Control.Comonad.Trans.Coiter

The coiterative comonad generated by a comonad

Documentation

Coiterative comonads represent non-terminating, productive computations.

They are the dual notion of iterative monads. While iterative computations produce no values or eventually terminate with one, coiterative computations constantly produce values and they never terminate.

It's simpler form, Coiter, is an infinite stream of data. CoiterT extends this so that each step of the computation can be performed in a comonadic context.

The coiterative comonad transformer

newtype CoiterT w a

This is the coiterative comonad generated by a comonad

Constructors

CoiterT

Fields

runCoiterT :: w (a, CoiterT w a)

Instances

ComonadHoist CoiterT

ComonadTrans CoiterT

ComonadTraced m w => ComonadTraced m (CoiterT w)

ComonadStore s w => ComonadStore s (CoiterT w)

ComonadEnv e w => ComonadEnv e (CoiterT w)

Comonad w => ComonadCofree Identity (CoiterT w)

Functor w => Functor (CoiterT w)

Foldable w => Foldable (CoiterT w)

Traversable w => Traversable (CoiterT w)

Comonad w => Comonad (CoiterT w)

(Functor w, Eq1 w) => Eq1 (CoiterT w)

(Functor w, Ord1 w) => Ord1 (CoiterT w)

(Functor w, Show1 w) => Show1 (CoiterT w)

(Functor w, Read1 w) => Read1 (CoiterT w)

Eq (w (a, CoiterT w a)) => Eq (CoiterT w a)

(Typeable (* -> *) w, Typeable * a, Data (w (a, CoiterT w a)), Data a) => Data (CoiterT w a)

Ord (w (a, CoiterT w a)) => Ord (CoiterT w a)

Read (w (a, CoiterT w a)) => Read (CoiterT w a)

Show (w (a, CoiterT w a)) => Show (CoiterT w a)

The coiterative comonad

type Coiter = CoiterT Identity

The coiterative comonad

coiter :: a -> Coiter a -> Coiter a

Prepends a result to a coiterative computation.

runCoiter . uncurry coiter == id

runCoiter :: Coiter a -> (a, Coiter a)

Extracts the first result from a coiterative computation.

uncurry coiter . runCoiter == id

Generating coiterative comonads

unfold :: Comonad w => (w a -> a) -> w a -> CoiterT w a

Unfold a CoiterT comonad transformer from a cokleisli arrow and an initial comonadic seed.

Cofree comonads

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)

Examples

Newton's method