Papa.Base.Export.Control.Applicative

Documentation

class Functor f => Applicative (f :: * -> *) where

A functor with application, providing operations to

• embed pure expressions (pure), and
• sequence computations and combine their results (<*> and liftA2).

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:

• u *> v = (id <$ u) <*> v

• u <* v = liftA2 const u v

As a consequence of these laws, the Functor instance for f will satisfy

• fmap f x = pure f <*> x

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

• pure = return

• (<*>) = ap

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a

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: 2.1

Methods

pure :: a -> [a]

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

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c]

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

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

Applicative Maybe

Since: 2.1

Methods

pure :: a -> Maybe a

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

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c

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

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

Applicative IO

Since: 2.1

Methods

pure :: a -> IO a

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

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c

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

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

Applicative Min

Since: 4.9.0.0

Methods

pure :: a -> Min a

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

liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c

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

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

Applicative Max

Since: 4.9.0.0

Methods

pure :: a -> Max a

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

liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c

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

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

Applicative First

Since: 4.9.0.0

Methods

pure :: a -> First a

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

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

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

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

Applicative Last

Since: 4.9.0.0

Methods

pure :: a -> Last a

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

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

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

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

Applicative Option

Since: 4.9.0.0

Methods

pure :: a -> Option a

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

liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c

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

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

Applicative NonEmpty

Since: 4.9.0.0

Methods

pure :: a -> NonEmpty a

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

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c

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

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

Applicative ZipList

f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN

ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\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: 2.1

Methods

pure :: a -> ZipList a

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

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

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

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

Applicative Dual

Since: 4.8.0.0

Methods

pure :: a -> Dual a

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

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

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

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

Applicative Sum

Since: 4.8.0.0

Methods

pure :: a -> Sum a

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

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

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

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

Applicative Product

Since: 4.8.0.0

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

(*>) :: Product a -> Product b -> Product b

(<*) :: Product a -> Product b -> Product a

Applicative First

Methods

pure :: a -> First a

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

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

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

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

Applicative Last

Methods

pure :: a -> Last a

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

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

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

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

Applicative (Either e)

Since: 3.0

Methods

pure :: a -> Either e a

(<*>) :: Either e (a -> b) -> Either e a -> Either e b

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c

(*>) :: Either e a -> Either e b -> Either e b

(<*) :: Either e a -> Either e b -> Either e a

Monoid a => Applicative ((,) a)

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: 2.1

Methods

pure :: a -> (a, a)

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

liftA2 :: (a -> b -> c) -> (a, a) -> (a, b) -> (a, c)

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

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

Monad m => Applicative (WrappedMonad m)

Since: 2.1

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

Arrow a => Applicative (WrappedArrow a b)

Since: 2.1

Methods

pure :: a -> WrappedArrow a b a

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

liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c

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

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

Monoid m => Applicative (Const * m)

Since: 2.0.1

Methods

pure :: a -> Const * m a

(<*>) :: Const * m (a -> b) -> Const * m a -> Const * m b

liftA2 :: (a -> b -> c) -> Const * m a -> Const * m b -> Const * m c

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

(<*) :: Const * m a -> Const * m b -> Const * m a

Applicative f => Applicative (Alt * f)

Methods

pure :: a -> Alt * f a

(<*>) :: Alt * f (a -> b) -> Alt * f a -> Alt * f b

liftA2 :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c

(*>) :: Alt * f a -> Alt * f b -> Alt * f b

(<*) :: Alt * f a -> Alt * f b -> Alt * f a

Applicative ((->) LiftedRep LiftedRep a)

Since: 2.1

Methods

pure :: a -> (LiftedRep -> LiftedRep) a a

(<*>) :: (LiftedRep -> LiftedRep) a (a -> b) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b

liftA2 :: (a -> b -> c) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a c

(*>) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a b

(<*) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a a

class Applicative f => Alternative (f :: * -> *) where

A monoid on applicative functors.

If defined, some and many should be the least solutions of the equations:

• some v = (:) <$> v <*> many v

• many v = some v <|> pure []

Minimal complete definition

empty, (<|>)

Methods

empty :: f a

The identity of <|>

(<|>) :: f a -> f a -> f a infixl 3

An associative binary operation

some :: f a -> f [a]

One or more.

many :: f a -> f [a]

Zero or more.

