{-# LANGUAGE AllowAmbiguousTypes #-} module Pandora.Paradigm.Structure.Ability.Morphable where import Pandora.Core.Functor (type (~>)) import Pandora.Pattern.Category ((.)) import Pandora.Paradigm.Primary.Functor.Tagged (Tagged (Tag)) import Pandora.Paradigm.Schemes.TU (TU (TU), type (<:.>)) class Morphable f t where type Morphing (f :: k) (t :: * -> *) :: * -> * morphing :: Tagged f <:.> t ~> Morphing f t morph :: forall f t . Morphable f t => t ~> Morphing f t morph :: t ~> Morphing f t morph = (<:.>) (Tagged f) t a -> Morphing f t a forall k (f :: k) (t :: * -> *). Morphable f t => (Tagged f <:.> t) ~> Morphing f t morphing ((<:.>) (Tagged f) t a -> Morphing f t a) -> (t a -> (<:.>) (Tagged f) t a) -> t a -> Morphing f t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((Tagged f :. t) := a) -> (<:.>) (Tagged f) t 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 (((Tagged f :. t) := a) -> (<:.>) (Tagged f) t a) -> (t a -> (Tagged f :. t) := a) -> t a -> (<:.>) (Tagged f) t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . forall a. a -> Tagged f a forall k (tag :: k) a. a -> Tagged tag a Tag @f data Walk a = Preorder a | Inorder a | Postorder a | Levelorder a data Morph a = Rotate a | Into a rotate :: forall f t . Morphable (Rotate f) t => t ~> Morphing (Rotate f) t rotate :: t ~> Morphing ('Rotate f) t rotate = (<:.>) (Tagged ('Rotate f)) t a -> Morphing ('Rotate f) t a forall k (f :: k) (t :: * -> *). Morphable f t => (Tagged f <:.> t) ~> Morphing f t morphing ((<:.>) (Tagged ('Rotate f)) t a -> Morphing ('Rotate f) t a) -> (t a -> (<:.>) (Tagged ('Rotate f)) t a) -> t a -> Morphing ('Rotate f) t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((Tagged ('Rotate f) :. t) := a) -> (<:.>) (Tagged ('Rotate f)) t 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 (((Tagged ('Rotate f) :. t) := a) -> (<:.>) (Tagged ('Rotate f)) t a) -> (t a -> (Tagged ('Rotate f) :. t) := a) -> t a -> (<:.>) (Tagged ('Rotate f)) t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . forall a. a -> Tagged ('Rotate f) a forall k (tag :: k) a. a -> Tagged tag a Tag @(Rotate f) into :: forall f t . Morphable (Into f) t => t ~> Morphing (Into f) t into :: t ~> Morphing ('Into f) t into = (<:.>) (Tagged ('Into f)) t a -> Morphing ('Into f) t a forall k (f :: k) (t :: * -> *). Morphable f t => (Tagged f <:.> t) ~> Morphing f t morphing ((<:.>) (Tagged ('Into f)) t a -> Morphing ('Into f) t a) -> (t a -> (<:.>) (Tagged ('Into f)) t a) -> t a -> Morphing ('Into f) t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . ((Tagged ('Into f) :. t) := a) -> (<:.>) (Tagged ('Into f)) t 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 (((Tagged ('Into f) :. t) := a) -> (<:.>) (Tagged ('Into f)) t a) -> (t a -> (Tagged ('Into f) :. t) := a) -> t a -> (<:.>) (Tagged ('Into f)) t a forall (m :: * -> * -> *) b c a. Category m => m b c -> m a b -> m a c . forall a. a -> Tagged ('Into f) a forall k (tag :: k) a. a -> Tagged tag a Tag @(Into f)