| 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 | Trustworthy |
| Language | Haskell2010 |
Data.Functor.Apply
Description
Synopsis
- class Functor (f :: Type -> Type) where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- ($>) :: Functor f => f a -> b -> f b
- class Functor f => Apply f where
- (<..>) :: Apply w => w a -> w (a -> b) -> w b
- liftF3 :: Apply w => (a -> b -> c -> d) -> w a -> w b -> w c -> w d
- newtype WrappedApplicative f a = WrapApplicative {
- unwrapApplicative :: f a
- newtype MaybeApply f a = MaybeApply {
- runMaybeApply :: Either (f a) a
- (<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b
- (<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b
Functors
class Functor (f :: Type -> Type) where Source #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
See https://www.schoolofhaskell.com/user/edwardk/snippets/fmap or
https://github.com/quchen/articles/blob/master/second_functor_law.md
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
fmap is used to apply a function of type (a -> b) to a value of type f a,
where f is a functor, to produce a value of type f b.
Note that for any type constructor with more than one parameter (e.g., Either),
only the last type parameter can be modified with fmap (e.g., b in `Either a b`).
Some type constructors with two parameters or more have a Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither Int String using show:
>>>fmap show (Left 17)Left 17>>>fmap show (Right 17)Right "17"
Double each element of a list:
>>>fmap (*2) [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>fmap even (2,2)(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance
is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over
with fmap).
It explains why fmap can be used with tuples containing values of different types as in the
following example:
>>>fmap even ("hello", 1.0, 4)("hello",1.0,True)
Instances
| Functor ZipList | Since: base-2.1 |
| Functor Handler | Since: base-4.6.0.0 |
| Functor Complex | Since: base-4.9.0.0 |
| Functor Identity | Since: base-4.8.0.0 |
| Functor First | Since: base-4.8.0.0 |
| Functor Last | Since: base-4.8.0.0 |
| Functor Down | Since: base-4.11.0.0 |
| Functor First | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Functor Par1 | Since: base-4.9.0.0 |
| Functor P | Since: base-4.8.0.0 |
| Functor ReadP | Since: base-2.1 |
| Functor IntMap | |
| Functor Digit | |
| Functor Elem | |
| Functor FingerTree | |
Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b Source # (<$) :: a -> FingerTree b -> FingerTree a Source # | |
| Functor Node | |
| Functor Seq | |
| Functor ViewL | |
| Functor ViewR | |
| Functor Tree | |
| Functor IO | Since: base-2.1 |
| Functor AnnotDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b Source # (<$) :: a -> AnnotDetails b -> AnnotDetails a Source # | |
| Functor Doc | |
| Functor Span | |
| Functor Q | |
| Functor TyVarBndr | |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Functor Maybe | Since: base-2.1 |
| Functor Solo | Since: base-4.15 |
| Functor [] | Since: base-2.1 |
| Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (Either a) | Since: base-3.0 |
| Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Functor (Arg a) | Since: base-4.9.0.0 |
| Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (Map k) | |
| Functor f => Functor (MaybeApply f) Source # | |
Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> MaybeApply f a -> MaybeApply f b Source # (<$) :: a -> MaybeApply f b -> MaybeApply f a Source # | |
| Functor f => Functor (WrappedApplicative f) Source # | |
Defined in Data.Functor.Bind.Class Methods fmap :: (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b Source # (<$) :: a -> WrappedApplicative f b -> WrappedApplicative f a Source # | |
| Functor f => Functor (Lift f) | |
| Functor m => Functor (ListT m) | |
| Functor m => Functor (MaybeT m) | |
| Functor (HashMap k) | |
| Functor ((,) a) | Since: base-2.1 |
| Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | Since: base-4.17.0.0 |
Defined in GHC.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (Mag a b) | |
| Bifunctor p => Functor (Join p) | |
| Functor w => Functor (EnvT e w) | |
| Functor w => Functor (StoreT s w) | |
| Functor w => Functor (TracedT m w) | |
| (Applicative f, Monad f) => Functor (WhenMissing f x) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a Source # | |
| Functor f => Functor (Static f a) Source # | |
| Functor (Tagged s) | |
| Functor f => Functor (Backwards f) | Derived instance. |
| Functor m => Functor (AccumT w m) | |
| Functor m => Functor (ErrorT e m) | |
| Functor m => Functor (ExceptT e m) | |
| Functor m => Functor (IdentityT m) | |
| Functor m => Functor (ReaderT r m) | |
| Functor m => Functor (SelectT r m) | |
| Functor m => Functor (StateT s m) | |
| Functor m => Functor (StateT s m) | |
| Functor m => Functor (WriterT w m) | |
| Functor m => Functor (WriterT w m) | |
| Functor m => Functor (WriterT w m) | |
| Functor (Constant a :: Type -> Type) | |
| Functor f => Functor (Reverse f) | Derived instance. |
| Functor ((,,) a b) | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (Cokleisli w a) | |
| Functor f => Functor (WhenMatched f x y) | Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a Source # | |
| (Applicative f, Monad f) => Functor (WhenMissing f k x) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a Source # | |
| Functor (ContT r m) | |
| Functor ((,,,) a b c) | Since: base-4.14.0.0 |
| Functor ((->) r) | Since: base-2.1 |
| (Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
| Functor (Clown f a :: Type -> Type) | |
| Bifunctor p => Functor (Flip p a) | |
| Functor g => Functor (Joker g a) | |
| Bifunctor p => Functor (WrappedBifunctor p a) | |
Defined in Data.Bifunctor.Wrapped Methods fmap :: (a0 -> b) -> WrappedBifunctor p a a0 -> WrappedBifunctor p a b Source # (<$) :: a0 -> WrappedBifunctor p a b -> WrappedBifunctor p a a0 Source # | |
| Functor f => Functor (WhenMatched f k x y) | Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # | |
| Functor m => Functor (RWST r w s m) | |
| Functor m => Functor (RWST r w s m) | |
| Functor m => Functor (RWST r w s m) | |
| (Functor (f a), Functor (g a)) => Functor (Product f g a) | |
| (Functor f, Bifunctor p) => Functor (Tannen f p a) | |
| (Bifunctor p, Functor g) => Functor (Biff p f g a) | |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [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 Source #
Flipped version of <$.
Examples
Replace the contents of a Maybe IntString:
>>>Nothing $> "foo"Nothing>>>Just 90210 $> "foo"Just "foo"
Replace the contents of an Either Int IntString, 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) $> "foo"(1,"foo")
Since: base-4.7.0.0
Apply - a strong lax semimonoidal endofunctor
class Functor f => Apply f where Source #
A strong lax semi-monoidal endofunctor.
This is equivalent to an Applicative without pure.
Laws:
(.)<$>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)
Methods
(<.>) :: f (a -> b) -> f a -> f b infixl 4 Source #
(.>) :: f a -> f b -> f b infixl 4 Source #
(<.) :: f a -> f b -> f a infixl 4 Source #
liftF2 :: (a -> b -> c) -> f a -> f b -> f c Source #
Lift a binary function into a comonad with zipping
Instances
(<..>) :: Apply w => w a -> w (a -> b) -> w b infixl 4 Source #
A variant of <.> with the arguments reversed.
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
| |
Instances
newtype MaybeApply f a Source #
Transform an Apply into an Applicative by adding a unit.
Constructors
| MaybeApply | |
Fields
| |
Instances
(<.*>) :: Apply f => f (a -> b) -> MaybeApply f a -> f b infixl 4 Source #
Apply a non-empty container of functions to a possibly-empty-with-unit container of values.
(<*.>) :: Apply f => MaybeApply f (a -> b) -> f a -> f b infixl 4 Source #
Apply a possibly-empty-with-unit container of functions to a non-empty container of values.