Instances

Alternative []

Since: 2.1

Methods

empty :: [a]

(<|>) :: [a] -> [a] -> [a]

some :: [a] -> [[a]]

many :: [a] -> [[a]]

Alternative Maybe

Since: 2.1

Methods

empty :: Maybe a

(<|>) :: Maybe a -> Maybe a -> Maybe a

some :: Maybe a -> Maybe [a]

many :: Maybe a -> Maybe [a]

Alternative IO

Since: 4.9.0.0

Methods

empty :: IO a

(<|>) :: IO a -> IO a -> IO a

some :: IO a -> IO [a]

many :: IO a -> IO [a]

Alternative Option

Since: 4.9.0.0

Methods

empty :: Option a

(<|>) :: Option a -> Option a -> Option a

some :: Option a -> Option [a]

many :: Option a -> Option [a]

MonadPlus m => Alternative (WrappedMonad m)

Since: 2.1

Methods

empty :: WrappedMonad m a

(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a

some :: WrappedMonad m a -> WrappedMonad m [a]

many :: WrappedMonad m a -> WrappedMonad m [a]

(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Since: 2.1

Methods

empty :: WrappedArrow a b a

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

some :: WrappedArrow a b a -> WrappedArrow a b [a]

many :: WrappedArrow a b a -> WrappedArrow a b [a]

Alternative f => Alternative (Alt * f)

Methods

empty :: Alt * f a

(<|>) :: Alt * f a -> Alt * f a -> Alt * f a

some :: Alt * f a -> Alt * f [a]

many :: Alt * f a -> Alt * f [a]

data Const k a (b :: k) :: forall k. * -> k -> *

The Const functor.

Instances

Generic1 k (Const k a)

Associated Types

type Rep1 (Const k a) (f :: Const k a -> *) :: k -> *

Methods

from1 :: f a -> Rep1 (Const k a) f a

to1 :: Rep1 (Const k a) f a -> f a

Functor (Const * m)

Since: 2.1

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b

(<$) :: a -> Const * m b -> Const * m a

Monoid m => Applicative (Const * m)

Since: 2.0.1

Methods

pure :: a -> Const * m a

(<*>) :: Const * m (a -> b) -> Const * m a -> Const * m b

liftA2 :: (a -> b -> c) -> Const * m a -> Const * m b -> Const * m c

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

(<*) :: Const * m a -> Const * m b -> Const * m a

Foldable (Const * m)

Since: 4.7.0.0

Methods

fold :: Monoid m => Const * m m -> m

foldMap :: Monoid m => (a -> m) -> Const * m a -> m

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

toList :: Const * m a -> [a]

null :: Const * m a -> Bool

length :: Const * m a -> Int

elem :: Eq a => a -> Const * m a -> Bool

maximum :: Ord a => Const * m a -> a

minimum :: Ord a => Const * m a -> a

sum :: Num a => Const * m a -> a

product :: Num a => Const * m a -> a

Traversable (Const * m)

Since: 4.7.0.0

Methods

traverse :: Applicative f => (a -> f b) -> Const * m a -> f (Const * m b)

sequenceA :: Applicative f => Const * m (f a) -> f (Const * m a)

mapM :: Monad m => (a -> m b) -> Const * m a -> m (Const * m b)

sequence :: Monad m => Const * m (m a) -> m (Const * m a)

Bounded a => Bounded (Const k a b)

Methods

minBound :: Const k a b

maxBound :: Const k a b

Enum a => Enum (Const k a b)

Methods

succ :: Const k a b -> Const k a b

pred :: Const k a b -> Const k a b

toEnum :: Int -> Const k a b

fromEnum :: Const k a b -> Int

enumFrom :: Const k a b -> [Const k a b]

enumFromThen :: Const k a b -> Const k a b -> [Const k a b]

enumFromTo :: Const k a b -> Const k a b -> [Const k a b]

enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b]

Eq a => Eq (Const k a b)

Methods

(==) :: Const k a b -> Const k a b -> Bool

(/=) :: Const k a b -> Const k a b -> Bool

Floating a => Floating (Const k a b)

Methods

pi :: Const k a b

exp :: Const k a b -> Const k a b

log :: Const k a b -> Const k a b

sqrt :: Const k a b -> Const k a b

(**) :: Const k a b -> Const k a b -> Const k a b

logBase :: Const k a b -> Const k a b -> Const k a b

sin :: Const k a b -> Const k a b

cos :: Const k a b -> Const k a b

tan :: Const k a b -> Const k a b

asin :: Const k a b -> Const k a b

acos :: Const k a b -> Const k a b

atan :: Const k a b -> Const k a b

sinh :: Const k a b -> Const k a b

cosh :: Const k a b -> Const k a b

tanh :: Const k a b -> Const k a b

asinh :: Const k a b -> Const k a b

acosh :: Const k a b -> Const k a b

atanh :: Const k a b -> Const k a b

log1p :: Const k a b -> Const k a b

expm1 :: Const k a b -> Const k a b

log1pexp :: Const k a b -> Const k a b

log1mexp :: Const k a b -> Const k a b

Fractional a => Fractional (Const k a b)

Methods

(/) :: Const k a b -> Const k a b -> Const k a b

recip :: Const k a b -> Const k a b

fromRational :: Rational -> Const k a b

Integral a => Integral (Const k a b)

