Copyright  Conor McBride and Ross Paterson 2005 

License  BSDstyle (see the LICENSE file in the distribution) 
Maintainer  libraries@haskell.org 
Stability  experimental 
Portability  portable 
Safe Haskell  Trustworthy 
Language  Haskell2010 
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. contextfree parsing, or the
Traversable
class.  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)
 asum :: (Foldable t, Alternative f) => t (f a) > f a
Applicative functors
class Functor f => Applicative f where Source #
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:
(<*>
) =liftA2
id
liftA2
f x y = f<$>
x<*>
y
Further, any definition must satisfy the following:
 Identity
pure
id
<*>
v = v Composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w) Homomorphism
pure
f<*>
pure
x =pure
(f x) Interchange
u
<*>
pure
y =pure
($
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
liftA2
p (liftA2
q u v) =liftA2
f u .liftA2
g v
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
Lift a value.
(<*>) :: f (a > b) > f a > f b infixl 4 Source #
Sequential application.
A few functors support an implementation of <*>
that is more
efficient than the default one.
Example
Used in combination with (
, <$>
)(
can be used to build a record.<*>
)
>>>
data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>
produceFoo :: Applicative f => f Foo
>>>
produceBar :: Applicative f => f Bar
>>>
produceBaz :: Applicative f => f Baz
>>>
mkState :: Applicative f => f MyState
>>>
mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
liftA2 :: (a > b > c) > f a > f b > f c Source #
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 <*>
.
This became a typeclass method in 4.10.0.0. Prior to that, it was
a function defined in terms of <*>
and fmap
.
Example
>>>
liftA2 (,) (Just 3) (Just 5)
Just (3,5)
(*>) :: f a > f b > f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe
,
you can chain Maybe computations, with a possible "early return"
in case of Nothing
.
>>>
Just 2 *> Just 3
Just 3
>>>
Nothing *> Just 3
Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>
import Data.Char
>>>
import Text.ParserCombinators.ReadP
>>>
let p = string "my name is " *> munch1 isAlpha <* eof
>>>
readP_to_S p "my name is Simon"
[("Simon","")]
(<*) :: f a > f b > f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Instances
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: base2.1 
Applicative Complex #  Since: base4.9.0.0 
Applicative Identity #  Since: base4.8.0.0 
Defined in Data.Functor.Identity  
Applicative First #  Since: base4.8.0.0 
Applicative Last #  Since: base4.8.0.0 
Applicative Down #  Since: base4.11.0.0 
Applicative First #  Since: base4.9.0.0 
Applicative Last #  Since: base4.9.0.0 
Applicative Max #  Since: base4.9.0.0 
Applicative Min #  Since: base4.9.0.0 
Applicative Dual #  Since: base4.8.0.0 
Applicative Product #  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Applicative Sum #  Since: base4.8.0.0 
Applicative NonEmpty #  Since: base4.9.0.0 
Applicative STM #  Since: base4.8.0.0 
Applicative NoIO #  Since: base4.8.0.0 
Applicative Par1 #  Since: base4.9.0.0 
Applicative ReadP #  Since: base4.6.0.0 
Applicative ReadPrec #  Since: base4.6.0.0 
Defined in Text.ParserCombinators.ReadPrec  
Applicative IO #  Since: base2.1 
Applicative Maybe #  Since: base2.1 
Applicative Solo #  Since: base4.15 
Applicative [] #  Since: base2.1 
Monad m => Applicative (WrappedMonad m) #  Since: base2.1 
Defined in Control.Applicative pure :: a > WrappedMonad m a Source # (<*>) :: WrappedMonad m (a > b) > WrappedMonad m a > WrappedMonad m b Source # liftA2 :: (a > b > c) > WrappedMonad m a > WrappedMonad m b > WrappedMonad m c Source # (*>) :: WrappedMonad m a > WrappedMonad m b > WrappedMonad m b Source # (<*) :: WrappedMonad m a > WrappedMonad m b > WrappedMonad m a Source #  
