Copyright	(C) 2011-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Data.Functor.Bind

Contents

Functors
Applyable functors
Wrappers
Bindable functors

Description

Synopsis

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 []
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 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 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 # (<$) :: a -> Seq b -> Seq a #
Functor ViewL
Methods fmap :: (a -> b) -> ViewL a -> ViewL b # (<$) :: a -> ViewL b -> ViewL a #
Functor ViewR
Methods fmap :: (a -> b) -> ViewR a -> ViewR b # (<$) :: a -> ViewR b -> ViewR a #
Functor ((->) r)
Methods fmap :: (a -> b) -> (r -> a) -> r -> b # (<$) :: 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) # (<$) :: a -> (a, b) -> (a, a) #
Functor (StateL s)
Methods fmap :: (a -> b) -> StateL s a -> StateL s b # (<$) :: 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 # (<$) :: a -> K1 i c b -> K1 i c a #
(Functor g, Functor f) => Functor ((:+:) f g)
Methods fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b # (<$) :: a -> (f :+: g) b -> (f :+: g) a #
(Functor g, Functor f) => Functor ((:*:) f g)
Methods fmap :: (a -> b) -> (f :: g) a -> (f :: g) b # (<$) :: a -> (f :: g) b -> (f :: g) a #
(Functor g, Functor f) => Functor ((:.:) f g)
Methods fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b # (<$) :: 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 (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 (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 Source #

