| Copyright | Conor McBride and Ross Paterson 2005 |
|---|---|
| License | BSD-style (see the LICENSE file in the distribution) |
| Maintainer | libraries@haskell.org |
| Stability | experimental |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Control.Applicative
Description
This module describes a structure intermediate between a functor and
a monad (technically, a strong lax monoidal functor). Compared with
monads, this interface lacks the full power of the binding operation
>>=, but
- it has more instances.
- it is sufficient for many uses, e.g. context-free parsing, or the
Traversableclass. - instances can perform analysis of computations before they are executed, and thus produce shared optimizations.
This interface was introduced for parsers by Niklas Röjemo, because it admits more sharing than the monadic interface. The names here are mostly based on parsing work by Doaitse Swierstra.
For more details, see Applicative Programming with Effects, by Conor McBride and Ross Paterson.
Synopsis
- class Functor f => Applicative f where
- class Applicative f => Alternative f where
- newtype Const a b = Const {
- getConst :: a
- newtype WrappedMonad m a = WrapMonad {
- unwrapMonad :: m a
- newtype WrappedArrow a b c = WrapArrow {
- unwrapArrow :: a b c
- newtype ZipList a = ZipList {
- getZipList :: [a]
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- (<$) :: Functor f => a -> f b -> f a
- (<**>) :: Applicative f => f a -> f (a -> b) -> f b
- liftA :: Applicative f => (a -> b) -> f a -> f b
- liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
- optional :: Alternative f => f a -> f (Maybe a)
Applicative functors
class Functor f => Applicative f where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- identity
pureid<*>v = v- composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- homomorphism
puref<*>purex =pure(f x)- interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
liftA2 :: (a -> b -> c) -> f a -> f b -> f c #
Lift a binary function to actions.
Some functors support an implementation of liftA2 that is more
efficient than the default one. In particular, if fmap is an
expensive operation, it is likely better to use liftA2 than to
fmap over the structure and then use <*>.
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
| Applicative [] # | Since: base-2.1 |
| Applicative Maybe # | Since: base-2.1 |
| Applicative IO # | Since: base-2.1 |
| Applicative Par1 # | Since: base-4.9.0.0 |
| Applicative NonEmpty # | Since: base-4.9.0.0 |
| Applicative ReadP # | Since: base-4.6.0.0 |
| Applicative ReadPrec # | Since: base-4.6.0.0 |
| Applicative Down # | Since: base-4.11.0.0 |
| Applicative Product # | Since: base-4.8.0.0 |
| Applicative Sum # | Since: base-4.8.0.0 |
| Applicative Dual # | Since: base-4.8.0.0 |
| Applicative Last # | Since: base-4.8.0.0 |
| Applicative First # | Since: base-4.8.0.0 |
| Applicative STM # | Since: base-4.8.0.0 |
| Applicative Identity # | Since: base-4.8.0.0 |
| Applicative ZipList # | f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN
= 'ZipList' (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
| Applicative Option # | Since: base-4.9.0.0 |
| Applicative Last # | Since: base-4.9.0.0 |
| Applicative First # | Since: base-4.9.0.0 |
| Applicative Max # | Since: base-4.9.0.0 |
| Applicative Min # | Since: base-4.9.0.0 |
| Applicative Complex # | Since: base-4.9.0.0 |
| Applicative (Either e) # | Since: base-3.0 |
| Applicative (U1 :: Type -> Type) # | Since: base-4.9.0.0 |
| Monoid a => Applicative ((,) a) # | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Applicative (ST s) # | Since: base-4.4.0.0 |
| Applicative (Proxy :: Type -> Type) # | Since: base-4.7.0.0 |
| Arrow a => Applicative (ArrowMonad a) # | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
| Monad m => Applicative (WrappedMonad m) # | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
| Applicative (ST s) # | Since: base-2.1 |
| Applicative f => Applicative (Rec1 f) # | Since: base-4.9.0.0 |
| Applicative f => Applicative (Alt f) # | Since: base-4.8.0.0 |
| Applicative f => Applicative (Ap f) # | Since: base-4.12.0.0 |
| Monoid m => Applicative (Const m :: Type -> Type) # | Since: base-2.0.1 |
| Arrow a => Applicative (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Applicative ((->) a :: Type -> Type) # | Since: base-2.1 |
| Monoid c => Applicative (K1 i c :: Type -> Type) # | Since: base-4.12.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) # | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Product f g) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
| Applicative f => Applicative (M1 i c f) # | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (f :.: g) # | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Compose f g) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
Alternatives
class Applicative f => Alternative f where #
A monoid on applicative functors.