Arrow a => Applicative (ArrowMonad a) #  Since: base4.6.0.0 
Defined in Control.Arrow pure :: a0 > ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 > b) > ArrowMonad a a0 > ArrowMonad a b Source # liftA2 :: (a0 > b > c) > ArrowMonad a a0 > ArrowMonad a b > ArrowMonad a c Source # (*>) :: ArrowMonad a a0 > ArrowMonad a b > ArrowMonad a b Source # (<*) :: ArrowMonad a a0 > ArrowMonad a b > ArrowMonad a a0 Source #  
Applicative (ST s) #  Since: base2.1 
Applicative (Either e) #  Since: base3.0 
Defined in Data.Either  
Applicative (Proxy :: Type > Type) #  Since: base4.7.0.0 
Applicative (U1 :: Type > Type) #  Since: base4.9.0.0 
Applicative (ST s) #  Since: base4.4.0.0 
Monoid a => Applicative ((,) a) #  For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) Since: base2.1 
Arrow a => Applicative (WrappedArrow a b) #  Since: base2.1 
Defined in Control.Applicative pure :: a0 > WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 > b0) > WrappedArrow a b a0 > WrappedArrow a b b0 Source # liftA2 :: (a0 > b0 > c) > WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b a0 Source #  
Applicative m => Applicative (Kleisli m a) #  Since: base4.14.0.0 
Defined in Control.Arrow pure :: a0 > Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 > b) > Kleisli m a a0 > Kleisli m a b Source # liftA2 :: (a0 > b > c) > Kleisli m a a0 > Kleisli m a b > Kleisli m a c Source # (*>) :: Kleisli m a a0 > Kleisli m a b > Kleisli m a b Source # (<*) :: Kleisli m a a0 > Kleisli m a b > Kleisli m a a0 Source #  
Monoid m => Applicative (Const m :: Type > Type) #  Since: base2.0.1 
Applicative f => Applicative (Ap f) #  Since: base4.12.0.0 
Applicative f => Applicative (Alt f) #  Since: base4.8.0.0 
Applicative f => Applicative (Rec1 f) #  Since: base4.9.0.0 
(Monoid a, Monoid b) => Applicative ((,,) a b) #  Since: base4.14.0.0 
Defined in GHC.Base  
(Applicative f, Applicative g) => Applicative (Product f g) #  Since: base4.9.0.0 
Defined in Data.Functor.Product pure :: a > Product f g a Source # (<*>) :: Product f g (a > b) > Product f g a > Product f g b Source # liftA2 :: (a > b > c) > Product f g a > Product f g b > Product f g c 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 #  
(Applicative f, Applicative g) => Applicative (f :*: g) #  Since: base4.9.0.0 
Defined in GHC.Generics  
Monoid c => Applicative (K1 i c :: Type > Type) #  Since: base4.12.0.0 
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) #  Since: base4.14.0.0 
Defined in GHC.Base pure :: a0 > (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 > b0) > (a, b, c, a0) > (a, b, c, b0) Source # liftA2 :: (a0 > b0 > c0) > (a, b, c, a0) > (a, b, c, b0) > (a, b, c, c0) Source # (*>) :: (a, b, c, a0) > (a, b, c, b0) > (a, b, c, b0) Source # (<*) :: (a, b, c, a0) > (a, b, c, b0) > (a, b, c, a0) Source #  
Applicative ((>) r) #  Since: base2.1 
(Applicative f, Applicative g) => Applicative (Compose f g) #  Since: base4.9.0.0 
Defined in Data.Functor.Compose pure :: a > Compose f g a Source # (<*>) :: Compose f g (a > b) > Compose f g a > Compose f g b Source # liftA2 :: (a > b > c) > Compose f g a > Compose f g b > Compose f g c 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 #  
(Applicative f, Applicative g) => Applicative (f :.: g) #  Since: base4.9.0.0 
Defined in GHC.Generics  
Applicative f => Applicative (M1 i c f) #  Since: base4.9.0.0 
Defined in GHC.Generics 
Alternatives
class Applicative f => Alternative f where Source #
A monoid on applicative functors.
If defined, some
and many
should be the least solutions
of the equations:
The identity of <>
(<>) :: f a > f a > f a infixl 3 Source #
An associative binary operation
One or more.
Zero or more.
Instances
Instances
The Const
functor.
