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)

Defined in Control.Comonad.Trans.Cofree

Methods

ask :: CofreeT f w a -> e

(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)

Functor f => ComonadHoist (CofreeT f)

Defined in Control.Comonad.Trans.Cofree

Methods

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

ComonadTrans (CofreeT f)

Defined in Control.Comonad.Trans.Cofree

Methods

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

Alternative f => MonadTrans (CofreeT f)

Defined in Control.Comonad.Trans.Cofree

Methods

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

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

Defined in Control.Comonad.Trans.Cofree

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)

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

Defined in Control.Comonad.Trans.Cofree

Methods

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

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

Defined in Control.Comonad.Trans.Cofree

Methods

traverse :: Applicative f0 => (a -> f0 b) -> CofreeT f w a -> f0 (CofreeT f w b)

sequenceA :: Applicative f0 => CofreeT f w (f0 a) -> f0 (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, Applicative w) => Applicative (CofreeT f w)

Defined in Control.Comonad.Trans.Cofree

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

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

Defined in Control.Comonad.Trans.Cofree

Methods

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

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

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

Defined in Control.Comonad.Trans.Cofree

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

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

Defined in Control.Comonad.Trans.Cofree

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

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

Defined in Control.Comonad.Trans.Cofree

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 :: forall r r'. (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)

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

Defined in Control.Comonad.Trans.Cofree

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)

Defined in Control.Comonad.Trans.Cofree

Methods

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

show :: CofreeT f w a -> String

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

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

Defined in Control.Comonad.Trans.Cofree

Methods

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

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

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

Defined in Control.Comonad.Trans.Cofree

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

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

Generic1 (CofreeF f a :: Type -> Type)

Defined in Control.Comonad.Trans.Cofree

Associated Types

type Rep1 (CofreeF f a) :: k -> Type

Methods

from1 :: forall (a0 :: k). CofreeF f a a0 -> Rep1 (CofreeF f a) a0

to1 :: forall (a0 :: k). Rep1 (CofreeF f a) a0 -> CofreeF f a a0

Foldable f => Bifoldable (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

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)

Defined in Control.Comonad.Trans.Cofree

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

Traversable f => Bitraversable (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> CofreeF f a b -> f0 (CofreeF f c d)

Eq1 f => Eq2 (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> CofreeF f a c -> CofreeF f b d -> Bool

Ord1 f => Ord2 (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> CofreeF f a c -> CofreeF f b d -> Ordering

Read1 f => Read2 (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (CofreeF f a b)

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [CofreeF f a b]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (CofreeF f a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [CofreeF f a b]

Show1 f => Show2 (CofreeF f)

Defined in Control.Comonad.Trans.Cofree

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> CofreeF f a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [CofreeF f a b] -> ShowS

Foldable f => Foldable (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

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

foldMap :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> CofreeF f a a0 -> m

foldr :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> CofreeF f a a0 -> b

foldl :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> CofreeF f a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> CofreeF f a a0 -> a0

toList :: CofreeF f a a0 -> [a0]

null :: CofreeF f a a0 -> Bool

length :: CofreeF f a a0 -> Int

elem :: Eq a0 => a0 -> CofreeF f a a0 -> Bool

maximum :: Ord a0 => CofreeF f a a0 -> a0

minimum :: Ord a0 => CofreeF f a a0 -> a0

sum :: Num a0 => CofreeF f a a0 -> a0

product :: Num a0 => CofreeF f a a0 -> a0

(Eq1 f, Eq a) => Eq1 (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

liftEq :: (a0 -> b -> Bool) -> CofreeF f a a0 -> CofreeF f a b -> Bool

(Ord1 f, Ord a) => Ord1 (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

liftCompare :: (a0 -> b -> Ordering) -> CofreeF f a a0 -> CofreeF f a b -> Ordering

(Read1 f, Read a) => Read1 (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (CofreeF f a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [CofreeF f a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (CofreeF f a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [CofreeF f a a0]

(Show1 f, Show a) => Show1 (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> CofreeF f a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [CofreeF f a a0] -> ShowS

Traversable f => Traversable (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

traverse :: Applicative f0 => (a0 -> f0 b) -> CofreeF f a a0 -> f0 (CofreeF f a b)

sequenceA :: Applicative f0 => CofreeF f a (f0 a0) -> f0 (CofreeF f a a0)

mapM :: Monad m => (a0 -> m b) -> CofreeF f a a0 -> m (CofreeF f a b)

sequence :: Monad m => CofreeF f a (m a0) -> m (CofreeF f a a0)

Functor f => Functor (CofreeF f a)

Defined in Control.Comonad.Trans.Cofree

Methods

fmap :: (a0 -> b) -> CofreeF f a a0 -> CofreeF f a b

(<$) :: a0 -> CofreeF f a b -> CofreeF f a a0

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

Defined in Control.Comonad.Trans.Cofree

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> CofreeF f a b -> c (CofreeF f a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> 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 b0. Data b0 => b0 -> b0) -> 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 :: forall r r'. (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)

Generic (CofreeF f a b)

Defined in Control.Comonad.Trans.Cofree

Associated Types

type Rep (CofreeF f a b) :: Type -> Type

Methods

from :: CofreeF f a b -> Rep (CofreeF f a b) x

to :: Rep (CofreeF f a b) x -> CofreeF f a b

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

Defined in Control.Comonad.Trans.Cofree

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

Defined in Control.Comonad.Trans.Cofree

Methods

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

show :: CofreeF f a b -> String

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

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

Defined in Control.Comonad.Trans.Cofree

Methods

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

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

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

Defined in Control.Comonad.Trans.Cofree

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

type Rep1 (CofreeF f a :: Type -> Type)

Defined in Control.Comonad.Trans.Cofree

type Rep1 (CofreeF f a :: Type -> Type) = D1 ('MetaData "CofreeF" "Control.Comonad.Trans.Cofree" "free-5.2-8yEobwXBbzsEnejCWouYBv" 'False) (C1 ('MetaCons ":<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

type Rep (CofreeF f a b)

Defined in Control.Comonad.Trans.Cofree

type Rep (CofreeF f a b) = D1 ('MetaData "CofreeF" "Control.Comonad.Trans.Cofree" "free-5.2-8yEobwXBbzsEnejCWouYBv" 'False) (C1 ('MetaCons ":<" ('InfixI 'RightAssociative 5) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f b))))

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)

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.