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 Source #

This is the coiterative comonad generated by a comonad

Constructors

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

Instances

Instances details

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

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.

Instances

Instances details

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

Examples

Newton's method