Matryoshka

type GAlgebraM w m f a = f (w a) -> m a

type GAlgebra w f a = f (w a) -> a

type ElgotAlgebra w f a = w (f a) -> a

type AlgebraM m f a = f a -> m a

type Algebra f a = f a -> a

class (Functor f) <= Corecursive t f | t -> f where

Members

• embed :: f t -> t

Instances

• (Functor f) => Corecursive (Mu f) f
• (Functor f) => Corecursive (Nu f) f
• (Functor f) => Corecursive (Free f a) (CoEnvT a f)
• (Functor f) => Corecursive (Cofree f a) (EnvT a f)

class (Functor f) <= Recursive t f | t -> f where

Members

• project :: t -> f t

Instances

• (Functor f) => Recursive (Mu f) f
• (Functor f) => Recursive (Nu f) f
• (Functor f) => Recursive (Free f a) (CoEnvT a f)
• (Functor f) => Recursive (Cofree f a) (EnvT a f)

type GCoalgebraM n m f a = a -> m (f (n a))

type GCoalgebra n f a = a -> f (n a)

type ElgotCoalgebra e f a = a -> e (f a)

type CoalgebraM m f a = a -> m (f a)

type Coalgebra f a = a -> f a

type DistributiveLaw f g = forall a. f (g a) -> g (f a)

distZygoT :: forall f w a. Functor f => Comonad w => Algebra f a -> DistributiveLaw f w -> DistributiveLaw f (EnvT a w)

distZygo :: forall f a. Functor f => Algebra f a -> DistributiveLaw f (Tuple a)

distParaT :: forall t f w. Corecursive t f => Comonad w => DistributiveLaw f w -> DistributiveLaw f (EnvT t w)

distPara :: forall t f. Corecursive t f => DistributiveLaw f (Tuple t)

distHisto :: forall f. Functor f => DistributiveLaw f (Cofree f)

distGHisto :: forall f h. Functor f => Functor h => DistributiveLaw f h -> DistributiveLaw f (Cofree h)

distGFutu :: forall f h. Functor f => Functor h => DistributiveLaw h f -> DistributiveLaw (Free h) f

distGApoT :: forall f m a. Functor f => Functor m => Coalgebra f a -> DistributiveLaw m f -> DistributiveLaw (ExceptT a m) f

distGApo :: forall f a. Functor f => Coalgebra f a -> DistributiveLaw (Either a) f

distFutu :: forall f. Functor f => DistributiveLaw (Free f) f

distDistributive :: forall f g. Traversable f => Distributive g => DistributiveLaw f g

distCata :: forall f. Functor f => DistributiveLaw f Identity

distApplicative :: forall f g. Traversable f => Applicative g => DistributiveLaw f g

distApo :: forall t f. Recursive t f => DistributiveLaw (Either t) f

distAna :: forall f. Functor f => DistributiveLaw Identity f

zygo :: forall t f a b. Recursive t f => Algebra f b -> GAlgebra (Tuple b) f a -> t -> a

universe :: forall t f. Recursive t f => Foldable f => t -> List t

transPrepro :: forall t f u g. Recursive t f => Corecursive t f => Corecursive u g => (f ~> f) -> Transform u f g -> t -> u

transParaT :: forall t f. Recursive t f => Corecursive t f => (t -> t -> t) -> t -> t

transPara :: forall t f u g. Recursive t f => Corecursive u g => AlgebraicGTransform (Tuple t) u f g -> t -> u

transCataTM :: forall t f m. Recursive t f => Corecursive t f => Monad m => Traversable f => (t -> m t) -> t -> m t

transCataT :: forall t f. Recursive t f => Corecursive t f => (t -> t) -> t -> t

transCataM :: forall t f u g m. Recursive t f => Corecursive u g => Monad m => Traversable f => TransformM m u f g -> t -> m u

transCata :: forall t f u g. Recursive t f => Corecursive u g => Transform u f g -> t -> u