Instances
Generic1 (Const a :: k > Type) #  
Bifoldable (Const :: Type > TYPE LiftedRep > Type) #  Since: base4.10.0.0 
Bifunctor (Const :: Type > Type > Type) #  Since: base4.8.0.0 
Bitraversable (Const :: Type > Type > Type) #  Since: base4.10.0.0 
Defined in Data.Bitraversable bitraverse :: Applicative f => (a > f c) > (b > f d) > Const a b > f (Const c d) Source #  
Eq2 (Const :: Type > Type > Type) #  Since: base4.9.0.0 
Ord2 (Const :: Type > Type > Type) #  Since: base4.9.0.0 
Defined in Data.Functor.Classes  
Read2 (Const :: Type > Type > Type) #  Since: base4.9.0.0 
Defined in Data.Functor.Classes liftReadsPrec2 :: (Int > ReadS a) > ReadS [a] > (Int > ReadS b) > ReadS [b] > Int > ReadS (Const a b) Source # liftReadList2 :: (Int > ReadS a) > ReadS [a] > (Int > ReadS b) > ReadS [b] > ReadS [Const a b] Source # liftReadPrec2 :: ReadPrec a > ReadPrec [a] > ReadPrec b > ReadPrec [b] > ReadPrec (Const a b) Source # liftReadListPrec2 :: ReadPrec a > ReadPrec [a] > ReadPrec b > ReadPrec [b] > ReadPrec [Const a b] Source #  
Show2 (Const :: Type > TYPE LiftedRep > Type) #  Since: base4.9.0.0 
Foldable (Const m :: TYPE LiftedRep > Type) #  Since: base4.7.0.0 
Defined in Data.Functor.Const fold :: Monoid m0 => Const m m0 > m0 Source # foldMap :: Monoid m0 => (a > m0) > Const m a > m0 Source # foldMap' :: Monoid m0 => (a > m0) > Const m a > m0 Source # foldr :: (a > b > b) > b > Const m a > b Source # foldr' :: (a > b > b) > b > Const m a > b Source # foldl :: (b > a > b) > b > Const m a > b Source # foldl' :: (b > a > b) > b > Const m a > b Source # foldr1 :: (a > a > a) > Const m a > a Source # foldl1 :: (a > a > a) > Const m a > a Source # toList :: Const m a > [a] Source # null :: Const m a > Bool Source # length :: Const m a > Int Source # elem :: Eq a => a > Const m a > Bool Source # maximum :: Ord a => Const m a > a Source # minimum :: Ord a => Const m a > a Source #  
Eq a => Eq1 (Const a :: Type > Type) #  Since: base4.9.0.0 
Ord a => Ord1 (Const a :: Type > Type) #  Since: base4.9.0.0 
Defined in Data.Functor.Classes  
Read a => Read1 (Const a :: Type > Type) #  Since: base4.9.0.0 
Defined in Data.Functor.Classes liftReadsPrec :: (Int > ReadS a0) > ReadS [a0] > Int > ReadS (Const a a0) Source # liftReadList :: (Int > ReadS a0) > ReadS [a0] > ReadS [Const a a0] Source # liftReadPrec :: ReadPrec a0 > ReadPrec [a0] > ReadPrec (Const a a0) Source # liftReadListPrec :: ReadPrec a0 > ReadPrec [a0] > ReadPrec [Const a a0] Source #  
Show a => Show1 (Const a :: TYPE LiftedRep > Type) #  Since: base4.9.0.0 
Contravariant (Const a :: Type > Type) #  
Traversable (Const m :: Type > Type) #  Since: base4.7.0.0 
Defined in Data.Traversable  
Monoid m => Applicative (Const m :: Type > Type) #  Since: base2.0.1 
Functor (Const m :: Type > Type) #  Since: base2.1 
(Typeable k, Data a, Typeable b) => Data (Const a b) #  Since: base4.10.0.0 
Defined in Data.Data gfoldl :: (forall d b0. Data d => c (d > b0) > d > c b0) > (forall g. g > c g) > Const a b > c (Const a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 > r) > c r) > (forall r. r > c r) > Constr > c (Const a b) Source # toConstr :: Const a b > Constr Source # dataTypeOf :: Const a b > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Const a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Const a b)) Source # gmapT :: (forall b0. Data b0 => b0 > b0) > Const a b > Const a b Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Const a b > r Source # gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Const a b > r Source # gmapQ :: (forall d. Data d => d > u) > Const a b > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Const a b > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Const a b > m (Const a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Const a b > m (Const a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Const a b > m (Const a b) Source #  
IsString a => IsString (Const a b) #  Since: base4.9.0.0 
Defined in Data.String fromString :: String > Const a b Source #  
