Control.Comonad.Coideal

Coideal Comonads

class Functor w => ComonadCoideal w where

Methods

coidealExtend :: (Coideal w a -> b) -> w a -> w b

Instances

(ComonadCoideal w, ComonadCoideal v) => ComonadCoideal (w :* v)

Defined in Control.Comonad.Coideal

Methods

coidealExtend :: (Coideal (w :* v) a -> b) -> (w :* v) a -> (w :* v) b

newtype Coideal f a

Constructors

Coideal

Fields

• runCoideal :: (a, f a)

Instances

Foldable f => Foldable (Coideal f)

Defined in Control.Comonad.Coideal

Methods

fold :: Monoid m => Coideal f m -> m

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

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

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

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

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

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

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

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

toList :: Coideal f a -> [a]

null :: Coideal f a -> Bool

length :: Coideal f a -> Int

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

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

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

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

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

Traversable f => Traversable (Coideal f)

Defined in Control.Comonad.Coideal

Methods

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

sequenceA :: Applicative f0 => Coideal f (f0 a) -> f0 (Coideal f a)

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

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

Functor f => Functor (Coideal f)

Defined in Control.Comonad.Coideal

Methods

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

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

ComonadCoideal w => Comonad (Coideal w)

Defined in Control.Comonad.Coideal

Methods

extract :: Coideal w a -> a

duplicate :: Coideal w a -> Coideal w (Coideal w a)

extend :: (Coideal w a -> b) -> Coideal w a -> Coideal w b

buildCoideal :: (a -> w a) -> a -> Coideal w a

Mutual recursion for (co)ideal (co)monad (co)products

newtype Mutual p m n a

Constructors

Mutual

Fields

• runMutual :: m (p a (Mutual p n m a))

Instances

(Bifoldable p, Foldable m, Foldable n) => Foldable (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

fold :: Monoid m0 => Mutual p m n m0 -> m0

foldMap :: Monoid m0 => (a -> m0) -> Mutual p m n a -> m0

foldMap' :: Monoid m0 => (a -> m0) -> Mutual p m n a -> m0

foldr :: (a -> b -> b) -> b -> Mutual p m n a -> b

foldr' :: (a -> b -> b) -> b -> Mutual p m n a -> b

foldl :: (b -> a -> b) -> b -> Mutual p m n a -> b

foldl' :: (b -> a -> b) -> b -> Mutual p m n a -> b

foldr1 :: (a -> a -> a) -> Mutual p m n a -> a

foldl1 :: (a -> a -> a) -> Mutual p m n a -> a

toList :: Mutual p m n a -> [a]

null :: Mutual p m n a -> Bool

length :: Mutual p m n a -> Int

elem :: Eq a => a -> Mutual p m n a -> Bool

maximum :: Ord a => Mutual p m n a -> a

minimum :: Ord a => Mutual p m n a -> a

sum :: Num a => Mutual p m n a -> a

product :: Num a => Mutual p m n a -> a

(Bitraversable p, Traversable m, Traversable n) => Traversable (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

traverse :: Applicative f => (a -> f b) -> Mutual p m n a -> f (Mutual p m n b)

sequenceA :: Applicative f => Mutual p m n (f a) -> f (Mutual p m n a)

mapM :: Monad m0 => (a -> m0 b) -> Mutual p m n a -> m0 (Mutual p m n b)

sequence :: Monad m0 => Mutual p m n (m0 a) -> m0 (Mutual p m n a)

(Bifunctor p, Functor m, Functor n) => Functor (Mutual p m n)

Defined in Control.Functor.Internal.Mutual

Methods

fmap :: (a -> b) -> Mutual p m n a -> Mutual p m n b

(<$) :: a -> Mutual p m n b -> Mutual p m n a

(Show (m (p a (Mutual p n m a))), Show (n (p a (Mutual p m n a)))) => Show (Mutual p n m a)

