Control.Comonad.Trans.Cofree

The cofree comonad transformer

Documentation

newtype CofreeT f w a

This is a cofree comonad of some functor f, with a comonad w threaded through it at each level.

Constructors

CofreeT

Fields

• runCofreeT :: w (CofreeF f a (CofreeT f w a))

Instances

(Functor f, ComonadEnv e w) => ComonadEnv e (CofreeT f w)

Methods

ask :: CofreeT f w a -> e

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

Methods

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

ComonadTrans (CofreeT f)

Methods

lower :: Comonad w => CofreeT f w a -> w a

Functor f => ComonadHoist (CofreeT f)

Methods

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

Alternative f => MonadTrans (CofreeT f)

Methods

lift :: Monad m => m a -> CofreeT f m a

(Alternative f, Monad w) => Monad (CofreeT f w)

Methods

(>>=) :: CofreeT f w a -> (a -> CofreeT f w b) -> CofreeT f w b

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

return :: a -> CofreeT f w a

fail :: String -> CofreeT f w a

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

Methods

fmap :: (a -> b) -> CofreeT f w a -> CofreeT f w b

(<$) :: a -> CofreeT f w b -> CofreeT f w a

(Alternative f, Applicative w) => Applicative (CofreeT f w)

Methods

pure :: a -> CofreeT f w a

(<*>) :: CofreeT f w (a -> b) -> CofreeT f w a -> CofreeT f w b

liftA2 :: (a -> b -> c) -> CofreeT f w a -> CofreeT f w b -> CofreeT f w c

(*>) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w b

(<*) :: CofreeT f w a -> CofreeT f w b -> CofreeT f w a

(Foldable f, Foldable w) => Foldable (CofreeT f w)

Methods

fold :: Monoid m => CofreeT f w m -> m

foldMap :: Monoid m => (a -> m) -> CofreeT f w a -> m

foldr :: (a -> b -> b) -> b -> CofreeT f w a -> b

foldr' :: (a -> b -> b) -> b -> CofreeT f w a -> b

foldl :: (b -> a -> b) -> b -> CofreeT f w a -> b

foldl' :: (b -> a -> b) -> b -> CofreeT f w a -> b

foldr1 :: (a -> a -> a) -> CofreeT f w a -> a

foldl1 :: (a -> a -> a) -> CofreeT f w a -> a

toList :: CofreeT f w a -> [a]

null :: CofreeT f w a -> Bool

length :: CofreeT f w a -> Int

elem :: Eq a => a -> CofreeT f w a -> Bool

maximum :: Ord a => CofreeT f w a -> a

minimum :: Ord a => CofreeT f w a -> a

sum :: Num a => CofreeT f w a -> a

product :: Num a => CofreeT f w a -> a

(Traversable f, Traversable w) => Traversable (CofreeT f w)

Methods

traverse :: Applicative f => (a -> f b) -> CofreeT f w a -> f (CofreeT f w b)

sequenceA :: Applicative f => CofreeT f w (f a) -> f (CofreeT f w a)

mapM :: Monad m => (a -> m b) -> CofreeT f w a -> m (CofreeT f w b)

sequence :: Monad m => CofreeT f w (m a) -> m (CofreeT f w a)

(Alternative f, MonadZip f, MonadZip m) => MonadZip (CofreeT f m)

Methods

mzip :: CofreeT f m a -> CofreeT f m b -> CofreeT f m (a, b)

mzipWith :: (a -> b -> c) -> CofreeT f m a -> CofreeT f m b -> CofreeT f m c

munzip :: CofreeT f m (a, b) -> (CofreeT f m a, CofreeT f m b)

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

Methods

extract :: CofreeT f w a -> a

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

extend :: (CofreeT f w a -> b) -> CofreeT f w a -> CofreeT f w b

Eq (w (CofreeF f a (CofreeT f w a))) => Eq (CofreeT f w a)

