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

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

ComonadEnv e w => ComonadEnv e (CoiterT w)

Methods

ask :: CoiterT w a -> e

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

ComonadTraced m w => ComonadTraced m (CoiterT w)

Methods

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

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)

Eq1 w => Eq1 (CoiterT w)

Methods

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

Ord1 w => Ord1 (CoiterT w)

Methods

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

Read1 w => Read1 (CoiterT w)

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)

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)

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)

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)

(Ord1 w, Ord 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

(Read1 w, Read 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]

(Show1 w, Show 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