{-# OPTIONS_GHC -fno-warn-orphans #-}
module Pandora.Paradigm.Structure.Stack where
import Pandora.Core.Functor (type (:.), type (:=), type (|->))
import Pandora.Pattern ((.|..))
import Pandora.Pattern.Category ((.), ($), identity)
import Pandora.Pattern.Functor.Covariant (Covariant ((<$>)))
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.Extendable (Extendable ((=>>)))
import Pandora.Pattern.Functor.Bindable (Bindable (join))
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.Object.Numerator (Numerator (Numerator))
import Pandora.Paradigm.Primary.Object.Denumerator (Denumerator (One))
import Pandora.Paradigm.Primary.Functor.Delta (Delta ((:^:)))
import Pandora.Paradigm.Primary.Functor.Function ((!), (%), (&))
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 (view, (^.))
import Pandora.Paradigm.Controlflow.Effect.Interpreted (run, unite)
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.Measurable (Measurable (Measural, measurement), Scale (Length), measure)
import Pandora.Paradigm.Structure.Ability.Monotonic (Monotonic (reduce))
import Pandora.Paradigm.Structure.Ability.Rotatable (Rotatable (Rotational, rotation), rotate)
import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substructural, substructure), Command (Delete), Segment (All, First, Tail), sub)
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 (Stack a <-| Tagged 'Head
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> 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
& Lens (Stack a) (Stack a) -> Stack a -> Stack a
forall src tgt. Lens src tgt -> src -> tgt
view (forall k (f :: k) (t :: * -> *) a.
Substructure f t a =>
t a :-. Substructural f t a
forall (t :: * -> *) a.
Substructure 'Tail t a =>
t a :-. Substructural 'Tail t a
sub @Tail) 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
$ forall k (f :: k) (t :: * -> *) a.
Substructure f t a =>
t a :-. Substructural f t a
forall (t :: * -> *) a.
Substructure 'Tail t a =>
t a :-. Substructural 'Tail t a
sub @Tail Lens (Stack a) (Stack a) -> Stack a -> Stack a
forall src tgt. Lens src tgt -> src -> tgt
^. Stack a
stack
instance Insertable Stack where
insert :: a -> Stack a -> Stack a
insert a
x (Stack a -> Primary Stack a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run -> Primary Stack a
stack) = ((Maybe :. Construction Maybe) := a) -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite (((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
<$> Primary Stack a
(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 Measurable Length Stack where
type Measural Length Stack a = Numerator
measurement :: Tagged 'Length (Stack a) -> Measural 'Length Stack a
measurement (Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> Maybe (Construction Maybe a))
-> (Tagged 'Length (Stack a) -> Stack a)
-> Tagged 'Length (Stack a)
-> Maybe (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Length (Stack a) -> Stack a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Maybe (Construction Maybe a)
Nothing) = Measural 'Length Stack a
forall a. Monoid a => a
zero
measurement (Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> Maybe (Construction Maybe a))
-> (Tagged 'Length (Stack a) -> Stack a)
-> Tagged 'Length (Stack a)
-> Maybe (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Length (Stack a) -> Stack a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Just Construction Maybe a
xs) = Denumerator -> Numerator
Numerator (Denumerator -> Numerator) -> Denumerator -> Numerator
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Construction Maybe a -> Measural 'Length (Construction Maybe) a
forall k (f :: k) (t :: * -> *) a.
Measurable f t =>
t a -> Measural f t a
measure @Length Construction Maybe a
xs
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 }
instance Substructure Tail Stack a where
type Substructural Tail Stack a = Stack a
substructure :: Tagged 'Tail (Stack a) :-. Substructural 'Tail Stack a
substructure (Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> Maybe (Construction Maybe a))
-> (Tagged 'Tail (Stack a) -> Stack a)
-> Tagged 'Tail (Stack a)
-> Maybe (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Tail (Stack a) -> Stack a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Just Construction Maybe a
ns) = Stack a |-> Tagged 'Tail
forall (t :: * -> *) a. Pointable t => a |-> t
point (Stack a |-> Tagged 'Tail)
-> (Construction Maybe a -> Stack a)
-> Construction Maybe a
-> Tagged 'Tail (Stack a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Maybe (Construction Maybe a) -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite (Maybe (Construction Maybe a) -> Stack a)
-> (Construction Maybe a -> Maybe (Construction Maybe a))
-> Construction Maybe a
-> Stack 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 -> Tagged 'Tail (Stack a))
-> Store (Stack a) (Construction Maybe a)
-> Store (Stack a) (Tagged 'Tail (Stack a))
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> Construction Maybe a :-. Substructural 'Tail (Construction Maybe) a
forall k (f :: k) (t :: * -> *) a.
