Data.Functor.Bind

Functors

class Functor f where

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Instances

Functor []

Methods

fmap :: (a -> b) -> [a] -> [b]

(<$) :: a -> [b] -> [a]

Functor Maybe

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b

(<$) :: a -> Maybe b -> Maybe a

Functor IO

Methods

fmap :: (a -> b) -> IO a -> IO b

(<$) :: a -> IO b -> IO a

Functor V1

Methods

fmap :: (a -> b) -> V1 a -> V1 b

(<$) :: a -> V1 b -> V1 a

Functor U1

Methods

fmap :: (a -> b) -> U1 a -> U1 b

(<$) :: a -> U1 b -> U1 a

Functor Par1

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b

(<$) :: a -> Par1 b -> Par1 a

Functor Id

Methods

fmap :: (a -> b) -> Id a -> Id b

(<$) :: a -> Id b -> Id a

Functor Identity

Methods

fmap :: (a -> b) -> Identity a -> Identity b

(<$) :: a -> Identity b -> Identity a

Functor Min

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Functor Max

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Functor First

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Last

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Option

Methods

fmap :: (a -> b) -> Option a -> Option b

(<$) :: a -> Option b -> Option a

Functor NonEmpty

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b

(<$) :: a -> NonEmpty b -> NonEmpty a

Functor Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b

(<$) :: a -> Complex b -> Complex a

Functor ZipList

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b

(<$) :: a -> ZipList b -> ZipList a

Functor Handler

Methods

fmap :: (a -> b) -> Handler a -> Handler b

(<$) :: a -> Handler b -> Handler a

Functor Dual

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Functor Sum

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Functor Product

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Functor First

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Functor Last

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Functor Id

Methods

fmap :: (a -> b) -> Id a -> Id b

(<$) :: a -> Id b -> Id a

Functor Digit

Methods

fmap :: (a -> b) -> Digit a -> Digit b

(<$) :: a -> Digit b -> Digit a

Functor Node

Methods

fmap :: (a -> b) -> Node a -> Node b

(<$) :: a -> Node b -> Node a

Functor Elem

Methods

fmap :: (a -> b) -> Elem a -> Elem b

(<$) :: a -> Elem b -> Elem a

Functor FingerTree

Methods

fmap :: (a -> b) -> FingerTree a -> FingerTree b

(<$) :: a -> FingerTree b -> FingerTree a

Functor Tree

Methods

fmap :: (a -> b) -> Tree a -> Tree b

(<$) :: a -> Tree b -> Tree a

Functor Seq

Methods

fmap :: (a -> b) -> Seq a -> Seq b

(<$) :: a -> Seq b -> Seq a

Functor ViewL

Methods

fmap :: (a -> b) -> ViewL a -> ViewL b

(<$) :: a -> ViewL b -> ViewL a

Functor ViewR

Methods

fmap :: (a -> b) -> ViewR a -> ViewR b

(<$) :: a -> ViewR b -> ViewR a

Functor IntMap

Methods

fmap :: (a -> b) -> IntMap a -> IntMap b

(<$) :: a -> IntMap b -> IntMap a

Functor ((->) r)

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b

(<$) :: a -> (r -> b) -> r -> a

Functor (Either a)

Methods

fmap :: (a -> b) -> Either a a -> Either a b

(<$) :: a -> Either a b -> Either a a

Functor f => Functor (Rec1 f)

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b

(<$) :: a -> Rec1 f b -> Rec1 f a

Functor (URec Char)

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b

(<$) :: a -> URec Char b -> URec Char a

Functor (URec Double)

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b

(<$) :: a -> URec Double b -> URec Double a

Functor (URec Float)

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b

(<$) :: a -> URec Float b -> URec Float a

Functor (URec Int)

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b

(<$) :: a -> URec Int b -> URec Int a

Functor (URec Word)

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b

(<$) :: a -> URec Word b -> URec Word a

Functor (URec (Ptr ()))

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a

Functor ((,) a)

Methods

fmap :: (a -> b) -> (a, a) -> (a, b)

(<$) :: a -> (a, b) -> (a, a)

Functor (Array i)

Methods

fmap :: (a -> b) -> Array i a -> Array i b

(<$) :: a -> Array i b -> Array i a

Functor (StateL s)

Methods

fmap :: (a -> b) -> StateL s a -> StateL s b

(<$) :: a -> StateL s b -> StateL s a

Functor (StateR s)