Storable a => Storable (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const sizeOf :: Const a b > Int Source # alignment :: Const a b > Int Source # peekElemOff :: Ptr (Const a b) > Int > IO (Const a b) Source # pokeElemOff :: Ptr (Const a b) > Int > Const a b > IO () Source # peekByteOff :: Ptr b0 > Int > IO (Const a b) Source # pokeByteOff :: Ptr b0 > Int > Const a b > IO () Source #  
Monoid a => Monoid (Const a b) #  Since: base4.9.0.0 
Semigroup a => Semigroup (Const a b) #  Since: base4.9.0.0 
Bits a => Bits (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const (.&.) :: Const a b > Const a b > Const a b Source # (..) :: Const a b > Const a b > Const a b Source # xor :: Const a b > Const a b > Const a b Source # complement :: Const a b > Const a b Source # shift :: Const a b > Int > Const a b Source # rotate :: Const a b > Int > Const a b Source # zeroBits :: Const a b Source # bit :: Int > Const a b Source # setBit :: Const a b > Int > Const a b Source # clearBit :: Const a b > Int > Const a b Source # complementBit :: Const a b > Int > Const a b Source # testBit :: Const a b > Int > Bool Source # bitSizeMaybe :: Const a b > Maybe Int Source # bitSize :: Const a b > Int Source # isSigned :: Const a b > Bool Source # shiftL :: Const a b > Int > Const a b Source # unsafeShiftL :: Const a b > Int > Const a b Source # shiftR :: Const a b > Int > Const a b Source # unsafeShiftR :: Const a b > Int > Const a b Source # rotateL :: Const a b > Int > Const a b Source #  
FiniteBits a => FiniteBits (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const finiteBitSize :: Const a b > Int Source # countLeadingZeros :: Const a b > Int Source # countTrailingZeros :: Const a b > Int Source #  
Bounded a => Bounded (Const a b) #  Since: base4.9.0.0 
Enum a => Enum (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const succ :: Const a b > Const a b Source # pred :: Const a b > Const a b Source # toEnum :: Int > Const a b Source # fromEnum :: Const a b > Int Source # enumFrom :: Const a b > [Const a b] Source # enumFromThen :: Const a b > Const a b > [Const a b] Source # enumFromTo :: Const a b > Const a b > [Const a b] Source # enumFromThenTo :: Const a b > Const a b > Const a b > [Const a b] Source #  
Floating a => Floating (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const exp :: Const a b > Const a b Source # log :: Const a b > Const a b Source # sqrt :: Const a b > Const a b Source # (**) :: Const a b > Const a b > Const a b Source # logBase :: Const a b > Const a b > Const a b Source # sin :: Const a b > Const a b Source # cos :: Const a b > Const a b Source # tan :: Const a b > Const a b Source # asin :: Const a b > Const a b Source # acos :: Const a b > Const a b Source # atan :: Const a b > Const a b Source # sinh :: Const a b > Const a b Source # cosh :: Const a b > Const a b Source # tanh :: Const a b > Const a b Source # asinh :: Const a b > Const a b Source # acosh :: Const a b > Const a b Source # atanh :: Const a b > Const a b Source # log1p :: Const a b > Const a b Source # expm1 :: Const a b > Const a b Source #  
RealFloat a => RealFloat (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const floatRadix :: Const a b > Integer Source # floatDigits :: Const a b > Int Source # floatRange :: Const a b > (Int, Int) Source # decodeFloat :: Const a b > (Integer, Int) Source # encodeFloat :: Integer > Int > Const a b Source # exponent :: Const a b > Int Source # significand :: Const a b > Const a b Source # scaleFloat :: Int > Const a b > Const a b Source # isNaN :: Const a b > Bool Source # isInfinite :: Const a b > Bool Source # isDenormalized :: Const a b > Bool Source # isNegativeZero :: Const a b > Bool Source #  
Generic (Const a b) #  
Ix a => Ix (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const  
Num a => Num (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const (+) :: Const a b > Const a b > Const a b Source # () :: Const a b > Const a b > Const a b Source # (*) :: Const a b > Const a b > Const a b Source # negate :: Const a b > Const a b Source # abs :: Const a b > Const a b Source # signum :: Const a b > Const a b Source # fromInteger :: Integer > Const a b Source #  
Read a => Read (Const a b) #  This instance would be equivalent to the derived instances of the
