free-4.11: Monads for free

Copyright(C) 2008-2013 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityprovisional
PortabilityMPTCs, fundeps
Safe HaskellSafe-Inferred
LanguageHaskell2010

Control.Comonad.Trans.Coiter

Contents

Description

The coiterative comonad generated by a comonad

Synopsis

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 Source

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) 
Typeable ((* -> *) -> * -> *) CoiterT 

The coiterative comonad

type Coiter = CoiterT Identity Source

The coiterative comonad

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

Prepends a result to a coiterative computation.

runCoiter . uncurry coiter == id

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

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 Source

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 Source

Allows you to peel a layer off a cofree comonad.

Methods

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

Remove a layer.

Examples