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

newtype CoiterT w a = CoiterT {
- runCoiterT :: w (a, CoiterT w a)
}
type Coiter = CoiterT Identity
coiter :: a -> Coiter a -> Coiter a
runCoiter :: Coiter a -> (a, Coiter a)
unfold :: Comonad w => (w a -> a) -> w a -> CoiterT w a
class (Functor f, Comonad w) => ComonadCofree f w | w -> f where
- unwrap :: w a -> f (w a)

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

Instances details

ComonadTrans CoiterT #
Instance details Defined in Control.Comonad.Trans.Coiter Methods lower :: Comonad w => CoiterT w a -> w a #
ComonadHoist CoiterT #
Instance details Defined in Control.Comonad.Trans.Coiter Methods cohoist :: (Comonad w, Comonad v) => (forall x. w x -> v x) -> CoiterT w a -> CoiterT v a #
ComonadEnv e w => ComonadEnv e (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods ask :: CoiterT w a -> e #
ComonadStore s w => ComonadStore s (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter 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 #
ComonadTraced m w => ComonadTraced m (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods trace :: m -> CoiterT w a -> a #
Comonad w => ComonadCofree Identity (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
Functor w => Functor (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods fmap :: (a -> b) -> CoiterT w a -> CoiterT w b # (<$) :: a -> CoiterT w b -> CoiterT w a #
Foldable w => Foldable (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods fold :: Monoid m => CoiterT w m -> m # foldMap :: Monoid m => (a -> m) -> CoiterT w a -> 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) #
Instance details Defined in Control.Comonad.Trans.Coiter 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) #
Eq1 w => Eq1 (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods liftEq :: (a -> b -> Bool) -> CoiterT w a -> CoiterT w b -> Bool #
Ord1 w => Ord1 (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods liftCompare :: (a -> b -> Ordering) -> CoiterT w a -> CoiterT w b -> Ordering #
Read1 w => Read1 (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (CoiterT w a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [CoiterT w a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (CoiterT w a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [CoiterT w a] #
Show1 w => Show1 (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> CoiterT w a -> ShowS # liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [CoiterT w a] -> ShowS #
Comonad w => Comonad (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter 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 #
(Eq1 w, Eq a) => Eq (CoiterT w a) #
Instance details Defined in Control.Comonad.Trans.Coiter 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) #
Instance details Defined in Control.Comonad.Trans.Coiter 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 :: forall r r'. (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) #
(Ord1 w, Ord a) => Ord (CoiterT w a) #
Instance details Defined in Control.Comonad.Trans.Coiter 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 #
(Read1 w, Read a) => Read (CoiterT w a) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods readsPrec :: Int -> ReadS (CoiterT w a) # readList :: ReadS [CoiterT w a] # readPrec :: ReadPrec (CoiterT w a) # readListPrec :: ReadPrec [CoiterT w a] #
(Show1 w, Show a) => Show (CoiterT w a) #
Instance details Defined in Control.Comonad.Trans.Coiter 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.

Methods

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

Remove a layer.

Instances

Instances details

ComonadCofree [] Tree #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: Tree a -> [Tree a] #
ComonadCofree Maybe NonEmpty #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: NonEmpty a -> Maybe (NonEmpty a) #
Functor f => ComonadCofree f (Cofree f) #
Instance details Defined in Control.Comonad.Cofree Methods unwrap :: Cofree f a -> f (Cofree f a) #
Comonad w => ComonadCofree Identity (CoiterT w) #
Instance details Defined in Control.Comonad.Trans.Coiter Methods unwrap :: CoiterT w a -> Identity (CoiterT w a) #
(ComonadCofree f w, Monoid m) => ComonadCofree f (TracedT m w) #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: TracedT m w a -> f (TracedT m w a) #
ComonadCofree f w => ComonadCofree f (StoreT s w) #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: StoreT s w a -> f (StoreT s w a) #
ComonadCofree f w => ComonadCofree f (EnvT e w) #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: EnvT e w a -> f (EnvT e w a) #
ComonadCofree f w => ComonadCofree f (IdentityT w) #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: IdentityT w a -> f (IdentityT w a) #
(Functor f, Comonad w) => ComonadCofree f (CofreeT f w) #
Instance details Defined in Control.Comonad.Trans.Cofree Methods unwrap :: CofreeT f w a -> f (CofreeT f w a) #
ComonadCofree (Const b :: Type -> Type) ((,) b) #
Instance details Defined in Control.Comonad.Cofree.Class Methods unwrap :: (b, a) -> Const b (b, a) #

Examples

Newton's method