Methods

fmap :: (a -> b) -> StateR s a -> StateR s b

(<$) :: a -> StateR s b -> StateR s a

Functor (Arg a)

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b

(<$) :: a -> Arg a b -> Arg a a

Monad m => Functor (WrappedMonad m)

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a

Arrow a => Functor (ArrowMonad a)

Methods

fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b

(<$) :: a -> ArrowMonad a b -> ArrowMonad a a

Functor (Proxy *)

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b

(<$) :: a -> Proxy * b -> Proxy * a

Functor (StateL s)

Methods

fmap :: (a -> b) -> StateL s a -> StateL s b

(<$) :: a -> StateL s b -> StateL s a

Functor (StateR s)

Methods

fmap :: (a -> b) -> StateR s a -> StateR s b

(<$) :: a -> StateR s b -> StateR s a

Functor (State s)

Methods

fmap :: (a -> b) -> State s a -> State s b

(<$) :: a -> State s b -> State s a

Functor (Map k)

Methods

fmap :: (a -> b) -> Map k a -> Map k b

(<$) :: a -> Map k b -> Map k a

Functor f => Functor (Lift f)

Methods

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

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

Functor m => Functor (MaybeT m)

Methods

fmap :: (a -> b) -> MaybeT m a -> MaybeT m b

(<$) :: a -> MaybeT m b -> MaybeT m a

Functor m => Functor (ListT m)

Methods

fmap :: (a -> b) -> ListT m a -> ListT m b

(<$) :: a -> ListT m b -> ListT m a

Functor f => Functor (MaybeApply f)

Methods

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

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

Functor f => Functor (WrappedApplicative f)

Methods

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

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

Functor (K1 i c)

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b

(<$) :: a -> K1 i c b -> K1 i c a

(Functor f, Functor g) => Functor ((:+:) f g)

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b

(<$) :: a -> (f :+: g) b -> (f :+: g) a

(Functor f, Functor g) => Functor ((:*:) f g)

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b

(<$) :: a -> (f :*: g) b -> (f :*: g) a

(Functor f, Functor g) => Functor ((:.:) f g)

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b

(<$) :: a -> (f :.: g) b -> (f :.: g) a

Arrow a => Functor (WrappedArrow a b)

Methods

fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b

(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a

Functor (Const * m)

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b

(<$) :: a -> Const * m b -> Const * m a

Functor f => Functor (Alt * f)

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b

(<$) :: a -> Alt * f b -> Alt * f a

Bifunctor p => Functor (Join * p)

Methods

fmap :: (a -> b) -> Join * p a -> Join * p b

(<$) :: a -> Join * p b -> Join * p a

Functor w => Functor (TracedT m w)

Methods

fmap :: (a -> b) -> TracedT m w a -> TracedT m w b

(<$) :: a -> TracedT m w b -> TracedT m w a

Functor w => Functor (StoreT s w)

Methods

fmap :: (a -> b) -> StoreT s w a -> StoreT s w b

(<$) :: a -> StoreT s w b -> StoreT s w a

Functor w => Functor (EnvT e w)

Methods

fmap :: (a -> b) -> EnvT e w a -> EnvT e w b

(<$) :: a -> EnvT e w b -> EnvT e w a

Functor (Cokleisli w a)

Methods

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

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

Functor m => Functor (IdentityT * m)

Methods

fmap :: (a -> b) -> IdentityT * m a -> IdentityT * m b

(<$) :: a -> IdentityT * m b -> IdentityT * m a

Functor (Tagged k s)

Methods

fmap :: (a -> b) -> Tagged k s a -> Tagged k s b

(<$) :: a -> Tagged k s b -> Tagged k s a

Functor f => Functor (Reverse * f)

Derived instance.

Methods

fmap :: (a -> b) -> Reverse * f a -> Reverse * f b

(<$) :: a -> Reverse * f b -> Reverse * f a

Functor f => Functor (Backwards * f)

Derived instance.