Since: base4.8.0.0 
Fractional a => Fractional (Const a b) #  Since: base4.9.0.0 
Integral a => Integral (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const quot :: Const a b > Const a b > Const a b Source # rem :: Const a b > Const a b > Const a b Source # div :: Const a b > Const a b > Const a b Source # mod :: Const a b > Const a b > Const a b Source # quotRem :: Const a b > Const a b > (Const a b, Const a b) Source # divMod :: Const a b > Const a b > (Const a b, Const a b) Source #  
Real a => Real (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const toRational :: Const a b > Rational Source #  
RealFrac a => RealFrac (Const a b) #  Since: base4.9.0.0 
Show a => Show (Const a b) #  This instance would be equivalent to the derived instances of the
Since: base4.8.0.0 
Eq a => Eq (Const a b) #  Since: base4.9.0.0 
Ord a => Ord (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const  
type Rep1 (Const a :: k > Type) #  Since: base4.9.0.0 
Defined in Data.Functor.Const  
type Rep (Const a b) #  Since: base4.9.0.0 
Defined in Data.Functor.Const 
newtype WrappedMonad m a Source #
WrapMonad  

Instances
newtype WrappedArrow a b c Source #
WrapArrow  

Instances
Generic1 (WrappedArrow a b :: Type > Type) #  
Defined in Control.Applicative type Rep1 (WrappedArrow a b) :: k > Type Source # from1 :: forall (a0 :: k). WrappedArrow a b a0 > Rep1 (WrappedArrow a b) a0 Source # to1 :: forall (a0 :: k). Rep1 (WrappedArrow a b) a0 > WrappedArrow a b a0 Source #  
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) #  Since: base2.1 
Defined in Control.Applicative empty :: WrappedArrow a b a0 Source # (<>) :: WrappedArrow a b a0 > WrappedArrow a b a0 > WrappedArrow a b a0 Source # some :: WrappedArrow a b a0 > WrappedArrow a b [a0] Source # many :: WrappedArrow a b a0 > WrappedArrow a b [a0] Source #  
Arrow a => Applicative (WrappedArrow a b) #  Since: base2.1 
Defined in Control.Applicative pure :: a0 > WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 > b0) > WrappedArrow a b a0 > WrappedArrow a b b0 Source # liftA2 :: (a0 > b0 > c) > WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 > WrappedArrow a b b0 > WrappedArrow a b a0 Source #  
Arrow a => Functor (WrappedArrow a b) #  Since: base2.1 
Defined in Control.Applicative fmap :: (a0 > b0) > WrappedArrow a b a0 > WrappedArrow a b b0 Source # (<$) :: a0 > WrappedArrow a b b0 > WrappedArrow a b a0 Source #  
(Typeable a, Typeable b, Typeable c, Data (a b c)) => Data (WrappedArrow a b c) #  Since: base4.14.0.0 
Defined in Data.Data gfoldl :: (forall d b0. Data d => c0 (d > b0) > d > c0 b0) > (forall g. g > c0 g) > WrappedArrow a b c > c0 (WrappedArrow a b c) Source # gunfold :: (forall b0 r. Data b0 => c0 (b0 > r) > c0 r) > (forall r. r > c0 r) > Constr > c0 (WrappedArrow a b c) Source # toConstr :: WrappedArrow a b c > Constr Source # dataTypeOf :: WrappedArrow a b c > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c0 (t d)) > Maybe (c0 (WrappedArrow a b c)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c0 (t d e)) > Maybe (c0 (WrappedArrow a b c)) Source # gmapT :: (forall b0. Data b0 => b0 > b0) > WrappedArrow a b c > WrappedArrow a b c Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > WrappedArrow a b c > r Source # gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > WrappedArrow a b c > r Source # gmapQ :: (forall d. Data d => d > u) > WrappedArrow a b c > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > WrappedArrow a b c > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > WrappedArrow a b c > m (WrappedArrow a b c) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > WrappedArrow a b c > m (WrappedArrow a b c) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > WrappedArrow a b c > m (WrappedArrow a b c) Source #  
Generic (WrappedArrow a b c) #  
Defined in Control.Applicative from :: WrappedArrow a b c > Rep (WrappedArrow a b c) x Source # to :: Rep (WrappedArrow a b c) x > WrappedArrow a b c Source #  
type Rep1 (WrappedArrow a b :: Type > Type) #  Since: base4.7.0.0 
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: base4.7.0.0 
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.