Substructure f t a =>
t a :-. Substructural f t a
sub @Tail Construction Maybe a
ns
substructure (Stack a -> Maybe (Construction Maybe a)
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> Maybe (Construction Maybe a))
-> (Tagged 'Tail (Stack a) -> Stack a)
-> Tagged 'Tail (Stack a)
-> Maybe (Construction Maybe a)
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Tail (Stack a) -> Stack a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Maybe (Construction Maybe a)
Nothing) = (((:*:) (Stack a) :. (->) (Stack a)) := Tagged 'Tail (Stack a))
-> Store (Stack a) (Tagged 'Tail (Stack a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (Stack a) :. (->) (Stack a)) := Tagged 'Tail (Stack a))
-> Store (Stack a) (Tagged 'Tail (Stack a)))
-> (((:*:) (Stack a) :. (->) (Stack a)) := Tagged 'Tail (Stack a))
-> Store (Stack a) (Tagged 'Tail (Stack a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Primary Stack a -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite Primary Stack a
forall a. Maybe a
Nothing Stack a
-> (Stack a |-> Tagged 'Tail)
-> ((:*:) (Stack a) :. (->) (Stack a)) := Tagged 'Tail (Stack a)
forall s a. s -> a -> Product s a
:*: Stack a |-> Tagged 'Tail
forall (t :: * -> *) a. Pointable t => a |-> t
point (Stack a |-> Tagged 'Tail)
-> (Stack a -> Stack a) -> Stack a |-> Tagged 'Tail
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Stack a -> Stack a
forall (m :: * -> * -> *) a. Category m => m a a
identity
instance Setoid a => Substructure (Delete First) Stack a where
type Substructural (Delete First) Stack a = a |-> Stack
substructure :: Tagged ('Delete 'First) (Stack a)
:-. Substructural ('Delete 'First) Stack a
substructure (Stack a <-| Tagged ('Delete 'First)
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Stack a
xs) = (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Stack a))
-> Store (a -> Stack a) (Tagged ('Delete 'First) (Stack a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Stack a))
-> Store (a -> Stack a) (Tagged ('Delete 'First) (Stack a)))
-> (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Stack a))
-> Store (a -> Stack a) (Tagged ('Delete 'First) (Stack a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a -> Stack a -> Stack a
Setoid a => a -> Stack a -> Stack a
delete (a -> Stack a -> Stack a) -> Stack a -> a -> Stack a
forall a b c. (a -> b -> c) -> b -> a -> c
% Stack a
xs (a -> Stack a)
-> ((a -> Stack a) -> Tagged ('Delete 'First) (Stack a))
-> ((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Stack a)
forall s a. s -> a -> Product s a
:*: (Stack a |-> Tagged ('Delete 'First)
forall (t :: * -> *) a. Pointable t => a |-> t
point Stack a
xs Tagged ('Delete 'First) (Stack a)
-> (a -> Stack a) -> Tagged ('Delete 'First) (Stack a)
forall a b. a -> b -> a
!) where
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
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)
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 (Construction Maybe a <-| Tagged 'Head
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> 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 Measurable Length (Construction Maybe) where
type Measural Length (Construction Maybe) a = Denumerator
measurement :: Tagged 'Length (Construction Maybe a)
-> Measural 'Length (Construction Maybe) a
measurement (Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> (Tagged 'Length (Construction Maybe a) -> Construction Maybe a)
-> Tagged 'Length (Construction Maybe a)
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Length (Construction Maybe a) -> Construction Maybe a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> (Maybe :. Construction Maybe) := a
Nothing) = Denumerator
Measural 'Length (Construction Maybe) a
One
measurement (Construction Maybe a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a.
Construction t a -> (t :. Construction t) := a
deconstruct (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> (Tagged 'Length (Construction Maybe a) -> Construction Maybe a)
-> Tagged 'Length (Construction Maybe a)
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. Tagged 'Length (Construction Maybe a) -> Construction Maybe a
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Just Construction Maybe a
xs) = Denumerator
One Denumerator -> Denumerator -> Denumerator
forall a. Semigroup a => a -> a -> a
+ Construction Maybe a -> Measural 'Length (Construction Maybe) a
forall k (f :: k) (t :: * -> *) a.