Methods

fmap :: (a -> b) -> Backwards * f a -> Backwards * f b

(<$) :: a -> Backwards * f b -> Backwards * f a

Functor m => Functor (WriterT w m)

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b

(<$) :: a -> WriterT w m b -> WriterT w m a

Functor m => Functor (WriterT w m)

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b

(<$) :: a -> WriterT w m b -> WriterT w m a

Functor m => Functor (StateT s m)

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b

(<$) :: a -> StateT s m b -> StateT s m a

Functor m => Functor (StateT s m)

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b

(<$) :: a -> StateT s m b -> StateT s m a

Functor m => Functor (ErrorT e m)

Methods

fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b

(<$) :: a -> ErrorT e m b -> ErrorT e m a

Functor m => Functor (ExceptT e m)

Methods

fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b

(<$) :: a -> ExceptT e m b -> ExceptT e m a

Functor (Constant * a)

Methods

fmap :: (a -> b) -> Constant * a a -> Constant * a b

(<$) :: a -> Constant * a b -> Constant * a a

Functor f => Functor (Static f a)

Methods

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

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

Functor f => Functor (M1 i c f)

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b

(<$) :: a -> M1 i c f b -> M1 i c f a

(Functor f, Functor g) => Functor (Sum * f g)

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b

(<$) :: a -> Sum * f g b -> Sum * f g a

(Functor f, Functor g) => Functor (Product * f g)

Methods

fmap :: (a -> b) -> Product * f g a -> Product * f g b

(<$) :: a -> Product * f g b -> Product * f g a

Functor m => Functor (ReaderT * r m)

Methods

fmap :: (a -> b) -> ReaderT * r m a -> ReaderT * r m b

(<$) :: a -> ReaderT * r m b -> ReaderT * r m a

Functor (ContT k r m)

Methods

fmap :: (a -> b) -> ContT k r m a -> ContT k r m b

(<$) :: a -> ContT k r m b -> ContT k r m a

(Functor f, Functor g) => Functor (Compose * * f g)

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b

(<$) :: a -> Compose * * f g b -> Compose * * f g a

Bifunctor p => Functor (WrappedBifunctor * * p a)

Methods

fmap :: (a -> b) -> WrappedBifunctor * * p a a -> WrappedBifunctor * * p a b

(<$) :: a -> WrappedBifunctor * * p a b -> WrappedBifunctor * * p a a

Functor g => Functor (Joker k * g a)

Methods

fmap :: (a -> b) -> Joker k * g a a -> Joker k * g a b

(<$) :: a -> Joker k * g a b -> Joker k * g a a

Bifunctor p => Functor (Flip * * p a)

Methods

fmap :: (a -> b) -> Flip * * p a a -> Flip * * p a b

(<$) :: a -> Flip * * p a b -> Flip * * p a a

Functor (Clown * k f a)

Methods

fmap :: (a -> b) -> Clown * k f a a -> Clown * k f a b

(<$) :: a -> Clown * k f a b -> Clown * k f a a

Functor m => Functor (RWST r w s m)

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b

(<$) :: a -> RWST r w s m b -> RWST r w s m a

Functor m => Functor (RWST r w s m)

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b

(<$) :: a -> RWST r w s m b -> RWST r w s m a

(Functor f, Bifunctor p) => Functor (Tannen * * * f p a)

Methods

fmap :: (a -> b) -> Tannen * * * f p a a -> Tannen * * * f p a b

(<$) :: a -> Tannen * * * f p a b -> Tannen * * * f p a a

(Bifunctor p, Functor g) => Functor (Biff * k * * p f g a)

Methods

fmap :: (a -> b) -> Biff * k * * p f g a a -> Biff * k * * p f g a b

(<$) :: a -> Biff * k * * p f g a b -> Biff * k * * p f g a a

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

($>) :: Functor f => f a -> b -> f b infixl 4

Flipped version of <$.

Examples

Replace the contents of a Maybe Int with a constant String:

>>> Nothing $> "foo"
Nothing
>>> Just 90210 $> "foo"
Just "foo"

Replace the contents of an Either Int Int with a constant String, resulting in an Either Int String:

>>> Left 8675309 $> "foo"
Left 8675309
>>> Right 8675309 $> "foo"
Right "foo"

Replace each element of a list with a constant String:

>>> [1,2,3] $> "foo"
["foo","foo","foo"]

Replace the second element of a pair with a constant String:

>>> (1,2) $> "foo"
(1,"foo")

Since: 4.7.0.0

Applyable functors

class Functor f => Apply f where

A strong lax semi-monoidal endofunctor. This is equivalent to an Applicative without pure.