ZipList  

Instances
Foldable ZipList #  Since: base4.9.0.0 
Defined in Control.Applicative fold :: Monoid m => ZipList m > m Source # foldMap :: Monoid m => (a > m) > ZipList a > m Source # foldMap' :: Monoid m => (a > m) > ZipList a > m Source # foldr :: (a > b > b) > b > ZipList a > b Source # foldr' :: (a > b > b) > b > ZipList a > b Source # foldl :: (b > a > b) > b > ZipList a > b Source # foldl' :: (b > a > b) > b > ZipList a > b Source # foldr1 :: (a > a > a) > ZipList a > a Source # foldl1 :: (a > a > a) > ZipList a > a Source # toList :: ZipList a > [a] Source # null :: ZipList a > Bool Source # length :: ZipList a > Int Source # elem :: Eq a => a > ZipList a > Bool Source # maximum :: Ord a => ZipList a > a Source # minimum :: Ord a => ZipList a > a Source #  
Traversable ZipList #  Since: base4.9.0.0 
Defined in Data.Traversable  
Alternative ZipList #  Since: base4.11.0.0 
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: base2.1 
Functor ZipList #  Since: base2.1 
Generic1 ZipList #  
Data a => Data (ZipList a) #  Since: base4.14.0.0 
Defined in Data.Data gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > ZipList a > c (ZipList a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (ZipList a) Source # toConstr :: ZipList a > Constr Source # dataTypeOf :: ZipList a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (ZipList a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (ZipList a)) Source # gmapT :: (forall b. Data b => b > b) > ZipList a > ZipList a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > ZipList a > r Source # gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > ZipList a > r Source # gmapQ :: (forall d. Data d => d > u) > ZipList a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > ZipList a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > ZipList a > m (ZipList a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > ZipList a > m (ZipList a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > ZipList a > m (ZipList a) Source #  
IsList (ZipList a) #  Since: base4.15.0.0 
Generic (ZipList a) #  
Read a => Read (ZipList a) #  Since: base4.7.0.0 
Show a => Show (ZipList a) #  Since: base4.7.0.0 
Eq a => Eq (ZipList a) #  Since: base4.7.0.0 
Ord a => Ord (ZipList a) #  Since: base4.7.0.0 
Defined in Control.Applicative  
type Rep1 ZipList #  Since: base4.7.0.0 
Defined in Control.Applicative  
type Item (ZipList a) #  
type Rep (ZipList a) #  Since: base4.7.0.0 
Defined in Control.Applicative 
Utility functions
(<$>) :: 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, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing>>>
show <$> Just 3
Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> 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)
(<**>) :: Applicative f => f a > f (a > b) > f b infixl 4 Source #
A variant of <*>
with the arguments reversed.
liftA :: Applicative f => (a > b) > f a > f b Source #
Lift a function to actions.
Equivalent to Functor's fmap
but implemented using only Applicative
's methods:
`liftA f a = pure f * a`
As such this function may be used to implement a Functor
instance from an Applicative
one.
liftA3 :: Applicative f => (a > b > c > d) > f a > f b > f c > f d Source #
Lift a ternary function to actions.
optional :: Alternative f => f a > f (Maybe a) Source #
One or none.
It is useful for modelling any computation that is allowed to fail.
Examples
Using the Alternative
instance of Control.Monad.Except, the following functions:
>>>
import Control.Monad.Except
>>>
canFail = throwError "it failed" :: Except String Int
>>>
final = return 42 :: Except String Int
Can be combined by allowing the first function to fail:
>>>
runExcept $ canFail *> final
Left "it failed">>>
runExcept $ optional canFail *> final
Right 42
asum :: (Foldable t, Alternative f) => t (f a) > f a Source #
The sum of a collection of actions, generalizing concat
.
asum
is just like msum
, but generalised to Alternative
.
Examples
Basic usage:
>>>
asum [Just "Hello", Nothing, Just "World"]
Just "Hello"