topDownCataM :: forall t f m a. Recursive t f => Corecursive t f => Monad m => Traversable f => (a -> t -> m (Tuple a t)) -> a -> t -> m t

topDownCata :: forall t f a. Recursive t f => Corecursive t f => (a -> t -> Tuple a t) -> a -> t -> t

prepro :: forall t f a. Recursive t f => Corecursive t f => (f ~> f) -> Algebra f a -> t -> a

paraM :: forall t f m a. Recursive t f => Monad m => Traversable f => GAlgebraM (Tuple t) m f a -> t -> m a

para :: forall t f a. Recursive t f => GAlgebra (Tuple t) f a -> t -> a

mutu :: forall t f a b. Recursive t f => GAlgebra (Tuple a) f b -> GAlgebra (Tuple b) f a -> t -> a

lambek :: forall t f. Recursive t f => Corecursive t f => t -> f t

isLeaf :: forall t f. Recursive t f => Foldable f => t -> Boolean

histo :: forall t f a. Recursive t f => GAlgebra (Cofree f) f a -> t -> a

gzygo :: forall t f w a b. Recursive t f => Comonad w => Algebra f b -> DistributiveLaw f w -> GAlgebra (EnvT b w) f a -> t -> a

gprepro :: forall t f w a. Recursive t f => Corecursive t f => Comonad w => DistributiveLaw f w -> (f ~> f) -> GAlgebra w f a -> t -> a

gpara :: forall t f w a. Recursive t f => Corecursive t f => Comonad w => DistributiveLaw f w -> GAlgebra (EnvT t w) f a -> t -> a

ghisto :: forall t f h a. Recursive t f => Functor h => DistributiveLaw f h -> GAlgebra (Cofree h) f a -> t -> a

gcataM :: forall t f w m a. Recursive t f => Monad m => Comonad w => Traversable f => Traversable w => DistributiveLaw f w -> GAlgebraM w m f a -> t -> m a

gcata :: forall t f w a. Recursive t f => Comonad w => DistributiveLaw f w -> GAlgebra w f a -> t -> a

gElgotZygo :: forall t f w a b. Recursive t f => Comonad w => Algebra f b -> DistributiveLaw f w -> ElgotAlgebra (EnvT b w) f a -> t -> a

elgotZygo :: forall t f a b. Recursive t f => Algebra f b -> ElgotAlgebra (Tuple b) f a -> t -> a

elgotPara :: forall t f a. Recursive t f => ElgotAlgebra (Tuple t) f a -> t -> a

elgotHisto :: forall t f a. Recursive t f => ElgotAlgebra (Cofree f) f a -> t -> a

elgotCata :: forall t f w a. Recursive t f => Comonad w => DistributiveLaw f w -> ElgotAlgebra w f a -> t -> a

children :: forall t f. Recursive t f => Foldable f => t -> List t

cataM :: forall t f m a. Recursive t f => Monad m => Traversable f => AlgebraM m f a -> t -> m a

cata :: forall t f a. Recursive t f => Algebra f a -> t -> a

annotateTopDownM :: forall t f m a. Recursive t f => Monad m => Traversable f => (a -> f t -> m a) -> a -> t -> m (Cofree f a)

annotateTopDown :: forall t f a. Recursive t f => (a -> f t -> a) -> a -> t -> Cofree f a

transHylo :: forall t f g h u. Recursive t f => Corecursive u h => Functor g => Transform u g h -> Transform t f g -> t -> u

hyloM :: forall f m a b. Monad m => Traversable f => AlgebraM m f b -> CoalgebraM m f a -> a -> m b

hylo :: forall f a b. Functor f => Algebra f b -> Coalgebra f a -> a -> b

ghyloM :: forall f w n m a b. Monad m => Monad n => Comonad w => Traversable f => Traversable w => Traversable n => DistributiveLaw f w -> DistributiveLaw n f -> GAlgebraM w m f b -> GCoalgebraM n m f a -> a -> m b

