Data.Functor.Apply

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

Methods

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

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

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

Functor []

Since: 2.1

Methods

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

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

Functor Maybe

Since: 2.1

Methods

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

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

Functor IO

Since: 2.1

Methods

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

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

Functor Par1

Methods

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

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

Functor Q

Methods

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

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

Functor Complex

Methods

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

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

Functor Min

Since: 4.9.0.0

Methods

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

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

Functor Max

Since: 4.9.0.0

Methods

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

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

Functor First

Since: 4.9.0.0

Methods

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

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

Functor Last

Since: 4.9.0.0

Methods

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

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

Functor Option

Since: 4.9.0.0

Methods

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

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

Functor NonEmpty

Since: 4.9.0.0

Methods

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

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

Functor ZipList

Methods

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

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

Functor Identity

Since: 4.8.0.0

Methods

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

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

Functor Handler

Since: 4.6.0.0

Methods

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

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

Functor STM

Since: 4.3.0.0

Methods

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

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

Functor Dual

Since: 4.8.0.0

Methods

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

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

Functor Sum

Since: 4.8.0.0

Methods

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

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

Functor Product

Since: 4.8.0.0

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 IntMap

Methods

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

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

Methods

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

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

Methods

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

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

Functor AnnotDetails

Methods

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

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

Functor Span

Methods

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

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

Functor (Either a)

Since: 3.0

Methods

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

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

Functor (V1 *)

Methods

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

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

Functor (U1 *)

Since: 4.9.0.0

Methods

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

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

Functor ((,) a)

Since: 2.1

Methods

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

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

Functor (Array i)

Since: 2.1

Methods

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

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

Functor (Arg a)

Since: 4.9.0.0

Methods

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

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

Monad m => Functor (WrappedMonad m)

Since: 2.1

Methods

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

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

Arrow a => Functor (ArrowMonad a)

Since: 4.6.0.0

Methods

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

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

Functor (Proxy *)

Since: 4.7.0.0

Methods

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

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

Methods

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

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

Arrow a => Functor (WrappedArrow a b)

Since: 2.1

Methods

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

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

Functor (Const * m)

Since: 2.1

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

(Applicative f, Monad f) => Functor (WhenMissing f x)

Methods

fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b

(<$) :: a -> WhenMissing f x b -> WhenMissing f x 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 (Constant * a)

Methods

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

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

Derived instance.

Methods

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

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

Since: 2.1

Methods

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

(<$) :: a -> (LiftedRep -> LiftedRep) r b -> (LiftedRep -> LiftedRep) r 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 g, Functor f) => Functor ((:+:) * f g)

Methods

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

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

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

Since: 4.9.0.0

Methods

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

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

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

Since: 4.9.0.0

Methods

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

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

Functor f => Functor (WhenMatched f x y)

Methods

fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b

(<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a

(Applicative f, Monad f) => Functor (WhenMissing f k x)

Methods

fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b

(<$) :: a -> WhenMissing f k x b -> WhenMissing f k x 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 (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 g, Functor f) => 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 (Compose * * f g)

Since: 4.9.0.0

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 f => Functor (WhenMatched f k x y)

Methods

fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b

(<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y 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

Apply - a strong lax semimonoidal endofunctor

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

(<.>) | liftF2

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

liftF2 :: (a -> b -> c) -> f a -> f b -> f c

Lift a binary function into a comonad with zipping

Instances

Apply []

Methods

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

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

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

liftF2 :: (a -> b -> c) -> [a] -> [b] -> [c]

Apply Maybe

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

Apply IO

Methods

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

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

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

liftF2 :: (a -> b -> c) -> IO a -> IO b -> IO c

Apply Q

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Q a -> Q b -> Q c

Apply Complex

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c

Apply Option

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Option a -> Option b -> Option c

