 -> TU Covariant Covariant Delta Stack a
 -> Tap (Delta <:.> Stack) a)
-> TU Covariant Covariant Delta Stack a
-> a
-> Tap (Delta <:.> Stack) a
forall a b c. (a -> b -> c) -> b -> a -> c
% (Delta (Stack a) -> TU Covariant Covariant Delta Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (Delta (Stack a) -> TU Covariant Covariant Delta Stack a)
-> Delta (Stack a) -> TU Covariant Covariant Delta Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Stack a -> Stack a
Stack ~> Stack
pop Stack a
bs Stack a -> Stack a -> Delta (Stack a)
forall a. a -> a -> Delta a
:^: a -> Stack a -> Stack a
forall (t :: * -> *) a. Insertable t => a -> t a -> t a
insert a
x Stack a
fs) (a -> Tap (Delta <:.> Stack) a)
-> Maybe a -> Maybe (Tap (Delta <:.> Stack) a)
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> forall k (f :: * -> k) (t :: * -> *) a.
Focusable f t =>
t a :-. Focusing f t a
forall (t :: * -> *) a.
Focusable 'Head t =>
t a :-. Focusing 'Head t a
focus @Head (Stack a -> Store (Maybe a) (Stack a)) -> Stack a -> Maybe a
forall src tgt. Lens src tgt -> src -> tgt
^. Stack a
bs

instance Rotatable Right (Tap (Delta <:.> Stack)) where
	type Rotational Right (Tap (Delta <:.> Stack)) a = Maybe :. Zipper Stack := a
	rotation :: Tagged 'Right (Tap (Delta <:.> Stack) a)
-> Rotational 'Right (Tap (Delta <:.> Stack)) a
rotation (Tap (Delta <:.> Stack) a <-| Tagged 'Right
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Tap a
x (TU (Stack a
bs :^: Stack a
fs))) = a
-> TU Covariant Covariant Delta Stack a -> Tap (Delta <:.> Stack) a
forall (t :: * -> *) a. a -> t a -> Tap t a
Tap (a
 -> TU Covariant Covariant Delta Stack a
 -> Tap (Delta <:.> Stack) a)
-> TU Covariant Covariant Delta Stack a
-> a
-> Tap (Delta <:.> Stack) a
forall a b c. (a -> b -> c) -> b -> a -> c
% (Delta (Stack a) -> TU Covariant Covariant Delta Stack a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (Delta (Stack a) -> TU Covariant Covariant Delta Stack a)
-> Delta (Stack a) -> TU Covariant Covariant Delta Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a -> Stack a -> Stack a
forall (t :: * -> *) a. Insertable t => a -> t a -> t a
insert a
x Stack a
bs Stack a -> Stack a -> Delta (Stack a)
forall a. a -> a -> Delta a
:^: Stack a -> Stack a
Stack ~> Stack
pop Stack a
fs) (a -> Tap (Delta <:.> Stack) a)
-> Maybe a -> Maybe (Tap (Delta <:.> Stack) a)
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> forall k (f :: * -> k) (t :: * -> *) a.
Focusable f t =>
t a :-. Focusing f t a
forall (t :: * -> *) a.
Focusable 'Head t =>
t a :-. Focusing 'Head t a
focus @Head (Stack a -> Store (Maybe a) (Stack a)) -> Stack a -> Maybe a
forall src tgt. Lens src tgt -> src -> tgt
^. Stack a
fs

type instance Zipper (Construction Maybe) = Tap (Delta <:.> Construction Maybe)