Methods

(==) :: CofreeT f w a -> CofreeT f w a -> Bool

(/=) :: CofreeT f w a -> CofreeT f w a -> Bool

(Typeable (* -> *) f, Typeable (* -> *) w, Typeable * a, Data (w (CofreeF f a (CofreeT f w a))), Data a) => Data (CofreeT f w a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> CofreeT f w a -> c (CofreeT f w a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (CofreeT f w a)

toConstr :: CofreeT f w a -> Constr

dataTypeOf :: CofreeT f w a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (CofreeT f w a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (CofreeT f w a))

gmapT :: (forall b. Data b => b -> b) -> CofreeT f w a -> CofreeT f w a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CofreeT f w a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CofreeT f w a -> r

gmapQ :: (forall d. Data d => d -> u) -> CofreeT f w a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> CofreeT f w a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> CofreeT f w a -> m (CofreeT f w a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CofreeT f w a -> m (CofreeT f w a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CofreeT f w a -> m (CofreeT f w a)

Ord (w (CofreeF f a (CofreeT f w a))) => Ord (CofreeT f w a)

Methods

compare :: CofreeT f w a -> CofreeT f w a -> Ordering

(<) :: CofreeT f w a -> CofreeT f w a -> Bool

(<=) :: CofreeT f w a -> CofreeT f w a -> Bool

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

(>=) :: CofreeT f w a -> CofreeT f w a -> Bool

max :: CofreeT f w a -> CofreeT f w a -> CofreeT f w a

min :: CofreeT f w a -> CofreeT f w a -> CofreeT f w a

Read (w (CofreeF f a (CofreeT f w a))) => Read (CofreeT f w a)

Methods

readsPrec :: Int -> ReadS (CofreeT f w a)

readList :: ReadS [CofreeT f w a]

readPrec :: ReadPrec (CofreeT f w a)

readListPrec :: ReadPrec [CofreeT f w a]

Show (w (CofreeF f a (CofreeT f w a))) => Show (CofreeT f w a)

Methods

showsPrec :: Int -> CofreeT f w a -> ShowS

show :: CofreeT f w a -> String

showList :: [CofreeT f w a] -> ShowS

type Cofree f = CofreeT f Identity

The cofree Comonad of a functor f.

cofree :: CofreeF f a (Cofree f a) -> Cofree f a

Wrap another layer around a cofree comonad value.

cofree is a right inverse of runCofree.

runCofree . cofree == id

runCofree :: Cofree f a -> CofreeF f a (Cofree f a)

Unpeel the first layer off a cofree comonad value.

runCofree is a right inverse of cofree.

cofree . runCofree == id

data CofreeF f a b

This is the base functor of the cofree comonad transformer.

Constructors

a :< (f b) infixr 5

Instances

Traversable f => Bitraversable (CofreeF f)

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> CofreeF f a b -> f (CofreeF f c d)

Foldable f => Bifoldable (CofreeF f)

Methods

bifold :: Monoid m => CofreeF f m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> CofreeF f a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> CofreeF f a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> CofreeF f a b -> c

Functor f => Bifunctor (CofreeF f)

Methods

bimap :: (a -> b) -> (c -> d) -> CofreeF f a c -> CofreeF f b d

first :: (a -> b) -> CofreeF f a c -> CofreeF f b c

second :: (b -> c) -> CofreeF f a b -> CofreeF f a c

Functor f => Functor (CofreeF f a)

Methods

fmap :: (a -> b) -> CofreeF f a a -> CofreeF f a b

(<$) :: a -> CofreeF f a b -> CofreeF f a a

Foldable f => Foldable (CofreeF f a)