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 Source #

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

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

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

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

Instances

Apply [] Source #
Methods (<.>) :: [a -> b] -> [a] -> [b] Source # (.>) :: [a] -> [b] -> [b] Source # (<.) :: [a] -> [b] -> [a] Source #
Apply Maybe Source #
Methods (<.>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source # (.>) :: Maybe a -> Maybe b -> Maybe b Source # (<.) :: Maybe a -> Maybe b -> Maybe a Source #
Apply IO Source #
Methods (<.>) :: IO (a -> b) -> IO a -> IO b Source # (.>) :: IO a -> IO b -> IO b Source # (<.) :: IO a -> IO b -> IO a Source #
Apply Identity Source #
Methods (<.>) :: Identity (a -> b) -> Identity a -> Identity b Source # (.>) :: Identity a -> Identity b -> Identity b Source # (<.) :: Identity a -> Identity b -> Identity a Source #
Apply Option Source #
Methods (<.>) :: Option (a -> b) -> Option a -> Option b Source # (.>) :: Option a -> Option b -> Option b Source # (<.) :: Option a -> Option b -> Option a Source #
Apply NonEmpty Source #
Methods (<.>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # (.>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<.) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Apply ZipList Source #
Methods (<.>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source # (.>) :: ZipList a -> ZipList b -> ZipList b Source # (<.) :: ZipList a -> ZipList b -> ZipList a Source #
Apply IntMap Source #	An IntMap is not `Applicative`, but it is an instance of `Apply`
Methods (<.>) :: IntMap (a -> b) -> IntMap a -> IntMap b Source # (.>) :: IntMap a -> IntMap b -> IntMap b Source # (<.) :: IntMap a -> IntMap b -> IntMap a Source #
Apply Tree Source #
Methods (<.>) :: Tree (a -> b) -> Tree a -> Tree b Source # (.>) :: Tree a -> Tree b -> Tree b Source # (<.) :: Tree a -> Tree b -> Tree a Source #
Apply Seq Source #
Methods (<.>) :: Seq (a -> b) -> Seq a -> Seq b Source # (.>) :: Seq a -> Seq b -> Seq b Source # (<.) :: Seq a -> Seq b -> Seq a Source #
Apply ((->) m) Source #
Methods (<.>) :: (m -> a -> b) -> (m -> a) -> m -> b Source # (.>) :: (m -> a) -> (m -> b) -> m -> b Source # (<.) :: (m -> a) -> (m -> b) -> m -> a Source #
Apply (Either a) Source #
Methods (<.>) :: Either a (a -> b) -> Either a a -> Either a b Source # (.>) :: Either a a -> Either a b -> Either a b Source # (<.) :: Either a a -> Either a b -> Either a a Source #
Semigroup m => Apply ((,) m) Source #
Methods (<.>) :: (m, a -> b) -> (m, a) -> (m, b) Source # (.>) :: (m, a) -> (m, b) -> (m, b) Source # (<.) :: (m, a) -> (m, b) -> (m, a) Source #
Monad m => Apply (WrappedMonad m) Source #
Methods (<.>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (.>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<.) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #
Apply (Proxy *) Source #
Methods (<.>) :: Proxy * (a -> b) -> Proxy * a -> Proxy * b Source # (.>) :: Proxy * a -> Proxy * b -> Proxy * b Source # (<.) :: Proxy * a -> Proxy * b -> Proxy * a Source #
Ord k => Apply (Map k) Source #	A Map is not `Applicative`, but it is an instance of `Apply`
Methods (<.>) :: Map k (a -> b) -> Map k a -> Map k b Source # (.>) :: Map k a -> Map k b -> Map k b Source # (<.) :: Map k a -> Map k b -> Map k a Source #
Apply f => Apply (Lift f) Source #
Methods (<.>) :: Lift f (a -> b) -> Lift f a -> Lift f b Source # (.>) :: Lift f a -> Lift f b -> Lift f b Source # (<.) :: Lift f a -> Lift f b -> Lift f a Source #
(Functor m, Monad m) => Apply (MaybeT m) Source #
Methods (<.>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b Source # (.>) :: MaybeT m a -> MaybeT m b -> MaybeT m b Source # (<.) :: MaybeT m a -> MaybeT m b -> MaybeT m a Source #
Apply m => Apply (ListT m) Source #
Methods (<.>) :: ListT m (a -> b) -> ListT m a -> ListT m b Source # (.>) :: ListT m a -> ListT m b -> ListT m b Source # (<.) :: ListT m a -> ListT m b -> ListT m a Source #
Apply f => Apply (MaybeApply f) Source #
Methods (<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b Source # (.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b Source # (<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a Source #
Applicative f => Apply (WrappedApplicative f) Source #
Methods (<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b Source # (.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b Source # (<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a Source #
Arrow a => Apply (WrappedArrow a b) Source #
Methods (<.>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source # (.>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source # (<.) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source #
Semigroup m => Apply (Const * m) Source #
Methods (<.>) :: Const * m (a -> b) -> Const * m a -> Const * m b Source # (.>) :: Const * m a -> Const * m b -> Const * m b Source # (<.) :: Const * m a -> Const * m b -> Const * m a Source #
Biapply p => Apply (Join * p) Source #
Methods (<.>) :: Join * p (a -> b) -> Join * p a -> Join * p b Source # (.>) :: Join * p a -> Join * p b -> Join * p b Source # (<.) :: Join * p a -> Join * p b -> Join * p a Source #
Apply w => Apply (TracedT m w) Source #
