Copyright	(C) 2008-2013 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	MPTCs, fundeps
Safe Haskell	Safe
Language	Haskell2010

Control.Comonad.Trans.Coiter

Contents

The coiterative comonad transformer
The coiterative comonad
Generating coiterative comonads
Cofree comonads
Examples

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 #

This is the coiterative comonad generated by a comonad

Constructors

CoiterT
Fields runCoiterT :: w (a, CoiterT w a)

Instances

ComonadTrans CoiterT #
Methods lower :: Comonad w => CoiterT w a -> w a #
ComonadHoist CoiterT #
Methods cohoist :: (Comonad w, Comonad v) => (forall x. w x -> v x) -> CoiterT w a -> CoiterT v a #
ComonadTraced m w => ComonadTraced m (CoiterT w) #
Methods trace :: m -> CoiterT w a -> a #
ComonadStore s w => ComonadStore s (CoiterT w) #
Methods pos :: CoiterT w a -> s # peek :: s -> CoiterT w a -> a # peeks :: (s -> s) -> CoiterT w a -> a # seek :: s -> CoiterT w a -> CoiterT w a # seeks :: (s -> s) -> CoiterT w a -> CoiterT w a # experiment :: Functor f => (s -> f s) -> CoiterT w a -> f a #
ComonadEnv e w => ComonadEnv e (CoiterT w) #
Methods ask :: CoiterT w a -> e #
Comonad w => ComonadCofree Identity (CoiterT w) #
Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
Functor w => Functor (CoiterT w) #
Methods fmap :: (a -> b) -> CoiterT w a -> CoiterT w b # (<$) :: a -> CoiterT w b -> CoiterT w a #
Foldable w => Foldable (CoiterT w) #
Methods fold :: Monoid m => CoiterT w m -> m # foldMap :: Monoid m => (a -> m) -> CoiterT w a -> m # foldr :: (a -> b -> b) -> b -> CoiterT w a -> b # foldr' :: (a -> b -> b) -> b -> CoiterT w a -> b # foldl :: (b -> a -> b) -> b -> CoiterT w a -> b # foldl' :: (b -> a -> b) -> b -> CoiterT w a -> b # foldr1 :: (a -> a -> a) -> CoiterT w a -> a # foldl1 :: (a -> a -> a) -> CoiterT w a -> a # toList :: CoiterT w a -> [a] # null :: CoiterT w a -> Bool # length :: CoiterT w a -> Int # elem :: Eq a => a -> CoiterT w a -> Bool # maximum :: Ord a => CoiterT w a -> a # minimum :: Ord a => CoiterT w a -> a # sum :: Num a => CoiterT w a -> a # product :: Num a => CoiterT w a -> a #
Traversable w => Traversable (CoiterT w) #
Methods traverse :: Applicative f => (a -> f b) -> CoiterT w a -> f (CoiterT w b) # sequenceA :: Applicative f => CoiterT w (f a) -> f (CoiterT w a) # mapM :: Monad m => (a -> m b) -> CoiterT w a -> m (CoiterT w b) # sequence :: Monad m => CoiterT w (m a) -> m (CoiterT w a) #
Comonad w => Comonad (CoiterT w) #
Methods extract :: CoiterT w a -> a # duplicate :: CoiterT w a -> CoiterT w (CoiterT w a) # extend :: (CoiterT w a -> b) -> CoiterT w a -> CoiterT w b #
(Functor w, Eq1 w) => Eq1 (CoiterT w) #
Methods (==#) :: Eq a => CoiterT w a -> CoiterT w a -> Bool #
(Functor w, Ord1 w) => Ord1 (CoiterT w) #
Methods compare1 :: Ord a => CoiterT w a -> CoiterT w a -> Ordering #
(Functor w, Show1 w) => Show1 (CoiterT w) #
Methods showsPrec1 :: Show a => Int -> CoiterT w a -> ShowS # showList1 :: Show a => [CoiterT w a] -> ShowS #
(Functor w, Read1 w) => Read1 (CoiterT w) #
Methods readsPrec1 :: Read a => Int -> ReadS (CoiterT w a) # readList1 :: Read a => ReadS [CoiterT w a] #
Eq (w (a, CoiterT w a)) => Eq (CoiterT w a) #
Methods (==) :: CoiterT w a -> CoiterT w a -> Bool # (/=) :: CoiterT w a -> CoiterT w a -> Bool #
(Typeable (* -> ) w, Typeable a, Data (w (a, CoiterT w a)), Data a) => Data (CoiterT w a) #
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CoiterT w a -> c (CoiterT w a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (CoiterT w a) # toConstr :: CoiterT w a -> Constr # dataTypeOf :: CoiterT w a -> DataType # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (CoiterT w a)) # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (CoiterT w a)) # gmapT :: (forall b. Data b => b -> b) -> CoiterT w a -> CoiterT w a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CoiterT w a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CoiterT w a -> r # gmapQ :: (forall d. Data d => d -> u) -> CoiterT w a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> CoiterT w a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> CoiterT w a -> m (CoiterT w a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CoiterT w a -> m (CoiterT w a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CoiterT w a -> m (CoiterT w a) #
Ord (w (a, CoiterT w a)) => Ord (CoiterT w a) #
Methods compare :: CoiterT w a -> CoiterT w a -> Ordering # (<) :: CoiterT w a -> CoiterT w a -> Bool # (<=) :: CoiterT w a -> CoiterT w a -> Bool # (>) :: CoiterT w a -> CoiterT w a -> Bool # (>=) :: CoiterT w a -> CoiterT w a -> Bool # max :: CoiterT w a -> CoiterT w a -> CoiterT w a # min :: CoiterT w a -> CoiterT w a -> CoiterT w a #
Read (w (a, CoiterT w a)) => Read (CoiterT w a) #
Methods readsPrec :: Int -> ReadS (CoiterT w a) # readList :: ReadS [CoiterT w a] # readPrec :: ReadPrec (CoiterT w a) # readListPrec :: ReadPrec [CoiterT w a] #
Show (w (a, CoiterT w a)) => Show (CoiterT w a) #
Methods showsPrec :: Int -> CoiterT w a -> ShowS # show :: CoiterT w a -> String # showList :: [CoiterT w a] -> ShowS #

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.

Minimal complete definition

unwrap

Methods

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

Remove a layer.

Instances

ComonadCofree [] Tree #
Methods unwrap :: Tree a -> [Tree a] #
ComonadCofree Maybe NonEmpty #
Methods unwrap :: NonEmpty a -> Maybe (NonEmpty a) #
Functor f => ComonadCofree f (Cofree f) #
Methods unwrap :: Cofree f a -> f (Cofree f a) #
Comonad w => ComonadCofree Identity (CoiterT w) #
Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
(ComonadCofree f w, Monoid m) => ComonadCofree f (TracedT m w) #
Methods unwrap :: TracedT m w a -> f (TracedT m w a) #
ComonadCofree f w => ComonadCofree f (StoreT s w) #
Methods unwrap :: StoreT s w a -> f (StoreT s w a) #
ComonadCofree f w => ComonadCofree f (EnvT e w) #
Methods unwrap :: EnvT e w a -> f (EnvT e w a) #
ComonadCofree f w => ComonadCofree f (IdentityT * w) #
Methods unwrap :: IdentityT * w a -> f (IdentityT * w a) #
(Functor f, Comonad w) => ComonadCofree f (CofreeT f w) #
Methods unwrap :: CofreeT f w a -> f (CofreeT f w a) #
ComonadCofree (Const * b) ((,) b) #
Methods unwrap :: (b, a) -> Const * b (b, a) #

Examples

Newton's method