Measurable f t =>
t a -> Measural f t a
measure @Length Construction Maybe a
xs
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
instance Substructure Tail (Construction Maybe) a where
type Substructural Tail (Construction Maybe) a = Stack a
substructure :: Tagged 'Tail (Construction Maybe a)
:-. Substructural 'Tail (Construction Maybe) a
substructure (Construction Maybe a <-| Tagged 'Tail
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Construct a
x (Maybe :. Construction Maybe) := a
xs) = (((:*:) (TU Covariant Covariant Maybe (Construction Maybe) a)
:. (->) (TU Covariant Covariant Maybe (Construction Maybe) a))
:= Tagged 'Tail (Construction Maybe a))
-> Store
(TU Covariant Covariant Maybe (Construction Maybe) a)
(Tagged 'Tail (Construction Maybe a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (TU Covariant Covariant Maybe (Construction Maybe) a)
:. (->) (TU Covariant Covariant Maybe (Construction Maybe) a))
:= Tagged 'Tail (Construction Maybe a))
-> Store
(TU Covariant Covariant Maybe (Construction Maybe) a)
(Tagged 'Tail (Construction Maybe a)))
-> (((:*:) (TU Covariant Covariant Maybe (Construction Maybe) a)
:. (->) (TU Covariant Covariant Maybe (Construction Maybe) a))
:= Tagged 'Tail (Construction Maybe a))
-> Store
(TU Covariant Covariant Maybe (Construction Maybe) a)
(Tagged 'Tail (Construction Maybe a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Primary Stack a
-> TU Covariant Covariant Maybe (Construction Maybe) a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite Primary Stack a
(Maybe :. Construction Maybe) := a
xs TU Covariant Covariant Maybe (Construction Maybe) a
-> (TU Covariant Covariant Maybe (Construction Maybe) a
-> Tagged 'Tail (Construction Maybe a))
-> ((:*:) (TU Covariant Covariant Maybe (Construction Maybe) a)
:. (->) (TU Covariant Covariant Maybe (Construction Maybe) a))
:= Tagged 'Tail (Construction Maybe a)
forall s a. s -> a -> Product s a
:*: Construction Maybe a |-> Tagged 'Tail
forall (t :: * -> *) a. Pointable t => a |-> t
point (Construction Maybe a |-> Tagged 'Tail)
-> (TU Covariant Covariant Maybe (Construction Maybe) a
-> Construction Maybe a)
-> TU Covariant Covariant Maybe (Construction Maybe) a
-> Tagged 'Tail (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
x (((Maybe :. Construction Maybe) := a) -> Construction Maybe a)
-> (TU Covariant Covariant Maybe (Construction Maybe) a
-> (Maybe :. Construction Maybe) := a)
-> TU Covariant Covariant Maybe (Construction Maybe) a
-> Construction Maybe a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. TU Covariant Covariant Maybe (Construction Maybe) a
-> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run
instance Setoid a => Substructure (Delete First) (Construction Maybe) a where
type Substructural (Delete First) (Construction Maybe) a = a |-> Stack
substructure :: Tagged ('Delete 'First) (Construction Maybe a)
:-. Substructural ('Delete 'First) (Construction Maybe) a
substructure (Construction Maybe a <-| Tagged ('Delete 'First)
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Construction Maybe a
xs) = (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'First) (Construction Maybe a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'First) (Construction Maybe a)))
-> (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'First) (Construction Maybe a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a -> Construction Maybe a -> Stack a
Setoid a => a -> Nonempty Stack a -> Stack a
delete (a -> Construction Maybe a -> Stack a)
-> Construction Maybe a -> a -> Stack a
forall a b c. (a -> b -> c) -> b -> a -> c
% Construction Maybe a
xs (a -> Stack a)
-> ((a -> Stack a)
-> Tagged ('Delete 'First) (Construction Maybe a))
-> ((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'First) (Construction Maybe a)
forall s a. s -> a -> Product s a
:*: (Construction Maybe a |-> Tagged ('Delete 'First)
forall (t :: * -> *) a. Pointable t => a |-> t
point Construction Maybe a
xs Tagged ('Delete 'First) (Construction Maybe a)
-> (a -> Stack a) -> Tagged ('Delete 'First) (Construction Maybe a)
forall a b. a -> b -> a
!) where
delete :: Setoid a => a -> Nonempty Stack a -> Stack a
delete :: a -> Nonempty Stack a -> Stack a
delete a
x (Construct y 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
? Primary Stack a -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite Primary Stack a
(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
$ ((Maybe :. Construction Maybe) := a) -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite (((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
y (((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
. Stack a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> (Maybe :. Construction Maybe) := a)