ghylo :: forall f w n a b. Monad n => Comonad w => Functor f => DistributiveLaw f w -> DistributiveLaw n f -> GAlgebra w f b -> GCoalgebra n f a -> a -> b

dyna :: forall f a b. Functor f => GAlgebra (Cofree f) f b -> Coalgebra f a -> a -> b

convertTo :: forall t f r. Recursive t f => Corecursive r f => t -> r

codynaM :: forall f m a b. Monad m => Traversable f => AlgebraM m f b -> GCoalgebraM (Free f) m f a -> a -> m b

codyna :: forall f a b. Functor f => Algebra f b -> GCoalgebra (Free f) f a -> a -> b

chrono :: forall f a b. Functor f => GAlgebra (Cofree f) f b -> GCoalgebra (Free f) f a -> a -> b

type TransformM m t f g = f t -> m (g t)

type Transform t f g = f t -> g t

type CoalgebraicGTransform n t f g = f t -> g (n t)

type AlgebraicGTransform w t f g = f (w t) -> g t

transPostpro :: forall t f u g. Recursive t f => Recursive u g => Corecursive u g => (g ~> g) -> Transform t f g -> t -> u

transApoT :: forall t f. Recursive t f => Corecursive t f => (t -> Either t t) -> t -> t

transApo :: forall t f u g. Recursive t f => Corecursive u g => CoalgebraicGTransform (Either u) t f g -> t -> u

transAnaTM :: forall t f m. Recursive t f => Corecursive t f => Monad m => Traversable f => Coalgebra m t -> t -> m t

transAnaT :: forall t f. Recursive t f => Corecursive t f => (t -> t) -> t -> t

transAnaM :: forall t f u g m. Recursive t f => Corecursive u g => Monad m => Traversable g => TransformM m t f g -> t -> m u

transAna :: forall t f u g. Recursive t f => Corecursive u g => Transform t f g -> t -> u

postpro :: forall t f a. Recursive t f => Corecursive t f => (f ~> f) -> Coalgebra f a -> a -> t

gpostpro :: forall t f n a. Recursive t f => Corecursive t f => Monad n => DistributiveLaw n f -> (f ~> f) -> GCoalgebra n f a -> a -> t

gapo :: forall t f a b. Corecursive t f => Coalgebra f b -> GCoalgebra (Either b) f a -> a -> t

ganaM :: forall t f m n a. Corecursive t f => Monad m => Monad n => Traversable f => Traversable n => DistributiveLaw n f -> GCoalgebraM n m f a -> a -> m t

gana :: forall t f n a. Corecursive t f => Monad n => DistributiveLaw n f -> GCoalgebra n f a -> a -> t

futuM :: forall t f m a. Corecursive t f => Monad m => Traversable f => GCoalgebraM (Free f) m f a -> a -> m t

futu :: forall t f a. Corecursive t f => GCoalgebra (Free f) f a -> a -> t

elgotFutu :: forall t f a. Corecursive t f => ElgotCoalgebra (Free f) f a -> a -> t

elgotApo :: forall t f a. Corecursive t f => ElgotCoalgebra (Either t) f a -> a -> t

elgotAna :: forall t f n a. Corecursive t f => Monad n => DistributiveLaw n f -> ElgotCoalgebra n f a -> a -> t

colambek :: forall t f. Recursive t f => Corecursive t f => f t -> t

apoM :: forall t f m a. Corecursive t f => Monad m => Traversable f => GCoalgebraM (Either t) m f a -> a -> m t

apo :: forall t f a. Corecursive t f => GCoalgebra (Either t) f a -> a -> t

anaM :: forall t f m a. Corecursive t f => Monad m => Traversable f => CoalgebraM m f a -> a -> m t

ana :: forall t f a. Corecursive t f => Coalgebra f a -> a -> t

traverseR :: forall t f u g m. Recursive t f => Corecursive u g => Functor m => (f t -> m (g u)) -> t -> m u

mapR :: forall t f u g. Recursive t f => Corecursive u g => (f t -> g u) -> t -> u