Laws:

(.) <$> u <.> v <.> w = u <.> (v <.> w)
x <.> (f <$> y) = (. f) <$> x <.> y
f <$> (x <.> y) = (f .) <$> x <.> y

The laws imply that .> and <. really ignore their left and right results, respectively, and really return their right and left results, respectively. Specifically,

(mf <$> m) .> (nf <$> n) = nf <$> (m .> n)
(mf <$> m) <. (nf <$> n) = mf <$> (m <. n)

Minimal complete definition

(<.>)

Methods

(<.>) :: f (a -> b) -> f a -> f b infixl 4

(.>) :: f a -> f b -> f b infixl 4

 a .> b = const id <$> a <.> b

(<.) :: f a -> f b -> f a infixl 4

 a <. b = const <$> a <.> b

Instances

Apply []

Methods

(<.>) :: [a -> b] -> [a] -> [b]

(.>) :: [a] -> [b] -> [b]

(<.) :: [a] -> [b] -> [a]

Apply Maybe

Methods

(<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b

(.>) :: Maybe a -> Maybe b -> Maybe b

(<.) :: Maybe a -> Maybe b -> Maybe a

Apply IO

Methods

(<.>) :: IO (a -> b) -> IO a -> IO b

(.>) :: IO a -> IO b -> IO b

(<.) :: IO a -> IO b -> IO a

Apply Identity

Methods

(<.>) :: Identity (a -> b) -> Identity a -> Identity b

(.>) :: Identity a -> Identity b -> Identity b

(<.) :: Identity a -> Identity b -> Identity a

Apply Option

Methods

(<.>) :: Option (a -> b) -> Option a -> Option b

(.>) :: Option a -> Option b -> Option b

(<.) :: Option a -> Option b -> Option a

Apply NonEmpty

Methods

(<.>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b

(.>) :: NonEmpty a -> NonEmpty b -> NonEmpty b

(<.) :: NonEmpty a -> NonEmpty b -> NonEmpty a

Apply ZipList

Methods

(<.>) :: ZipList (a -> b) -> ZipList a -> ZipList b

(.>) :: ZipList a -> ZipList b -> ZipList b

(<.) :: ZipList a -> ZipList b -> ZipList a

Apply Tree

Methods

(<.>) :: Tree (a -> b) -> Tree a -> Tree b

(.>) :: Tree a -> Tree b -> Tree b

(<.) :: Tree a -> Tree b -> Tree a

Apply Seq

Methods

(<.>) :: Seq (a -> b) -> Seq a -> Seq b

(.>) :: Seq a -> Seq b -> Seq b

(<.) :: Seq a -> Seq b -> Seq a

Apply IntMap

An IntMap is not Applicative, but it is an instance of Apply

Methods

(<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b

(.>) :: IntMap a -> IntMap b -> IntMap b

(<.) :: IntMap a -> IntMap b -> IntMap a

Apply ((->) m)

Methods

(<.>) :: (m -> a -> b) -> (m -> a) -> m -> b

(.>) :: (m -> a) -> (m -> b) -> m -> b

(<.) :: (m -> a) -> (m -> b) -> m -> a

Apply (Either a)

Methods

(<.>) :: Either a (a -> b) -> Either a a -> Either a b

(.>) :: Either a a -> Either a b -> Either a b

(<.) :: Either a a -> Either a b -> Either a a

Semigroup m => Apply ((,) m)

Methods

(<.>) :: (m, a -> b) -> (m, a) -> (m, b)

(.>) :: (m, a) -> (m, b) -> (m, b)

(<.) :: (m, a) -> (m, b) -> (m, a)

Monad m => Apply (WrappedMonad m)

Methods

(<.>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b

(.>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b

(<.) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a

Ord k => Apply (Map k)

A Map is not Applicative, but it is an instance of Apply

Methods

(<.>) :: Map k (a -> b) -> Map k a -> Map k b

(.>) :: Map k a -> Map k b -> Map k b

(<.) :: Map k a -> Map k b -> Map k a

Apply f => Apply (Lift f)

Methods

(<.>) :: Lift f (a -> b) -> Lift f a -> Lift f b

(.>) :: Lift f a -> Lift f b -> Lift f b

(<.) :: Lift f a -> Lift f b -> Lift f a

(Functor m, Monad m) => Apply (MaybeT m)

Methods

(<.>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b

(.>) :: MaybeT m a -> MaybeT m b -> MaybeT m b

(<.) :: MaybeT m a -> MaybeT m b -> MaybeT m a

Apply m => Apply (ListT m)