Defined in Control.Functor.Internal.Mutual

Methods

showsPrec :: Int -> Mutual p n m a -> ShowS

show :: Mutual p n m a -> String

showList :: [Mutual p n m a] -> ShowS

(Eq (m (p a (Mutual p n m a))), Eq (n (p a (Mutual p m n a)))) => Eq (Mutual p n m a)

Defined in Control.Functor.Internal.Mutual

Methods

(==) :: Mutual p n m a -> Mutual p n m a -> Bool

(/=) :: Mutual p n m a -> Mutual p n m a -> Bool

Coideal Comonad Product

newtype (w :* v) a

Constructors

CoidealProduct

Fields

• runCoidealProduct :: (Mutual (,) w v a, Mutual (,) v w a)

Instances

(Foldable m0, Foldable n0) => Foldable (m0 :* n0)

Defined in Control.Comonad.Coideal

Methods

fold :: Monoid m => (m0 :* n0) m -> m

foldMap :: Monoid m => (a -> m) -> (m0 :* n0) a -> m

foldMap' :: Monoid m => (a -> m) -> (m0 :* n0) a -> m

foldr :: (a -> b -> b) -> b -> (m0 :* n0) a -> b

foldr' :: (a -> b -> b) -> b -> (m0 :* n0) a -> b

foldl :: (b -> a -> b) -> b -> (m0 :* n0) a -> b

foldl' :: (b -> a -> b) -> b -> (m0 :* n0) a -> b

foldr1 :: (a -> a -> a) -> (m0 :* n0) a -> a

foldl1 :: (a -> a -> a) -> (m0 :* n0) a -> a

toList :: (m0 :* n0) a -> [a]

null :: (m0 :* n0) a -> Bool

length :: (m0 :* n0) a -> Int

elem :: Eq a => a -> (m0 :* n0) a -> Bool

maximum :: Ord a => (m0 :* n0) a -> a

minimum :: Ord a => (m0 :* n0) a -> a

sum :: Num a => (m0 :* n0) a -> a

product :: Num a => (m0 :* n0) a -> a

(Traversable m0, Traversable n0) => Traversable (m0 :* n0)

Defined in Control.Comonad.Coideal

Methods

traverse :: Applicative f => (a -> f b) -> (m0 :* n0) a -> f ((m0 :* n0) b)

sequenceA :: Applicative f => (m0 :* n0) (f a) -> f ((m0 :* n0) a)

mapM :: Monad m => (a -> m b) -> (m0 :* n0) a -> m ((m0 :* n0) b)

sequence :: Monad m => (m0 :* n0) (m a) -> m ((m0 :* n0) a)

(Functor w, Functor v) => Functor (w :* v)

Defined in Control.Comonad.Coideal

Methods

fmap :: (a -> b) -> (w :* v) a -> (w :* v) b

(<$) :: a -> (w :* v) b -> (w :* v) a

(ComonadCoideal w, ComonadCoideal v) => ComonadCoideal (w :* v)

Defined in Control.Comonad.Coideal

Methods

coidealExtend :: (Coideal (w :* v) a -> b) -> (w :* v) a -> (w :* v) b

(Show (m0 (a, Mutual (,) n0 m0 a)), Show (n0 (a, Mutual (,) m0 n0 a))) => Show ((m0 :* n0) a)

Defined in Control.Comonad.Coideal

Methods

showsPrec :: Int -> (m0 :* n0) a -> ShowS

show :: (m0 :* n0) a -> String

showList :: [(m0 :* n0) a] -> ShowS

(Eq (m0 (a, Mutual (,) n0 m0 a)), Eq (n0 (a, Mutual (,) m0 n0 a))) => Eq ((m0 :* n0) a)

Defined in Control.Comonad.Coideal

Methods

(==) :: (m0 :* n0) a -> (m0 :* n0) a -> Bool

(/=) :: (m0 :* n0) a -> (m0 :* n0) a -> Bool

project1 :: Functor w => (w :* v) a -> w a

project2 :: Functor v => (w :* v) a -> v a

(&&&&) :: ComonadCoideal s => (forall a. s a -> w a) -> (forall a. s a -> v a) -> s b -> (w :* v) b