Apply NonEmpty

Methods

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

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

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

liftF2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

Apply ZipList

Methods

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

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

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

liftF2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

Apply Identity

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c

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

liftF2 :: (a -> b -> c) -> IntMap a -> IntMap b -> IntMap c

Apply Tree

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Tree a -> Tree b -> Tree c

Apply Seq

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Seq a -> Seq b -> Seq c

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

liftF2 :: (a -> b -> c) -> Either a a -> Either a b -> Either a c

Semigroup m => Apply ((,) m)

Methods

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

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

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

liftF2 :: (a -> b -> c) -> (m, a) -> (m, b) -> (m, c)

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

liftF2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c

Apply (Proxy *)

Methods

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

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

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

liftF2 :: (a -> b -> c) -> Proxy * a -> Proxy * b -> Proxy * c

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

liftF2 :: (a -> b -> c) -> Map k a -> Map k b -> Map k c

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

liftF2 :: (a -> b -> c) -> Lift f a -> Lift f b -> Lift f c

(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

liftF2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c

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

liftF2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c

(Hashable k, Eq k) => Apply (HashMap k)

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

Methods

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

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

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

liftF2 :: (a -> b -> c) -> HashMap k a -> HashMap k b -> HashMap k c

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

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

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

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

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

liftF2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c

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

liftF2 :: (a -> b -> c) -> Const * m a -> Const * m b -> Const * m c

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

liftF2 :: (a -> b -> c) -> Join * p a -> Join * p b -> Join * p c

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

liftF2 :: (a -> b -> c) -> TracedT m w a -> TracedT m w b -> TracedT m w c

(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

liftF2 :: (a -> b -> c) -> StoreT s w a -> StoreT s w b -> StoreT s w c

(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

liftF2 :: (a -> b -> c) -> EnvT e w a -> EnvT e w b -> EnvT e w c

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

liftF2 :: (a -> b -> c) -> Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a c

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

liftF2 :: (a -> b -> c) -> IdentityT * w a -> IdentityT * w b -> IdentityT * w c

Apply (Tagged * a)

Methods

(<.>) :: Tagged * a (a -> b) -> Tagged * a a -> Tagged * a b

(.>) :: Tagged * a a -> Tagged * a b -> Tagged * a b

(<.) :: Tagged * a a -> Tagged * a b -> Tagged * a a

liftF2 :: (a -> b -> c) -> Tagged * a a -> Tagged * a b -> Tagged * a c

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

liftF2 :: (a -> b -> c) -> Reverse * f a -> Reverse * f b -> Reverse * f c

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

liftF2 :: (a -> b -> c) -> Constant * f a -> Constant * f b -> Constant * f c

(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

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

(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

liftF2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c

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

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

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

liftF2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

(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

liftF2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c

(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

liftF2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c

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

liftF2 :: (a -> b -> c) -> Backwards * f a -> Backwards * f b -> Backwards * f c

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

liftF2 :: (a -> b -> c) -> Static f a a -> Static f a b -> Static f a c

Apply ((->) LiftedRep LiftedRep m)

Methods

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

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

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

liftF2 :: (a -> b -> c) -> (LiftedRep -> LiftedRep) m a -> (LiftedRep -> LiftedRep) m b -> (LiftedRep -> LiftedRep) m c

(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

liftF2 :: (a -> b -> c) -> Product * f g a -> Product * f g b -> Product * f g c

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

liftF2 :: (a -> b -> c) -> ReaderT * e m a -> ReaderT * e m b -> ReaderT * e m c

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

liftF2 :: (a -> b -> c) -> ContT * r m a -> ContT * r m b -> ContT * r m c

(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

liftF2 :: (a -> b -> c) -> Compose * * f g a -> Compose * * f g b -> Compose * * f g c

(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

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

(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

liftF2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c

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

A variant of <.> with the arguments reversed.

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

liftA2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

(*>) :: 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

liftF2 :: (a -> b -> c) -> WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f c

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

liftA2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c

(*>) :: 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

liftF2 :: (a -> b -> c) -> MaybeApply f a -> MaybeApply f b -> MaybeApply f c