Methods

(<.>) :: ListT m (a -> b) -> ListT m a -> ListT m b

(.>) :: ListT m a -> ListT m b -> ListT m b

(<.) :: ListT m a -> ListT m b -> ListT m a

Apply f => Apply (MaybeApply f)

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

Applicative f => Apply (WrappedApplicative f)

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Arrow a => Apply (WrappedArrow a b)

Methods

(<.>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b

(.>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b

(<.) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a

Semigroup m => Apply (Const * m)

Methods

(<.>) :: Const * m (a -> b) -> Const * m a -> Const * m b

(.>) :: Const * m a -> Const * m b -> Const * m b

(<.) :: Const * m a -> Const * m b -> Const * m a

Biapply p => Apply (Join * p)

Methods

(<.>) :: Join * p (a -> b) -> Join * p a -> Join * p b

(.>) :: Join * p a -> Join * p b -> Join * p b

(<.) :: Join * p a -> Join * p b -> Join * p a

Apply w => Apply (TracedT m w)

Methods

(<.>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b

(.>) :: TracedT m w a -> TracedT m w b -> TracedT m w b

(<.) :: TracedT m w a -> TracedT m w b -> TracedT m w a

(Apply w, Semigroup s) => Apply (StoreT s w)

Methods

(<.>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b

(.>) :: StoreT s w a -> StoreT s w b -> StoreT s w b

(<.) :: StoreT s w a -> StoreT s w b -> StoreT s w a

(Semigroup e, Apply w) => Apply (EnvT e w)

Methods

(<.>) :: EnvT e w (a -> b) -> EnvT e w a -> EnvT e w b

(.>) :: EnvT e w a -> EnvT e w b -> EnvT e w b

(<.) :: EnvT e w a -> EnvT e w b -> EnvT e w a

Apply (Cokleisli w a)

Methods

(<.>) :: Cokleisli w a (a -> b) -> Cokleisli w a a -> Cokleisli w a b

(.>) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a b

(<.) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a a

Apply w => Apply (IdentityT * w)

Methods

(<.>) :: IdentityT * w (a -> b) -> IdentityT * w a -> IdentityT * w b

(.>) :: IdentityT * w a -> IdentityT * w b -> IdentityT * w b

(<.) :: IdentityT * w a -> IdentityT * w b -> IdentityT * w a

Apply f => Apply (Reverse * f)

Methods

(<.>) :: Reverse * f (a -> b) -> Reverse * f a -> Reverse * f b

(.>) :: Reverse * f a -> Reverse * f b -> Reverse * f b

(<.) :: Reverse * f a -> Reverse * f b -> Reverse * f a

Apply f => Apply (Backwards * f)

Methods

(<.>) :: Backwards * f (a -> b) -> Backwards * f a -> Backwards * f b

(.>) :: Backwards * f a -> Backwards * f b -> Backwards * f b

(<.) :: Backwards * f a -> Backwards * f b -> Backwards * f a

(Apply m, Semigroup w) => Apply (WriterT w m)

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

(Apply m, Semigroup w) => Apply (WriterT w m)

Methods

(<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a

Bind m => Apply (StateT s m)

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(.>) :: StateT s m a -> StateT s m b -> StateT s m b

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

Bind m => Apply (StateT s m)

Methods

(<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(.>) :: StateT s m a -> StateT s m b -> StateT s m b

(<.) :: StateT s m a -> StateT s m b -> StateT s m a

(Functor m, Monad m) => Apply (ErrorT e m)

Methods

(<.>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b

(.>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b

(<.) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a

(Functor m, Monad m) => Apply (ExceptT e m)

Methods

(<.>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b

(.>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b

(<.) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a

Semigroup f => Apply (Constant * f)

Methods

(<.>) :: Constant * f (a -> b) -> Constant * f a -> Constant * f b

(.>) :: Constant * f a -> Constant * f b -> Constant * f b

(<.) :: Constant * f a -> Constant * f b -> Constant * f a

Apply f => Apply (Static f a)

Methods

(<.>) :: Static f a (a -> b) -> Static f a a -> Static f a b

(.>) :: Static f a a -> Static f a b -> Static f a b

(<.) :: Static f a a -> Static f a b -> Static f a a

(Apply f, Apply g) => Apply (Product * f g)