Methods

fold :: Monoid m => CofreeF f a m -> m

foldMap :: Monoid m => (a -> m) -> CofreeF f a a -> m

foldr :: (a -> b -> b) -> b -> CofreeF f a a -> b

foldr' :: (a -> b -> b) -> b -> CofreeF f a a -> b

foldl :: (b -> a -> b) -> b -> CofreeF f a a -> b

foldl' :: (b -> a -> b) -> b -> CofreeF f a a -> b

foldr1 :: (a -> a -> a) -> CofreeF f a a -> a

foldl1 :: (a -> a -> a) -> CofreeF f a a -> a

toList :: CofreeF f a a -> [a]

null :: CofreeF f a a -> Bool

length :: CofreeF f a a -> Int

elem :: Eq a => a -> CofreeF f a a -> Bool

maximum :: Ord a => CofreeF f a a -> a

minimum :: Ord a => CofreeF f a a -> a

sum :: Num a => CofreeF f a a -> a

product :: Num a => CofreeF f a a -> a

Traversable f => Traversable (CofreeF f a)

Methods

traverse :: Applicative f => (a -> f b) -> CofreeF f a a -> f (CofreeF f a b)

sequenceA :: Applicative f => CofreeF f a (f a) -> f (CofreeF f a a)

mapM :: Monad m => (a -> m b) -> CofreeF f a a -> m (CofreeF f a b)

sequence :: Monad m => CofreeF f a (m a) -> m (CofreeF f a a)

(Eq (f b), Eq a) => Eq (CofreeF f a b)

Methods

(==) :: CofreeF f a b -> CofreeF f a b -> Bool

(/=) :: CofreeF f a b -> CofreeF f a b -> Bool

(Typeable (* -> *) f, Typeable * a, Typeable * b, Data a, Data (f b), Data b) => Data (CofreeF f a b)

Methods

gfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> CofreeF f a b -> c (CofreeF f a b)

gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (CofreeF f a b)

toConstr :: CofreeF f a b -> Constr

dataTypeOf :: CofreeF f a b -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (CofreeF f a b))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (CofreeF f a b))

gmapT :: (forall c. Data c => c -> c) -> CofreeF f a b -> CofreeF f a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> CofreeF f a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> CofreeF f a b -> r

gmapQ :: (forall d. Data d => d -> u) -> CofreeF f a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> CofreeF f a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> CofreeF f a b -> m (CofreeF f a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> CofreeF f a b -> m (CofreeF f a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> CofreeF f a b -> m (CofreeF f a b)

(Ord (f b), Ord a) => Ord (CofreeF f a b)

Methods

compare :: CofreeF f a b -> CofreeF f a b -> Ordering

(<) :: CofreeF f a b -> CofreeF f a b -> Bool

(<=) :: CofreeF f a b -> CofreeF f a b -> Bool

(>) :: CofreeF f a b -> CofreeF f a b -> Bool

(>=) :: CofreeF f a b -> CofreeF f a b -> Bool

max :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b

min :: CofreeF f a b -> CofreeF f a b -> CofreeF f a b

(Read (f b), Read a) => Read (CofreeF f a b)

Methods

readsPrec :: Int -> ReadS (CofreeF f a b)

readList :: ReadS [CofreeF f a b]

readPrec :: ReadPrec (CofreeF f a b)

readListPrec :: ReadPrec [CofreeF f a b]

(Show (f b), Show a) => Show (CofreeF f a b)

Methods

showsPrec :: Int -> CofreeF f a b -> ShowS

show :: CofreeF f a b -> String

showList :: [CofreeF f a b] -> ShowS

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)

headF :: CofreeF f a b -> a

Extract the head of the base functor

tailF :: CofreeF f a b -> f b

Extract the tails of the base functor

transCofreeT :: (Functor g, Comonad w) => (forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a

Lift a natural transformation from f to g into a comonad homomorphism from CofreeT f w to CofreeT g w

coiterT :: (Functor f, Comonad w) => (w a -> f (w a)) -> w a -> CofreeT f w a

Unfold a CofreeT comonad transformer from a coalgebra and an initial comonad.