Methods (<.>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b Source # (.>) :: TracedT m w a -> TracedT m w b -> TracedT m w b Source # (<.) :: TracedT m w a -> TracedT m w b -> TracedT m w a Source #
(Apply w, Semigroup s) => Apply (StoreT s w) Source #
Methods (<.>) :: StoreT s w (a -> b) -> StoreT s w a -> StoreT s w b Source # (.>) :: StoreT s w a -> StoreT s w b -> StoreT s w b Source # (<.) :: StoreT s w a -> StoreT s w b -> StoreT s w a Source #
(Semigroup e, Apply w) => Apply (EnvT e w) Source #
Methods (<.>) :: EnvT e w (a -> b) -> EnvT e w a -> EnvT e w b Source # (.>) :: EnvT e w a -> EnvT e w b -> EnvT e w b Source # (<.) :: EnvT e w a -> EnvT e w b -> EnvT e w a Source #
Apply (Cokleisli w a) Source #
Methods (<.>) :: Cokleisli w a (a -> b) -> Cokleisli w a a -> Cokleisli w a b Source # (.>) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a b Source # (<.) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a a Source #
Apply w => Apply (IdentityT * w) Source #
Methods (<.>) :: IdentityT * w (a -> b) -> IdentityT * w a -> IdentityT * w b Source # (.>) :: IdentityT * w a -> IdentityT * w b -> IdentityT * w b Source # (<.) :: IdentityT * w a -> IdentityT * w b -> IdentityT * w a Source #
Apply (Tagged * a) Source #
Methods (<.>) :: Tagged * a (a -> b) -> Tagged * a a -> Tagged * a b Source # (.>) :: Tagged * a a -> Tagged * a b -> Tagged * a b Source # (<.) :: Tagged * a a -> Tagged * a b -> Tagged * a a Source #
Apply f => Apply (Reverse * f) Source #
Methods (<.>) :: Reverse * f (a -> b) -> Reverse * f a -> Reverse * f b Source # (.>) :: Reverse * f a -> Reverse * f b -> Reverse * f b Source # (<.) :: Reverse * f a -> Reverse * f b -> Reverse * f a Source #
Apply f => Apply (Backwards * f) Source #
Methods (<.>) :: Backwards * f (a -> b) -> Backwards * f a -> Backwards * f b Source # (.>) :: Backwards * f a -> Backwards * f b -> Backwards * f b Source # (<.) :: Backwards * f a -> Backwards * f b -> Backwards * f a Source #
(Apply m, Semigroup w) => Apply (WriterT w m) Source #
Methods (<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # (.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source #
(Apply m, Semigroup w) => Apply (WriterT w m) Source #
Methods (<.>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # (.>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<.) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source #
Bind m => Apply (StateT s m) Source #
Methods (<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # (.>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<.) :: StateT s m a -> StateT s m b -> StateT s m a Source #
Bind m => Apply (StateT s m) Source #
Methods (<.>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # (.>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<.) :: StateT s m a -> StateT s m b -> StateT s m a Source #
(Functor m, Monad m) => Apply (ExceptT e m) Source #
Methods (<.>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # (.>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<.) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source #
(Functor m, Monad m) => Apply (ErrorT e m) Source #
Methods (<.>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b Source # (.>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b Source # (<.) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a Source #
Semigroup f => Apply (Constant * f) Source #
Methods (<.>) :: Constant * f (a -> b) -> Constant * f a -> Constant * f b Source # (.>) :: Constant * f a -> Constant * f b -> Constant * f b Source # (<.) :: Constant * f a -> Constant * f b -> Constant * f a Source #
Apply f => Apply (Static f a) Source #
Methods (<.>) :: Static f a (a -> b) -> Static f a a -> Static f a b Source # (.>) :: Static f a a -> Static f a b -> Static f a b Source # (<.) :: Static f a a -> Static f a b -> Static f a a Source #
(Apply f, Apply g) => Apply (Product * f g) Source #
Methods (<.>) :: Product * f g (a -> b) -> Product * f g a -> Product * f g b Source # (.>) :: Product * f g a -> Product * f g b -> Product * f g b Source # (<.) :: Product * f g a -> Product * f g b -> Product * f g a Source #
Apply m => Apply (ReaderT * e m) Source #
Methods (<.>) :: ReaderT * e m (a -> b) -> ReaderT * e m a -> ReaderT * e m b Source # (.>) :: ReaderT * e m a -> ReaderT * e m b -> ReaderT * e m b Source # (<.) :: ReaderT * e m a -> ReaderT * e m b -> ReaderT * e m a Source #
Apply (ContT * r m) Source #
Methods (<.>) :: ContT * r m (a -> b) -> ContT * r m a -> ContT * r m b Source # (.>) :: ContT * r m a -> ContT * r m b -> ContT * r m b Source # (<.) :: ContT * r m a -> ContT * r m b -> ContT * r m a Source #
(Apply f, Apply g) => Apply (Compose * * f g) Source #
Methods (<.>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b Source # (.>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b Source # (<.) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g a Source #
(Bind m, Semigroup w) => Apply (RWST r w s m) Source #
Methods (<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # (.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source #
(Bind m, Semigroup w) => Apply (RWST r w s m) Source #
Methods (<.>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # (.>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<.) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source #

