Control.Comonad.Trans.Cofree

The cofree comonad transformer

Documentation

newtype CofreeT f w a

This is a cofree comonad of some functor f, with a comonad w threaded through it at each level.

Constructors

CofreeT

Fields

runCofreeT :: w (CofreeF f a (CofreeT f w a))

Instances

(Functor f, Comonad w) => ComonadCofree f (CofreeT f w)

Functor f => ComonadTrans (CofreeT f)

Alternative f => MonadTrans (CofreeT f)

(Alternative f, Monad w) => Monad (CofreeT f w)

(Functor f, Functor w) => Functor (CofreeT f w)

(Alternative f, Applicative w) => Applicative (CofreeT f w)

(Foldable f, Foldable w) => Foldable (CofreeT f w)

(Traversable f, Traversable w) => Traversable (CofreeT f w)

(Alternative f, MonadZip f, MonadZip m) => MonadZip (CofreeT f m)

(Functor f, Comonad w) => Comonad (CofreeT f w)

Eq (w (CofreeF f a (CofreeT f w a))) => Eq (CofreeT f w a)

(Typeable (* -> *) f, Typeable (* -> *) w, Typeable * a, Data (w (CofreeF f a (CofreeT f w a))), Data a) => Data (CofreeT f w a)

Ord (w (CofreeF f a (CofreeT f w a))) => Ord (CofreeT f w a)

Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a)

Show (w (CofreeF f a (CofreeT f w a))) => Show (CofreeT f w a)

type Cofree f = CofreeT f Identity

The cofree Comonad of a functor f.

cofree :: CofreeF f a (Cofree f a) -> Cofree f a

Wrap another layer around a cofree comonad value.

cofree is a right inverse of runCofree.

runCofree . cofree == id

runCofree :: Cofree f a -> CofreeF f a (Cofree f a)

Unpeel the first layer off a cofree comonad value.

runCofree is a right inverse of cofree.

cofree . runCofree == id

data CofreeF f a b

This is the base functor of the cofree comonad transformer.

Constructors

a :< (f b) infixr 5

Instances

Functor f => Bifunctor (CofreeF f)

Traversable f => Bitraversable (CofreeF f)

Foldable f => Bifoldable (CofreeF f)

Functor f => Functor (CofreeF f a)

Foldable f => Foldable (CofreeF f a)

Traversable f => Traversable (CofreeF f a)

(Eq a, Eq (f b)) => Eq (CofreeF f a b)

(Typeable (* -> *) f, Typeable * a, Typeable * b, Data a, Data (f b), Data b) => Data (CofreeF f a b)

(Ord a, Ord (f b)) => Ord (CofreeF f a b)

(Read a, Read (f b)) => Read (CofreeF f a b)

(Show a, Show (f b)) => Show (CofreeF f a b)

class (Functor f, Comonad w) => ComonadCofree f w | w -> f where

Allows you to peel a layer off a cofree comonad.

Methods

unwrap :: w a -> f (w a)

Remove a layer.

Instances

ComonadCofree Maybe NonEmpty

ComonadCofree f w => ComonadCofree f (IdentityT w)

Functor f => ComonadCofree f (Cofree f)

Comonad w => ComonadCofree Identity (CoiterT w)

(ComonadCofree f w, Semigroup m, Monoid m) => ComonadCofree f (TracedT m w)

ComonadCofree f w => ComonadCofree f (StoreT s w)

ComonadCofree f w => ComonadCofree f (EnvT e w)

(Functor f, Comonad w) => ComonadCofree f (CofreeT f w)

ComonadCofree (Const b) ((,) b)

headF :: CofreeF f a b -> a

Extract the head of the base functor

tailF :: CofreeF f a b -> f b

Extract the tails of the base functor

coiterT :: (Functor f, Comonad w) => (w a -> f (w a)) -> w a -> CofreeT f w a

Unfold a CofreeT comonad transformer from a coalgebra and an initial comonad.