If defined, some and many should be the least solutions
of the equations:
Methods
The identity of <|>
(<|>) :: f a -> f a -> f a infixl 3 #
An associative binary operation
One or more.
Zero or more.
Instances
Instances
The Const functor.
Instances
| Generic1 (Const a :: k -> Type) # | |
| Show2 (Const :: Type -> Type -> Type) # | Since: base-4.9.0.0 |
| Read2 (Const :: Type -> Type -> Type) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] # | |
| Ord2 (Const :: Type -> Type -> Type) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Eq2 (Const :: Type -> Type -> Type) # | Since: base-4.9.0.0 |
| Bifunctor (Const :: Type -> Type -> Type) # | Since: base-4.8.0.0 |
| Bifoldable (Const :: Type -> Type -> Type) # | Since: base-4.10.0.0 |
| Bitraversable (Const :: Type -> Type -> Type) # | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) # | |
| Functor (Const m :: Type -> Type) # | Since: base-2.1 |
| Monoid m => Applicative (Const m :: Type -> Type) # | Since: base-2.0.1 |
| Foldable (Const m :: Type -> Type) # | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
| Traversable (Const m :: Type -> Type) # | Since: base-4.7.0.0 |
| Show a => Show1 (Const a :: Type -> Type) # | Since: base-4.9.0.0 |
| Read a => Read1 (Const a :: Type -> Type) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] # | |
| Ord a => Ord1 (Const a :: Type -> Type) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Eq a => Eq1 (Const a :: Type -> Type) # | Since: base-4.9.0.0 |
| Contravariant (Const a :: Type -> Type) # | |
| Bounded a => Bounded (Const a b) # | Since: base-4.9.0.0 |
| Enum a => Enum (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods succ :: Const a b -> Const a b # pred :: Const a b -> Const a b # fromEnum :: Const a b -> Int # enumFrom :: Const a b -> [Const a b] # enumFromThen :: Const a b -> Const a b -> [Const a b] # enumFromTo :: Const a b -> Const a b -> [Const a b] # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] # | |
| Eq a => Eq (Const a b) # | Since: base-4.9.0.0 |
| Floating a => Floating (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods exp :: Const a b -> Const a b # log :: Const a b -> Const a b # sqrt :: Const a b -> Const a b # (**) :: Const a b -> Const a b -> Const a b # logBase :: Const a b -> Const a b -> Const a b # sin :: Const a b -> Const a b # cos :: Const a b -> Const a b # tan :: Const a b -> Const a b # asin :: Const a b -> Const a b # acos :: Const a b -> Const a b # atan :: Const a b -> Const a b # sinh :: Const a b -> Const a b # cosh :: Const a b -> Const a b # tanh :: Const a b -> Const a b # asinh :: Const a b -> Const a b # acosh :: Const a b -> Const a b # atanh :: Const a b -> Const a b # log1p :: Const a b -> Const a b # expm1 :: Const a b -> Const a b # | |
| Fractional a => Fractional (Const a b) # | Since: base-4.9.0.0 |
| Integral a => Integral (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # | |
| (Typeable k, Data a, Typeable b) => Data (Const a b) # | Since: base-4.10.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const a b) # toConstr :: Const a b -> Constr # dataTypeOf :: Const a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Const a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Const a b -> Const a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Const a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Const a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const a b -> m (Const a b) # | |
| Num a => Num (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Ord a => Ord (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Read a => Read (Const a b) # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Real a => Real (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # | |
| RealFloat a => RealFloat (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods floatRadix :: Const a b -> Integer # floatDigits :: Const a b -> Int # floatRange :: Const a b -> (Int, Int) # decodeFloat :: Const a b -> (Integer, Int) # encodeFloat :: Integer -> Int -> Const a b # exponent :: Const a b -> Int # significand :: Const a b -> Const a b # scaleFloat :: Int -> Const a b -> Const a b # isInfinite :: Const a b -> Bool # isDenormalized :: Const a b -> Bool # isNegativeZero :: Const a b -> Bool # | |
| RealFrac a => RealFrac (Const a b) # | Since: base-4.9.0.0 |
| Show a => Show (Const a b) # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Ix a => Ix (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int | |
| IsString a => IsString (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.String Methods fromString :: String -> Const a b # | |
| Generic (Const a b) # | |
| Semigroup a => Semigroup (Const a b) # | Since: base-4.9.0.0 |
| Monoid a => Monoid (Const a b) # | Since: base-4.9.0.0 |
| FiniteBits a => FiniteBits (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods finiteBitSize :: Const a b -> Int # countLeadingZeros :: Const a b -> Int # countTrailingZeros :: Const a b -> Int # | |
| Bits a => Bits (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods (.&.) :: Const a b -> Const a b -> Const a b # (.|.) :: Const a b -> Const a b -> Const a b # xor :: Const a b -> Const a b -> Const a b # complement :: Const a b -> Const a b # shift :: Const a b -> Int -> Const a b # rotate :: Const a b -> Int -> Const a b # setBit :: Const a b -> Int -> Const a b # clearBit :: Const a b -> Int -> Const a b # complementBit :: Const a b -> Int -> Const a b # testBit :: Const a b -> Int -> Bool # bitSizeMaybe :: Const a b -> Maybe Int # isSigned :: Const a b -> Bool # shiftL :: Const a b -> Int -> Const a b # unsafeShiftL :: Const a b -> Int -> Const a b # shiftR :: Const a b -> Int -> Const a b # unsafeShiftR :: Const a b -> Int -> Const a b # rotateL :: Const a b -> Int -> Const a b # | |
| Storable a => Storable (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| type Rep1 (Const a :: k -> Type) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| type Rep (Const a b) # | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
newtype WrappedMonad m a #
Constructors
| WrapMonad | |
Fields
| |
Instances
newtype WrappedArrow a b c #
Constructors
| WrapArrow | |
Fields
| |
Instances
| Generic1 (WrappedArrow a b :: Type -> Type) # | |
Defined in Control.Applicative Associated Types type Rep1 (WrappedArrow a b) :: k -> Type # Methods from1 :: WrappedArrow a b a0 -> Rep1 (WrappedArrow a b) a0 # to1 :: Rep1 (WrappedArrow a b) a0 -> WrappedArrow a b a0 # | |
| 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 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Arrow a => Applicative (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) # | Since: base-2.1 |
Defined in Control.Applicative Methods empty :: WrappedArrow a b a0 # (<|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 # some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] # many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] # | |
| Generic (WrappedArrow a b c) # | |
Defined in Control.Applicative Associated Types type Rep (WrappedArrow a b c) :: Type -> Type # Methods from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x # to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c # | |
| type Rep1 (WrappedArrow a b :: Type -> Type) # | Since: base-4.7.0.0 |
Defined in Control.Applicative type Rep1 (WrappedArrow a b :: Type -> Type) = D1 (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 (MetaCons "WrapArrow" PrefixI True) (S1 (MetaSel (Just "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (a b)))) | |
| type Rep (WrappedArrow a b c) # | Since: base-4.7.0.0 |
Defined in Control.Applicative type Rep (WrappedArrow a b c) = D1 (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 (MetaCons "WrapArrow" PrefixI True) (S1 (MetaSel (Just "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a b c)))) | |
Lists, but with an Applicative functor based on zipping.
Constructors
| ZipList | |
Fields
| |
Instances
| Functor ZipList # | Since: base-2.1 |
| Applicative ZipList # | f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN
= 'ZipList' (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
| Foldable ZipList # | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
| Traversable ZipList # | Since: base-4.9.0.0 |
| Alternative ZipList # | Since: base-4.11.0.0 |
| Eq a => Eq (ZipList a) # | Since: base-4.7.0.0 |
| Ord a => Ord (ZipList a) # | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
| Read a => Read (ZipList a) # | Since: base-4.7.0.0 |
| Show a => Show (ZipList a) # | Since: base-4.7.0.0 |
| Generic (ZipList a) # | |
| Generic1 ZipList # | |
| type Rep (ZipList a) # | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
| type Rep1 ZipList # | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
Utility functions
(<$>) :: 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, <$> is function
application lifted over a Functor.
Examples
Convert from a to a Maybe Int using Maybe Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an to an Either Int IntEither IntString using show:
>>>show <$> 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)
(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 #
A variant of <*> with the arguments reversed.
liftA :: Applicative f => (a -> b) -> f a -> f b #
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d #
Lift a ternary function to actions.
optional :: Alternative f => f a -> f (Maybe a) #
One or none.