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

A variant of <.> with the arguments reversed.

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

Lift a binary function into a comonad with zipping

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

Lift a ternary function into a comonad with zipping

Wrappers

newtype WrappedApplicative f a Source #

Wrap an Applicative to be used as a member of Apply

Constructors

WrapApplicative
Fields unwrapApplicative :: f a

Instances

Functor f => Functor (WrappedApplicative f) Source #
Methods fmap :: (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b # (<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a #
Applicative f => Applicative (WrappedApplicative f) Source #
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) Source #
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) Source #
Methods (<.>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b Source # (.>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b Source # (<.) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a Source #
Alternative f => Alt (WrappedApplicative f) Source #
Methods (<!>) :: WrappedApplicative f a -> WrappedApplicative f a -> WrappedApplicative f a Source # some :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a] Source # many :: Applicative (WrappedApplicative f) => WrappedApplicative f a -> WrappedApplicative f [a] Source #
Alternative f => Plus (WrappedApplicative f) Source #
Methods zero :: WrappedApplicative f a Source #

newtype MaybeApply f a Source #

Transform a Apply into an Applicative by adding a unit.

Constructors

MaybeApply
Fields runMaybeApply :: Either (f a) a

Instances

Functor f => Functor (MaybeApply f) Source #
Methods fmap :: (a -> b) -> MaybeApply f a -> MaybeApply f b # (<$) :: a -> MaybeApply f b -> MaybeApply f a #
Apply f => Applicative (MaybeApply f) Source #
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) Source #
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) Source #
Methods duplicated :: MaybeApply f a -> MaybeApply f (MaybeApply f a) Source # extended :: (MaybeApply f a -> b) -> MaybeApply f a -> MaybeApply f b Source #
Apply f => Apply (MaybeApply f) Source #
Methods (<.>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b Source # (.>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b Source # (<.) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a Source #

Bindable functors

class Apply m => Bind m where Source #

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 Source #

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

Instances

Bind [] Source #
Methods (>>-) :: [a] -> (a -> [b]) -> [b] Source # join :: [[a]] -> [a] Source #
Bind Maybe Source #
Methods (>>-) :: Maybe a -> (a -> Maybe b) -> Maybe b Source # join :: Maybe (Maybe a) -> Maybe a Source #
Bind IO Source #
Methods (>>-) :: IO a -> (a -> IO b) -> IO b Source # join :: IO (IO a) -> IO a Source #
Bind Identity Source #
Methods (>>-) :: Identity a -> (a -> Identity b) -> Identity b Source # join :: Identity (Identity a) -> Identity a Source #
Bind Option Source #
Methods (>>-) :: Option a -> (a -> Option b) -> Option b Source # join :: Option (Option a) -> Option a Source #
Bind NonEmpty Source #
Methods (>>-) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source # join :: NonEmpty (NonEmpty a) -> NonEmpty a Source #
Bind IntMap Source #	An `IntMap` is not a `Monad`, but it is an instance of `Bind`
Methods (>>-) :: IntMap a -> (a -> IntMap b) -> IntMap b Source # join :: IntMap (IntMap a) -> IntMap a Source #
Bind Tree Source #
Methods (>>-) :: Tree a -> (a -> Tree b) -> Tree b Source # join :: Tree (Tree a) -> Tree a Source #
Bind Seq Source #
Methods (>>-) :: Seq a -> (a -> Seq b) -> Seq b Source # join :: Seq (Seq a) -> Seq a Source #
Bind ((->) m) Source #
Methods (>>-) :: (m -> a) -> (a -> m -> b) -> m -> b Source # join :: (m -> m -> a) -> m -> a Source #
Bind (Either a) Source #
Methods (>>-) :: Either a a -> (a -> Either a b) -> Either a b Source # join :: Either a (Either a a) -> Either a a Source #
Semigroup m => Bind ((,) m) Source #
Methods (>>-) :: (m, a) -> (a -> (m, b)) -> (m, b) Source # join :: (m, (m, a)) -> (m, a) Source #
Monad m => Bind (WrappedMonad m) Source #
Methods (>>-) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # join :: WrappedMonad m (WrappedMonad m a) -> WrappedMonad m a Source #
Bind (Proxy *) Source #
Methods (>>-) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b Source # join :: Proxy * (Proxy * a) -> Proxy * a Source #
Ord k => Bind (Map k) Source #	A `Map` is not a `Monad`, but it is an instance of `Bind`
Methods (>>-) :: Map k a -> (a -> Map k b) -> Map k b Source # join :: Map k (Map k a) -> Map k a Source #
(Functor m, Monad m) => Bind (MaybeT m) Source #
Methods (>>-) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b Source # join :: MaybeT m (MaybeT m a) -> MaybeT m a Source #
(Apply m, Monad m) => Bind (ListT m) Source #
Methods (>>-) :: ListT m a -> (a -> ListT m b) -> ListT m b Source # join :: ListT m (ListT m a) -> ListT m a Source #
Bind m => Bind (IdentityT * m) Source #
Methods (>>-) :: IdentityT * m a -> (a -> IdentityT * m b) -> IdentityT * m b Source # join :: IdentityT * m (IdentityT * m a) -> IdentityT * m a Source #
Bind (Tagged * a) Source #
Methods (>>-) :: Tagged * a a -> (a -> Tagged * a b) -> Tagged * a b Source # join :: Tagged * a (Tagged * a a) -> Tagged * a a Source #
(Bind m, Semigroup w) => Bind (WriterT w m) Source #
Methods (>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b Source # join :: WriterT w m (WriterT w m a) -> WriterT w m a Source #
(Bind m, Semigroup w) => Bind (WriterT w m) Source #
Methods (>>-) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b Source # join :: WriterT w m (WriterT w m a) -> WriterT w m a Source #
Bind m => Bind (StateT s m) Source #
Methods (>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b Source # join :: StateT s m (StateT s m a) -> StateT s m a Source #
Bind m => Bind (StateT s m) Source #
Methods (>>-) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b Source # join :: StateT s m (StateT s m a) -> StateT s m a Source #
(Functor m, Monad m) => Bind (ExceptT e m) Source #
Methods (>>-) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b Source # join :: ExceptT e m (ExceptT e m a) -> ExceptT e m a Source #
(Functor m, Monad m) => Bind (ErrorT e m) Source #
Methods (>>-) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b Source # join :: ErrorT e m (ErrorT e m a) -> ErrorT e m a Source #
(Bind f, Bind g) => Bind (Product * f g) Source #
Methods (>>-) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b Source # join :: Product * f g (Product * f g a) -> Product * f g a Source #
Bind m => Bind (ReaderT * e m) Source #
Methods (>>-) :: ReaderT * e m a -> (a -> ReaderT * e m b) -> ReaderT * e m b Source # join :: ReaderT * e m (ReaderT * e m a) -> ReaderT * e m a Source #
Bind (ContT * r m) Source #
Methods (>>-) :: ContT * r m a -> (a -> ContT * r m b) -> ContT * r m b Source # join :: ContT * r m (ContT * r m a) -> ContT * r m a Source #
(Bind m, Semigroup w) => Bind (RWST r w s m) Source #
Methods (>>-) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b Source # join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a Source #
(Bind m, Semigroup w) => Bind (RWST r w s m) Source #
Methods (>>-) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b Source # join :: RWST r w s m (RWST r w s m a) -> RWST r w s m a Source #

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

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

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

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

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