Methods

(<.>) :: Product * f g (a -> b) -> Product * f g a -> Product * f g b

(.>) :: Product * f g a -> Product * f g b -> Product * f g b

(<.) :: Product * f g a -> Product * f g b -> Product * f g a

Apply m => Apply (ReaderT * e m)

Methods

(<.>) :: ReaderT * e m (a -> b) -> ReaderT * e m a -> ReaderT * e m b

(.>) :: ReaderT * e m a -> ReaderT * e m b -> ReaderT * e m b

(<.) :: ReaderT * e m a -> ReaderT * e m b -> ReaderT * e m a

Apply (ContT * r m)

Methods

(<.>) :: ContT * r m (a -> b) -> ContT * r m a -> ContT * r m b

(.>) :: ContT * r m a -> ContT * r m b -> ContT * r m b

(<.) :: ContT * r m a -> ContT * r m b -> ContT * r m a

(Apply f, Apply g) => Apply (Compose * * f g)

Methods

(<.>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b

(.>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b

(<.) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g a

(Bind m, Semigroup w) => Apply (RWST r w s m)

Methods

(<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

(Bind m, Semigroup w) => Apply (RWST r w s m)

Methods

(<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

(<..>) :: Apply w => w a -> w (a -> b) -> w b infixl 4

A variant of <.> with the arguments reversed.

liftF2 :: Apply w => (a -> b -> c) -> w a -> w b -> w c

Lift a binary function into a comonad with zipping

liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d

Lift a ternary function into a comonad with zipping

Wrappers

newtype WrappedApplicative f a

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative

Fields

• unwrapApplicative :: f a

Instances

Functor f => Functor (WrappedApplicative f)

Methods

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

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

Applicative f => Applicative (WrappedApplicative f)

Methods

pure :: a -> WrappedApplicative f a

(<*>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(*>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Alternative f => Alternative (WrappedApplicative f)

Methods

empty :: WrappedApplicative f a

(<|>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: WrappedApplicative f a -> WrappedApplicative f [a]

many :: WrappedApplicative f a -> WrappedApplicative f [a]

Applicative f => Apply (WrappedApplicative f)

Methods

(<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Alternative f => Alt (WrappedApplicative f)

Methods

(<!>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a

some :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

many :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a]

Alternative f => Plus (WrappedApplicative f)

Methods

zero :: WrappedApplicative f a

newtype MaybeApply f a

Transform a Apply into an Applicative by adding a unit.

Constructors

MaybeApply

Fields

• runMaybeApply :: Either (f a) a

Instances

Functor f => Functor (MaybeApply f)

Methods

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

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

Apply f => Applicative (MaybeApply f)

Methods

pure :: a -> MaybeApply f a

(<*>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(*>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

Comonad f => Comonad (MaybeApply f)

Methods

extract :: MaybeApply f a -> a

duplicate :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extend :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

Extend f => Extend (MaybeApply f)

Methods

duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a)

extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b

Apply f => Apply (MaybeApply f)

Methods

(<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

Bindable functors

class Apply m => Bind m where

A Monad sans return.

Minimal definition: Either join or >>-

If defining both, then the following laws (the default definitions) must hold:

join = (>>- id)
m >>- f = join (fmap f m)

Laws:

induced definition of <.>: f <.> x = f >>- (<$> x)

Finally, there are two associativity conditions:

associativity of (>>-):    (m >>- f) >>- g == m >>- (\x -> f x >>- g)
associativity of join:     join . join = join . fmap join

These can both be seen as special cases of the constraint that

associativity of (->-): (f ->- g) ->- h = f ->- (g ->- h)

Minimal complete definition

(>>-) | join

Methods

(>>-) :: m a -> (a -> m b) -> m b infixl 1

join :: m (m a) -> m a

Instances

Bind []

Methods

(>>-) :: [a] -> (a -> [b]) -> [b]

join :: [[a]] -> [a]