Methods

quot :: Const k a b -> Const k a b -> Const k a b

rem :: Const k a b -> Const k a b -> Const k a b

div :: Const k a b -> Const k a b -> Const k a b

mod :: Const k a b -> Const k a b -> Const k a b

quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b)

divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b)

toInteger :: Const k a b -> Integer

Num a => Num (Const k a b)

Methods

(+) :: Const k a b -> Const k a b -> Const k a b

(-) :: Const k a b -> Const k a b -> Const k a b

(*) :: Const k a b -> Const k a b -> Const k a b

negate :: Const k a b -> Const k a b

abs :: Const k a b -> Const k a b

signum :: Const k a b -> Const k a b

fromInteger :: Integer -> Const k a b

Ord a => Ord (Const k a b)

Methods

compare :: Const k a b -> Const k a b -> Ordering

(<) :: Const k a b -> Const k a b -> Bool

(<=) :: Const k a b -> Const k a b -> Bool

(>) :: Const k a b -> Const k a b -> Bool

(>=) :: Const k a b -> Const k a b -> Bool

max :: Const k a b -> Const k a b -> Const k a b

min :: Const k a b -> Const k a b -> Const k a b

Read a => Read (Const k a b)

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Since: 4.8.0.0

Methods

readsPrec :: Int -> ReadS (Const k a b)

readList :: ReadS [Const k a b]

readPrec :: ReadPrec (Const k a b)

readListPrec :: ReadPrec [Const k a b]

Real a => Real (Const k a b)

Methods

toRational :: Const k a b -> Rational

RealFloat a => RealFloat (Const k a b)

Methods

floatRadix :: Const k a b -> Integer

floatDigits :: Const k a b -> Int

floatRange :: Const k a b -> (Int, Int)

decodeFloat :: Const k a b -> (Integer, Int)

encodeFloat :: Integer -> Int -> Const k a b

exponent :: Const k a b -> Int

significand :: Const k a b -> Const k a b

scaleFloat :: Int -> Const k a b -> Const k a b

isNaN :: Const k a b -> Bool

isInfinite :: Const k a b -> Bool

isDenormalized :: Const k a b -> Bool

isNegativeZero :: Const k a b -> Bool

isIEEE :: Const k a b -> Bool

atan2 :: Const k a b -> Const k a b -> Const k a b

RealFrac a => RealFrac (Const k a b)

Methods

properFraction :: Integral b => Const k a b -> (b, Const k a b)

truncate :: Integral b => Const k a b -> b

round :: Integral b => Const k a b -> b

ceiling :: Integral b => Const k a b -> b

floor :: Integral b => Const k a b -> b

Show a => Show (Const k a b)

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Since: 4.8.0.0

Methods

showsPrec :: Int -> Const k a b -> ShowS

show :: Const k a b -> String

showList :: [Const k a b] -> ShowS

Ix a => Ix (Const k a b)

Methods

range :: (Const k a b, Const k a b) -> [Const k a b]

index :: (Const k a b, Const k a b) -> Const k a b -> Int

unsafeIndex :: (Const k a b, Const k a b) -> Const k a b -> Int

inRange :: (Const k a b, Const k a b) -> Const k a b -> Bool

rangeSize :: (Const k a b, Const k a b) -> Int

unsafeRangeSize :: (Const k a b, Const k a b) -> Int

IsString a => IsString (Const * a b)

Since: 4.9.0.0

Methods

fromString :: String -> Const * a b

Generic (Const k a b)

Associated Types

type Rep (Const k a b) :: * -> *

Methods

from :: Const k a b -> Rep (Const k a b) x

to :: Rep (Const k a b) x -> Const k a b

Semigroup a => Semigroup (Const k a b)

Since: 4.9.0.0

Methods

(<>) :: Const k a b -> Const k a b -> Const k a b

sconcat :: NonEmpty (Const k a b) -> Const k a b

stimes :: Integral b => b -> Const k a b -> Const k a b

Monoid a => Monoid (Const k a b)

Methods

mempty :: Const k a b

mappend :: Const k a b -> Const k a b -> Const k a b

mconcat :: [Const k a b] -> Const k a b

Storable a => Storable (Const k a b)

Methods

sizeOf :: Const k a b -> Int

alignment :: Const k a b -> Int

peekElemOff :: Ptr (Const k a b) -> Int -> IO (Const k a b)

pokeElemOff :: Ptr (Const k a b) -> Int -> Const k a b -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Const k a b)

pokeByteOff :: Ptr b -> Int -> Const k a b -> IO ()

peek :: Ptr (Const k a b) -> IO (Const k a b)

poke :: Ptr (Const k a b) -> Const k a b -> IO ()

Bits a => Bits (Const k a b)

Methods

(.&.) :: Const k a b -> Const k a b -> Const k a b

(.|.) :: Const k a b -> Const k a b -> Const k a b

xor :: