{-# OPTIONS_GHC -fno-warn-orphans #-} module Pandora.Paradigm.Structure.Some.Rose where import Pandora.Core.Functor (type (:.), type (:=)) import Pandora.Pattern.Category ((.), ($), (/)) import Pandora.Pattern.Functor.Covariant (Covariant (comap)) import Pandora.Pattern.Functor.Contravariant ((>$<)) import Pandora.Pattern.Functor.Extractable (extract) import Pandora.Pattern.Functor.Avoidable (Avoidable (empty)) import Pandora.Pattern.Functor.Bindable (Bindable ((>>=))) import Pandora.Pattern.Transformer.Liftable (lift) import Pandora.Pattern.Object.Setoid (Setoid ((==), (!=))) import Pandora.Paradigm.Primary.Object.Boolean (Boolean (True, False), (?)) import Pandora.Paradigm.Primary.Functor.Function ((!), (%)) import Pandora.Paradigm.Primary.Functor.Maybe (Maybe (Just, Nothing)) import Pandora.Paradigm.Primary.Functor.Predicate (Predicate (Predicate), equate) import Pandora.Paradigm.Primary.Functor.Product (Product ((:*:)), type (:*:), attached) import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag)) import Pandora.Paradigm.Primary.Transformer.Construction (Construction (Construct), deconstruct) import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>)) import Pandora.Paradigm.Controlflow.Effect.Interpreted (run) import Pandora.Paradigm.Inventory.Store (Store (Store)) import Pandora.Paradigm.Structure.Ability.Focusable (Focusable (Focusing, focusing), Location (Root)) import Pandora.Paradigm.Structure.Ability.Monotonic (resolve) import Pandora.Paradigm.Structure.Ability.Morphable (Morphable (Morphing, morphing), Morph (Lookup, Element), premorph, find) import Pandora.Paradigm.Structure.Ability.Nonempty (Nonempty) import Pandora.Paradigm.Structure.Ability.Nullable (Nullable (null)) import Pandora.Paradigm.Structure.Ability.Substructure (Substructure (Substructural, substructure)) import Pandora.Paradigm.Structure.Modification.Prefixed (Prefixed) import Pandora.Paradigm.Structure.Some.List (List) type Rose = Maybe <:.> Construction List instance Focusable Root Rose where type Focusing Root Rose a = Maybe a focusing :: Tagged 'Root (Rose a) :-. Focusing 'Root Rose a focusing (Rose a -> Maybe (Construction List a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (Rose a -> Maybe (Construction List a)) -> (Tagged 'Root (Rose a) -> Rose a) -> Tagged 'Root (Rose a) -> Maybe (Construction List a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Tagged 'Root (Rose a) -> Rose a forall (t :: * -> *) a. Extractable t => a <:= t extract -> Maybe (Construction List a) Nothing) = (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a)) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a))) -> (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a)) forall (m :: * -> * -> *). Category m => m ~~> m $ Maybe a forall a. Maybe a Nothing Maybe a -> (Maybe a -> Tagged 'Root (Rose a)) -> ((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a) forall s a. s -> a -> Product s a :*: Rose a -> Tagged 'Root (Rose a) forall k (tag :: k) a. a -> Tagged tag a Tag (Rose a -> Tagged 'Root (Rose a)) -> (Maybe a -> Rose a) -> Maybe a -> Tagged 'Root (Rose a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Maybe (Construction List a) -> Rose 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 List a) -> Rose a) -> (Maybe a -> Maybe (Construction List a)) -> Maybe a -> Rose a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (a -> Construction List a) -> Maybe a -> Maybe (Construction List a) forall (t :: * -> *) a b. Covariant t => (a -> b) -> t a -> t b comap (a -> ((List :. Construction List) := a) -> Construction List a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct (a -> ((List :. Construction List) := a) -> Construction List a) -> ((List :. Construction List) := a) -> a -> Construction List a forall a b c. (a -> b -> c) -> b -> a -> c % (List :. Construction List) := a forall (t :: * -> *) a. Avoidable t => t a empty) focusing (Rose a -> Maybe (Construction List a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (Rose a -> Maybe (Construction List a)) -> (Tagged 'Root (Rose a) -> Rose a) -> Tagged 'Root (Rose a) -> Maybe (Construction List a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Tagged 'Root (Rose a) -> Rose a forall (t :: * -> *) a. Extractable t => a <:= t extract -> Just Construction List a rose) = (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a)) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a))) -> (((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a)) -> Store (Maybe a) (Tagged 'Root (Rose a)) forall (m :: * -> * -> *). Category m => m ~~> m $ a -> Maybe a forall a. a -> Maybe a Just (a <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract Construction List a rose) Maybe a -> (Maybe a -> Tagged 'Root (Rose a)) -> ((:*:) (Maybe a) :. (->) (Maybe a)) := Tagged 'Root (Rose a) forall s a. s -> a -> Product s a :*: Rose a -> Tagged 'Root (Rose a) forall k (tag :: k) a. a -> Tagged tag a Tag (Rose a -> Tagged 'Root (Rose a)) -> (Maybe a -> Rose a) -> Maybe a -> Tagged 'Root (Rose a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (a -> Rose a) -> Rose a -> Maybe a -> Rose a forall a e r. Monotonic a e => (a -> r) -> r -> e -> r resolve (Construction List a -> Rose a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Liftable t, Covariant u) => u ~> t u lift (Construction List a -> Rose a) -> (a -> Construction List a) -> a -> Rose a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> ((List :. Construction List) := a) -> Construction List a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct (a -> ((List :. Construction List) := a) -> Construction List a) -> ((List :. Construction List) := a) -> a -> Construction List a forall a b c. (a -> b -> c) -> b -> a -> c % Construction List a -> (List :. Construction List) := a forall (t :: * -> *) a. Construction t a -> (t :. Construction t) := a deconstruct Construction List a rose) Rose a forall (t :: * -> *) a. Avoidable t => t a empty instance Nullable Rose where null :: (Predicate :. Rose) := a null = (Rose a -> Boolean) -> (Predicate :. Rose) := a forall a. (a -> Boolean) -> Predicate a Predicate ((Rose a -> Boolean) -> (Predicate :. Rose) := a) -> (Rose a -> Boolean) -> (Predicate :. Rose) := a forall (m :: * -> * -> *). Category m => m ~~> m $ \case { TU Maybe (Construction List a) Nothing -> Boolean True ; Rose a _ -> Boolean False } instance Substructure Just Rose where type Substructural Just Rose = List <:.> Construction List substructure :: Lens ((<:.>) (Tagged 'Just) Rose a) (Substructural 'Just Rose a) substructure (TU Covariant Covariant Maybe (Construction List) a -> Maybe (Construction List a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (TU Covariant Covariant Maybe (Construction List) a -> Maybe (Construction List a)) -> ((<:.>) (Tagged 'Just) Rose a -> TU Covariant Covariant Maybe (Construction List) a) -> (<:.>) (Tagged 'Just) Rose a -> Maybe (Construction List a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . TU Covariant Covariant Maybe (Construction List) a <:= Tagged 'Just forall (t :: * -> *) a. Extractable t => a <:= t extract (TU Covariant Covariant Maybe (Construction List) a <:= Tagged 'Just) -> ((<:.>) (Tagged 'Just) Rose a -> Tagged 'Just (TU Covariant Covariant Maybe (Construction List) a)) -> (<:.>) (Tagged 'Just) Rose a -> TU Covariant Covariant Maybe (Construction List) a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (<:.>) (Tagged 'Just) Rose a -> Tagged 'Just (TU Covariant Covariant Maybe (Construction List) a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run -> Maybe (Construction List a) Nothing) = (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a)) -> (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a) forall (m :: * -> * -> *). Category m => m ~~> m $ TU Covariant Covariant List (Construction List) a forall (t :: * -> *) a. Avoidable t => t a empty TU Covariant Covariant List (Construction List) a -> (TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) Rose a) -> ((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a forall s a. s -> a -> Product s a :*: (TU Covariant Covariant Maybe (Construction List) a -> (<:.>) (Tagged 'Just) Rose a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Liftable t, Covariant u) => u ~> t u lift TU Covariant Covariant Maybe (Construction List) a forall (t :: * -> *) a. Avoidable t => t a empty (<:.>) (Tagged 'Just) Rose a -> TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) Rose a forall a b. a -> b -> a !) substructure (TU Covariant Covariant Maybe (Construction List) a -> Maybe (Construction List a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (TU Covariant Covariant Maybe (Construction List) a -> Maybe (Construction List a)) -> ((<:.>) (Tagged 'Just) Rose a -> TU Covariant Covariant Maybe (Construction List) a) -> (<:.>) (Tagged 'Just) Rose a -> Maybe (Construction List a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . TU Covariant Covariant Maybe (Construction List) a <:= Tagged 'Just forall (t :: * -> *) a. Extractable t => a <:= t extract (TU Covariant Covariant Maybe (Construction List) a <:= Tagged 'Just) -> ((<:.>) (Tagged 'Just) Rose a -> Tagged 'Just (TU Covariant Covariant Maybe (Construction List) a)) -> (<:.>) (Tagged 'Just) Rose a -> TU Covariant Covariant Maybe (Construction List) a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (<:.>) (Tagged 'Just) Rose a -> Tagged 'Just (TU Covariant Covariant Maybe (Construction List) a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run -> Just (Construct a x (List :. Construction List) := a xs)) = (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a)) -> (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) Rose a) forall (m :: * -> * -> *). Category m => m ~~> m $ ((List :. Construction List) := a) -> TU Covariant Covariant List (Construction List) 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 (List :. Construction List) := a xs TU Covariant Covariant List (Construction List) a -> (TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) Rose a) -> ((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) Rose a forall s a. s -> a -> Product s a :*: TU Covariant Covariant Maybe (Construction List) a -> (<:.>) (Tagged 'Just) Rose a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Liftable t, Covariant u) => u ~> t u lift (TU Covariant Covariant Maybe (Construction List) a -> (<:.>) (Tagged 'Just) Rose a) -> (TU Covariant Covariant List (Construction List) a -> TU Covariant Covariant Maybe (Construction List) a) -> TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) Rose a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . Construction List a -> TU Covariant Covariant Maybe (Construction List) a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Liftable t, Covariant u) => u ~> t u lift (Construction List a -> TU Covariant Covariant Maybe (Construction List) a) -> (TU Covariant Covariant List (Construction List) a -> Construction List a) -> TU Covariant Covariant List (Construction List) a -> TU Covariant Covariant Maybe (Construction List) a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> ((List :. Construction List) := a) -> Construction List a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct a x (((List :. Construction List) := a) -> Construction List a) -> (TU Covariant Covariant List (Construction List) a -> (List :. Construction List) := a) -> TU Covariant Covariant List (Construction List) a -> Construction List a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . TU Covariant Covariant List (Construction List) a -> (List :. Construction List) := a forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run type instance Nonempty Rose = Construction List instance Focusable Root (Construction List) where type Focusing Root (Construction List) a = a focusing :: Tagged 'Root (Construction List a) :-. Focusing 'Root (Construction List) a focusing (Tag Construction List a rose) = (((:*:) a :. (->) a) := Tagged 'Root (Construction List a)) -> Store a (Tagged 'Root (Construction List a)) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) a :. (->) a) := Tagged 'Root (Construction List a)) -> Store a (Tagged 'Root (Construction List a))) -> (((:*:) a :. (->) a) := Tagged 'Root (Construction List a)) -> Store a (Tagged 'Root (Construction List a)) forall (m :: * -> * -> *). Category m => m ~~> m $ a <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract Construction List a rose a -> (a -> Tagged 'Root (Construction List a)) -> ((:*:) a :. (->) a) := Tagged 'Root (Construction List a) forall s a. s -> a -> Product s a :*: Construction List a -> Tagged 'Root (Construction List a) forall k (tag :: k) a. a -> Tagged tag a Tag (Construction List a -> Tagged 'Root (Construction List a)) -> (a -> Construction List a) -> a -> Tagged 'Root (Construction List a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> ((List :. Construction List) := a) -> Construction List a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct (a -> ((List :. Construction List) := a) -> Construction List a) -> ((List :. Construction List) := a) -> a -> Construction List a forall a b c. (a -> b -> c) -> b -> a -> c % Construction List a -> (List :. Construction List) := a forall (t :: * -> *) a. Construction t a -> (t :. Construction t) := a deconstruct Construction List a rose instance Substructure Just (Construction List) where type Substructural Just (Construction List) = List <:.> Construction List substructure :: Lens ((<:.>) (Tagged 'Just) (Construction List) a) (Substructural 'Just (Construction List) a) substructure (Construction List a <:= Tagged 'Just forall (t :: * -> *) a. Extractable t => a <:= t extract (Construction List a <:= Tagged 'Just) -> ((<:.>) (Tagged 'Just) (Construction List) a -> Tagged 'Just (Construction List a)) -> (<:.>) (Tagged 'Just) (Construction List) a -> Construction List a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (<:.>) (Tagged 'Just) (Construction List) a -> Tagged 'Just (Construction List a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run -> Construct a x (List :. Construction List) := a xs) = (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) (Construction List) a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) (Construction List) a) forall s a. (((:*:) s :. (->) s) := a) -> Store s a Store ((((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) (Construction List) a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) (Construction List) a)) -> (((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) (Construction List) a) -> Store (TU Covariant Covariant List (Construction List) a) ((<:.>) (Tagged 'Just) (Construction List) a) forall (m :: * -> * -> *). Category m => m ~~> m $ ((List :. Construction List) := a) -> TU Covariant Covariant List (Construction List) 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 (List :. Construction List) := a xs TU Covariant Covariant List (Construction List) a -> (TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) (Construction List) a) -> ((:*:) (TU Covariant Covariant List (Construction List) a) :. (->) (TU Covariant Covariant List (Construction List) a)) := (<:.>) (Tagged 'Just) (Construction List) a forall s a. s -> a -> Product s a :*: Construction List a -> (<:.>) (Tagged 'Just) (Construction List) a forall (t :: (* -> *) -> * -> *) (u :: * -> *). (Liftable t, Covariant u) => u ~> t u lift (Construction List a -> (<:.>) (Tagged 'Just) (Construction List) a) -> (TU Covariant Covariant List (Construction List) a -> Construction List a) -> TU Covariant Covariant List (Construction List) a -> (<:.>) (Tagged 'Just) (Construction List) a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . a -> ((List :. Construction List) := a) -> Construction List a forall (t :: * -> *) a. a -> ((t :. Construction t) := a) -> Construction t a Construct a x (((List :. Construction List) := a) -> Construction List a) -> (TU Covariant Covariant List (Construction List) a -> (List :. Construction List) := a) -> TU Covariant Covariant List (Construction List) a -> Construction List a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . TU Covariant Covariant List (Construction List) a -> (List :. Construction List) := a forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run instance Setoid k => Morphable (Lookup Element) (Prefixed Rose k) where type Morphing (Lookup Element) (Prefixed Rose k) = (->) (Nonempty List k) <:.> Maybe morphing :: (<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> Morphing ('Lookup 'Element) (Prefixed Rose k) a morphing (Prefixed Rose k a -> TU Covariant Covariant Maybe (Construction List) (Product k a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (Prefixed Rose k a -> TU Covariant Covariant Maybe (Construction List) (Product k a)) -> ((<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> Prefixed Rose k a) -> (<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> TU Covariant Covariant Maybe (Construction List) (Product k a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> Prefixed Rose k a forall k (f :: k) (t :: * -> *). Morphable f t => (Tagged f <:.> t) ~> t premorph -> TU Maybe (Construction List (Product k a)) Nothing) = (((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) 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 ((((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) Maybe a) -> (((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) Maybe a forall (m :: * -> * -> *). Category m => m ~~> m $ \Construction Maybe k _ -> Maybe a forall a. Maybe a Nothing morphing (Prefixed Rose k a -> TU Covariant Covariant Maybe (Construction List) (Product k a) forall (t :: * -> *) a. Interpreted t => t a -> Primary t a run (Prefixed Rose k a -> TU Covariant Covariant Maybe (Construction List) (Product k a)) -> ((<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> Prefixed Rose k a) -> (<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> TU Covariant Covariant Maybe (Construction List) (Product k a) forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (<:.>) (Tagged ('Lookup 'Element)) (Prefixed Rose k) a -> Prefixed Rose k a forall k (f :: k) (t :: * -> *). Morphable f t => (Tagged f <:.> t) ~> t premorph -> TU (Just Construction List (Product k a) tree)) = (((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) 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 ((((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) Maybe a) -> (((->) (Construction Maybe k) :. Maybe) := a) -> TU Covariant Covariant ((->) (Construction Maybe k)) Maybe a forall (m :: * -> * -> *). Category m => m ~~> m $ Construction Maybe k -> Construction List (Product k a) -> Maybe a forall k a. Setoid k => Nonempty List k -> (Nonempty Rose := (k :*: a)) -> Maybe a find_rose_sub_tree (Construction Maybe k -> Construction List (Product k a) -> Maybe a) -> Construction List (Product k a) -> ((->) (Construction Maybe k) :. Maybe) := a forall a b c. (a -> b -> c) -> b -> a -> c % Construction List (Product k a) tree find_rose_sub_tree :: forall k a . Setoid k => Nonempty List k -> Nonempty Rose := k :*: a -> Maybe a find_rose_sub_tree :: Nonempty List k -> (Nonempty Rose := (k :*: a)) -> Maybe a find_rose_sub_tree (Construct k Nothing) Nonempty Rose := (k :*: a) tree = k k k -> k -> Boolean forall a. Setoid a => a -> a -> Boolean == (k :*: a) -> k forall a b. (a :*: b) -> a attached ((k :*: a) <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract Nonempty Rose := (k :*: a) Construction List (k :*: a) tree) Boolean -> Maybe a -> Maybe a -> Maybe a forall a. Boolean -> a -> a -> a ? a -> Maybe a forall a. a -> Maybe a Just (a <:= Product k forall (t :: * -> *) a. Extractable t => a <:= t extract (a <:= Product k) -> a <:= Product k forall (m :: * -> * -> *). Category m => m ~~> m $ (k :*: a) <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract Nonempty Rose := (k :*: a) Construction List (k :*: a) tree) (Maybe a -> Maybe a) -> Maybe a -> Maybe a forall (m :: * -> * -> *). Category m => m ~~> m $ Maybe a forall a. Maybe a Nothing find_rose_sub_tree (Construct k (Just ks)) Nonempty Rose := (k :*: a) tree = k k k -> k -> Boolean forall a. Setoid a => a -> a -> Boolean != (k :*: a) -> k forall a b. (a :*: b) -> a attached ((k :*: a) <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract Nonempty Rose := (k :*: a) Construction List (k :*: a) tree) Boolean -> Maybe a -> Maybe a -> Maybe a forall a. Boolean -> a -> a -> a ? Maybe a forall a. Maybe a Nothing (Maybe a -> Maybe a) -> Maybe a -> Maybe a forall (m :: * -> * -> *). Category m => m ~~> m $ (Maybe :. Nonempty Rose) := (k :*: a) Maybe (Construction List (k :*: a)) subtree Maybe (Construction List (k :*: a)) -> (Construction List (k :*: a) -> Maybe a) -> Maybe a forall (t :: * -> *) a b. Bindable t => t a -> (a -> t b) -> t b >>= Nonempty List k -> (Nonempty Rose := (k :*: a)) -> Maybe a forall k a. Setoid k => Nonempty List k -> (Nonempty Rose := (k :*: a)) -> Maybe a find_rose_sub_tree Nonempty List k Construction Maybe k ks where subtree :: Maybe :. Nonempty Rose := k :*: a subtree :: (Maybe :. Nonempty Rose) := (k :*: a) subtree = forall a1 (f :: a1) (t :: * -> *) (u :: * -> *) a2. (Morphable ('Find f) t, Morphing ('Find f) t ~ ((Predicate <:.:> u) := (->))) => Predicate a2 -> t a2 -> u a2 forall (t :: * -> *) (u :: * -> *) a2. (Morphable ('Find 'Element) t, Morphing ('Find 'Element) t ~ ((Predicate <:.:> u) := (->))) => Predicate a2 -> t a2 -> u a2 find @Element (Predicate (Construction List (k :*: a)) -> List (Construction List (k :*: a)) -> Maybe (Construction List (k :*: a))) -> Predicate (Construction List (k :*: a)) -> List (Construction List (k :*: a)) -> Maybe (Construction List (k :*: a)) forall (m :: * -> * -> *). Category m => m ~~> m / (k :*: a) -> k forall a b. (a :*: b) -> a attached ((k :*: a) -> k) -> ((k :*: a) <:= Construction List) -> Construction List (k :*: a) -> k forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . (k :*: a) <:= Construction List forall (t :: * -> *) a. Extractable t => a <:= t extract (Construction List (k :*: a) -> k) -> Predicate k -> Predicate (Construction List (k :*: a)) forall (t :: * -> *) a b. Contravariant t => (a -> b) -> t b -> t a >$< k :=> Predicate forall a. Setoid a => a :=> Predicate equate (k <:= Construction Maybe forall (t :: * -> *) a. Extractable t => a <:= t extract Construction Maybe k ks) (List (Construction List (k :*: a)) -> Maybe (Construction List (k :*: a))) -> List (Construction List (k :*: a)) -> Maybe (Construction List (k :*: a)) forall (m :: * -> * -> *). Category m => m ~~> m / Construction List (k :*: a) -> List (Construction List (k :*: a)) forall (t :: * -> *) a. Construction t a -> (t :. Construction t) := a deconstruct Nonempty Rose := (k :*: a) Construction List (k :*: a) tree