Bind Maybe

Methods

(>>-) :: Maybe a -> (a -> Maybe b) -> Maybe b

join :: Maybe (Maybe a) -> Maybe a

Bind IO

Methods

(>>-) :: IO a -> (a -> IO b) -> IO b

join :: IO (IO a) -> IO a

Bind Identity

Methods

(>>-) :: Identity a -> (a -> Identity b) -> Identity b

join :: Identity (Identity a) -> Identity a

Bind Option

Methods

(>>-) :: Option a -> (a -> Option b) -> Option b

join :: Option (Option a) -> Option a

Bind NonEmpty

Methods

(>>-) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b

join :: NonEmpty (NonEmpty a) -> NonEmpty a

Bind Tree

Methods

(>>-) :: Tree a -> (a -> Tree b) -> Tree b

join :: Tree (Tree a) -> Tree a

Bind Seq

Methods

(>>-) :: Seq a -> (a -> Seq b) -> Seq b

join :: Seq (Seq a) -> Seq a

Bind IntMap

An IntMap is not a Monad, but it is an instance of Bind

Methods

(>>-) :: IntMap a -> (a -> IntMap b) -> IntMap b

join :: IntMap (IntMap a) -> IntMap a

Bind ((->) m)

Methods

(>>-) :: (m -> a) -> (a -> m -> b) -> m -> b

join :: (m -> m -> a) -> m -> a

Bind (Either a)

Methods

(>>-) :: Either a a -> (a -> Either a b) -> Either a b

join :: Either a (Either a a) -> Either a a

Semigroup m => Bind ((,) m)

Methods

(>>-) :: (m, a) -> (a -> (m, b)) -> (m, b)

join :: (m, (m, a)) -> (m, a)

Monad m => Bind (WrappedMonad m)

Methods

(>>-) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b

join :: WrappedMonad m (WrappedMonad m a) -> WrappedMonad m a

Ord k => Bind (Map k)

A Map is not a Monad, but it is an instance of Bind

Methods

(>>-) :: Map k a -> (a -> Map k b) -> Map k b

join :: Map k (Map k a) -> Map k a

(Functor m, Monad m) => Bind (MaybeT m)

Methods

(>>-) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b

join :: MaybeT m (MaybeT m a) -> MaybeT m a

(Apply m, Monad m) => Bind (ListT m)

Methods

(>>-) :: ListT m a -> (a -> ListT m b) -> ListT m b

join :: ListT m (ListT m a) -> ListT m a

Bind m => Bind (IdentityT * m)

Methods

(>>-) :: IdentityT * m a -> (a -> IdentityT * m b) -> IdentityT * m b

join :: IdentityT * m (IdentityT * m a) -> IdentityT * m a

(Bind m, Semigroup w) => Bind (WriterT w m)

Methods

(>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b

join :: WriterT w m (WriterT w m a) -> WriterT w m a

(Bind m, Semigroup w) => Bind (WriterT w m)

Methods

(>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b

join :: WriterT w m (WriterT w m a) -> WriterT w m a

Bind m => Bind (StateT s m)

Methods

(>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b

join :: StateT s m (StateT s m a) -> StateT s m a

Bind m => Bind (StateT s m)

Methods

(>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b

join :: StateT s m (StateT s m a) -> StateT s m a

(Functor m, Monad m) => Bind (ErrorT e m)

Methods

(>>-) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b

join :: ErrorT e m (ErrorT e m a) -> ErrorT e m a

(Functor m, Monad m) => Bind (ExceptT e m)

Methods

(>>-) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b

join :: ExceptT e m (ExceptT e m a) -> ExceptT e m a

(Bind f, Bind g) => Bind (Product * f g)

Methods

(>>-) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b

join :: Product * f g (Product * f g a) -> Product * f g a

Bind m => Bind (ReaderT * e m)

Methods

(>>-) :: ReaderT * e m a -> (a -> ReaderT * e m b) -> ReaderT * e m b

join :: ReaderT * e m (ReaderT * e m a) -> ReaderT * e m a

Bind (ContT * r m)

Methods

(>>-) :: ContT * r m a -> (a -> ContT * r m b) -> ContT * r m b

join :: ContT * r m (ContT * r m a) -> ContT * r m a

(Bind m, Semigroup w) => Bind (RWST r w s m)

Methods

(>>-) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b

join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a

(Bind m, Semigroup w) => Bind (RWST r w s m)

Methods

(>>-) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b

join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a

(-<<) :: Bind m => (a -> m b) -> m a -> m b infixr 1

(-<-) :: Bind m => (b -> m c) -> (a -> m b) -> a -> m c infixr 1

(->-) :: Bind m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1

apDefault :: Bind f => f (a -> b) -> f a -> f b

returning :: Functor f => f a -> (a -> b) -> f b