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

Defined in Control.Comonad.Trans.Coiter

Methods

cohoist :: (Comonad w, Comonad v) => (forall x. w x -> v x) -> CoiterT w a -> CoiterT v a

ComonadTrans CoiterT

Defined in Control.Comonad.Trans.Coiter

Methods

lower :: Comonad w => CoiterT w a -> w a

ComonadEnv e w => ComonadEnv e (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

ask :: CoiterT w a -> e

ComonadStore s w => ComonadStore s (CoiterT w)

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)

Defined in Control.Comonad.Trans.Coiter

Methods

trace :: m -> CoiterT w a -> a

Comonad w => ComonadCofree Identity (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

unwrap :: CoiterT w a -> Identity (CoiterT w a)

Foldable w => Foldable (CoiterT w)

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

Eq1 w => Eq1 (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

liftEq :: (a -> b -> Bool) -> CoiterT w a -> CoiterT w b -> Bool

Ord1 w => Ord1 (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

liftCompare :: (a -> b -> Ordering) -> CoiterT w a -> CoiterT w b -> Ordering

Read1 w => Read1 (CoiterT w)

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)

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

Traversable w => Traversable (CoiterT w)

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)

Functor w => Functor (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

fmap :: (a -> b) -> CoiterT w a -> CoiterT w b

(<$) :: a -> CoiterT w b -> CoiterT w a

Comonad w => Comonad (CoiterT w)

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

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

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)

(Read1 w, Read a) => Read (CoiterT w a)

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)

Defined in Control.Comonad.Trans.Coiter

Methods

showsPrec :: Int -> CoiterT w a -> ShowS

show :: CoiterT w a -> String

showList :: [CoiterT w a] -> ShowS

(Eq1 w, Eq a) => Eq (CoiterT w a)

Defined in Control.Comonad.Trans.Coiter

Methods

(==) :: CoiterT w a -> CoiterT w a -> Bool

(/=) :: CoiterT w a -> CoiterT w a -> Bool

(Ord1 w, Ord a) => Ord (CoiterT w a)

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

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

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: NonEmpty a -> Maybe (NonEmpty a)

ComonadCofree [] Tree

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: Tree a -> [Tree a]

Comonad w => ComonadCofree Identity (CoiterT w)

Defined in Control.Comonad.Trans.Coiter

Methods

unwrap :: CoiterT w a -> Identity (CoiterT w a)

Functor f => ComonadCofree f (Cofree f)

Defined in Control.Comonad.Cofree

Methods

unwrap :: Cofree f a -> f (Cofree f a)

ComonadCofree f w => ComonadCofree f (EnvT e w)

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: EnvT e w a -> f (EnvT e w a)

ComonadCofree f w => ComonadCofree f (StoreT s w)

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: StoreT s w a -> f (StoreT s w a)

(ComonadCofree f w, Monoid m) => ComonadCofree f (TracedT m w)

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: TracedT m w a -> f (TracedT m w a)

(Functor f, Comonad w) => ComonadCofree f (CofreeT f w)

Defined in Control.Comonad.Trans.Cofree

Methods

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

ComonadCofree f w => ComonadCofree f (IdentityT w)

Defined in Control.Comonad.Cofree.Class

Methods

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

ComonadCofree (Const b :: Type -> Type) ((,) b)

Defined in Control.Comonad.Cofree.Class

Methods

unwrap :: (b, a) -> Const b (b, a)

Examples

Newton's method