instance Rotatable Left (Tap (Delta <:.> Construction Maybe)) where
	type Rotational Left (Tap (Delta <:.> Construction Maybe)) a = Maybe :. Zipper (Construction Maybe) := a
	rotation :: Tagged 'Left (Tap (Delta <:.> Construction Maybe) a)
-> Rotational 'Left (Tap (Delta <:.> Construction Maybe)) a
rotation (Tap (Delta <:.> Construction Maybe) a <-| Tagged 'Left
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Tap a
x (TU (Construction Maybe a
bs :^: Construction Maybe a
fs))) = a
-> TU Covariant Covariant Delta (Construction Maybe) a
-> Tap (Delta <:.> Construction Maybe) a
forall (t :: * -> *) a. a -> t a -> Tap t a
Tap (a <-| Construction Maybe
forall (t :: * -> *) a. Extractable t => a <-| t
extract Construction Maybe a
bs) (TU Covariant Covariant Delta (Construction Maybe) a
 -> Tap (Delta <:.> Construction Maybe) a)
-> (Construction Maybe a
    -> TU Covariant Covariant Delta (Construction Maybe) a)
-> Construction Maybe a
-> Tap (Delta <:.> Construction Maybe) a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Delta (Construction Maybe a)
-> TU Covariant Covariant Delta (Construction Maybe) a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (Delta (Construction Maybe a)
 -> TU Covariant Covariant Delta (Construction Maybe) a)
-> (Construction Maybe a -> Delta (Construction Maybe a))
-> Construction Maybe a
-> TU Covariant Covariant Delta (Construction Maybe) a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (Construction Maybe a
-> Construction Maybe a -> Delta (Construction Maybe a)
forall a. a -> a -> Delta a
:^: a -> Construction Maybe a -> Construction Maybe a
forall (t :: * -> *) a. Insertable t => a -> t a -> t a
insert a
x Construction Maybe a
fs) (Construction Maybe a -> Tap (Delta <:.> Construction Maybe) a)
-> Maybe (Construction Maybe a)
-> Maybe (Tap (Delta <:.> Construction Maybe) a)
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> Construction Maybe a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct Construction Maybe a
bs

instance Rotatable Right (Tap (Delta <:.> Construction Maybe)) where
	type Rotational Right (Tap (Delta <:.> Construction Maybe)) a = Maybe :. Zipper (Construction Maybe) := a
	rotation :: Tagged 'Right (Tap (Delta <:.> Construction Maybe) a)
-> Rotational 'Right (Tap (Delta <:.> Construction Maybe)) a
rotation (Tap (Delta <:.> Construction Maybe) a <-| Tagged 'Right
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Tap a
x (TU (Construction Maybe a
bs :^: Construction Maybe a
fs))) = a
-> TU Covariant Covariant Delta (Construction Maybe) a
-> Tap (Delta <:.> Construction Maybe) a
forall (t :: * -> *) a. a -> t a -> Tap t a
Tap (a <-| Construction Maybe
forall (t :: * -> *) a. Extractable t => a <-| t
extract Construction Maybe a
fs) (TU Covariant Covariant Delta (Construction Maybe) a
 -> Tap (Delta <:.> Construction Maybe) a)
-> (Construction Maybe a
    -> TU Covariant Covariant Delta (Construction Maybe) a)
-> Construction Maybe a
-> Tap (Delta <:.> Construction Maybe) a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Delta (Construction Maybe a)
-> TU Covariant Covariant Delta (Construction Maybe) a
forall k k k k (ct :: k) (cu :: k) (t :: k -> *) (u :: k -> k)
       (a :: k).
((t :. u) := a) -> TU ct cu t u a
TU (Delta (Construction Maybe a)
 -> TU Covariant Covariant Delta (Construction Maybe) a)
-> (Construction Maybe a -> Delta (Construction Maybe a))
-> Construction Maybe a
-> TU Covariant Covariant Delta (Construction Maybe) a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (a -> Construction Maybe a -> Construction Maybe a
forall (t :: * -> *) a. Insertable t => a -> t a -> t a
insert a
x Construction Maybe a
bs Construction Maybe a
-> Construction Maybe a -> Delta (Construction Maybe a)
forall a. a -> a -> Delta a
:^:) (Construction Maybe a -> Tap (Delta <:.> Construction Maybe) a)
-> Maybe (Construction Maybe a)
-> Maybe (Tap (Delta <:.> Construction Maybe) a)
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> Construction Maybe a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct Construction Maybe a
fs

instance Monotonic a (Maybe <:.> Construction Maybe := a) where
	reduce :: (a -> r -> r) -> r -> (Stack := a) -> r
reduce a -> r -> r
f r
r = (a -> r -> r) -> r -> ((Maybe :. Construction Maybe) := a) -> r
forall a e r. Monotonic a e => (a -> r -> r) -> r -> e -> r
reduce a -> r -> r
f r
r (((Maybe :. Construction Maybe) := a) -> r)
-> ((Stack := a) -> (Maybe :. Construction Maybe) := a)
-> (Stack := a)
-> r
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. (Stack := a) -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run