module Control.Morphism.Cata where
import Control.Bifunctor
import Control.Bifunctor.Fix
import Control.Comonad
import Control.Comonad.Identity
import Control.Functor.Algebra
import Control.Functor.HigherOrder
import Control.Functor.Extras
import Control.Functor.Fix
import Control.Monad.Identity
cata :: Functor f => Alg f a -> Fix f -> a
cata f = f . fmap (cata f) . outF
g_cata :: (Functor f, Comonad w) => Dist f w -> AlgW f w a -> Fix f -> a
g_cata k g = extract . c where c = liftW g . k . fmap (duplicate . c) . outF
distCata :: Functor f => Dist f Identity
distCata = Identity . fmap runIdentity
bicata :: Bifunctor f => Alg (f b) a -> FixB f b -> a
bicata f = f . bimap id (bicata f) . outB
g_bicata :: (Bifunctor f, Comonad w) => Dist (f b) w -> AlgW (f b) w a -> FixB f b -> a
g_bicata k g = extract . c where c = liftW g . k . bimap id (duplicate . c) . outB
hcata :: HFunctor f => AlgH f a -> Natural (FixH f) a
hcata f = f . hfmap (hcata f) . outH