-> (Construction Maybe a -> Stack a)
-> Construction Maybe a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Nonempty Stack a -> Stack a
Setoid a => a -> Nonempty Stack a -> Stack a
delete a
x (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
ys
instance Setoid a => Substructure (Delete All) (Construction Maybe) a where
type Substructural (Delete All) (Construction Maybe) a = a |-> Stack
substructure :: Tagged ('Delete 'All) (Construction Maybe a)
:-. Substructural ('Delete 'All) (Construction Maybe) a
substructure (Construction Maybe a <-| Tagged ('Delete 'All)
forall (t :: * -> *) a. Extractable t => a <-| t
extract -> Construction Maybe a
xs) = (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'All) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'All) (Construction Maybe a))
forall s a. (((:*:) s :. (->) s) := a) -> Store s a
Store ((((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'All) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'All) (Construction Maybe a)))
-> (((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'All) (Construction Maybe a))
-> Store
(a -> Stack a) (Tagged ('Delete 'All) (Construction Maybe a))
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ a -> Construction Maybe a -> Stack a
Setoid a => a -> Nonempty Stack a -> Stack a
delete (a -> Construction Maybe a -> Stack a)
-> Construction Maybe a -> a -> Stack a
forall a b c. (a -> b -> c) -> b -> a -> c
% Construction Maybe a
xs (a -> Stack a)
-> ((a -> Stack a) -> Tagged ('Delete 'All) (Construction Maybe a))
-> ((:*:) (a -> Stack a) :. (->) (a -> Stack a))
:= Tagged ('Delete 'All) (Construction Maybe a)
forall s a. s -> a -> Product s a
:*: (Construction Maybe a |-> Tagged ('Delete 'All)
forall (t :: * -> *) a. Pointable t => a |-> t
point Construction Maybe a
xs Tagged ('Delete 'All) (Construction Maybe a)
-> (a -> Stack a) -> Tagged ('Delete 'All) (Construction Maybe a)
forall a b. a -> b -> a
!) where
delete :: Setoid a => a -> Nonempty Stack a -> Stack a
delete :: a -> Nonempty Stack a -> Stack a
delete a
x (Construct y 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 (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite (((Maybe :. Construction Maybe) := a) -> Stack a)
-> (((Maybe :. Maybe) := Construction Maybe a)
-> (Maybe :. Construction Maybe) := a)
-> ((Maybe :. Maybe) := Construction Maybe a)
-> Stack a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. ((Maybe :. Maybe) := Construction Maybe a)
-> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Bindable t => ((t :. t) := a) -> t a
join (((Maybe :. Maybe) := Construction Maybe a) -> Stack a)
-> ((Maybe :. Maybe) := Construction Maybe a) -> Stack a
forall (m :: * -> * -> *) a b. Category m => m a b -> m a b
$ Stack a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> (Maybe :. Construction Maybe) := a)
-> (Construction Maybe a -> Stack a)
-> Construction Maybe a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Nonempty Stack a -> Stack a
Setoid a => a -> Nonempty Stack a -> Stack a
delete a
x (Construction Maybe a -> (Maybe :. Construction Maybe) := a)
-> ((Maybe :. Construction Maybe) := a)
-> (Maybe :. Maybe) := Construction Maybe a
forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b
<$> (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
$ (((Maybe :. Construction Maybe) := a) -> Stack a
forall (t :: * -> *) a. Interpreted t => Primary t a -> t a
unite (((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
y (((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
. Stack a -> (Maybe :. Construction Maybe) := a
forall (t :: * -> *) a. Interpreted t => t a -> Primary t a
run (Stack a -> (Maybe :. Construction Maybe) := a)
-> (Construction Maybe a -> Stack a)
-> Construction Maybe a
-> (Maybe :. Construction Maybe) := a
forall (m :: * -> * -> *) b c a.
Category m =>
m b c -> m a b -> m a c
. a -> Nonempty Stack a -> Stack a
Setoid a => a -> Nonempty Stack a -> Stack a
delete a
x (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
ys)
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
$ forall k (f :: k) (t :: * -> *) a.
Substructure f t a =>
t a :-. Substructural f t a
forall (t :: * -> *) a.
Substructure 'Tail t a =>
t a :-. Substructural 'Tail t a
sub @Tail (Stack a -> Store (Stack a) (Stack a)) -> Stack a -> Stack a
forall src tgt. Lens src tgt -> src -> tgt
^. 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
:^: forall k (f :: k) (t :: * -> *) a.
Substructure f t a =>
t a :-. Substructural f t a
forall (t :: * -> *) a.
Substructure 'Tail t a =>
t a :-. Substructural 'Tail t a
sub @Tail (Stack a -> Store (Stack a) (Stack a)) -> Stack a -> Stack a
forall src tgt. Lens src tgt -> src -> tgt
^. 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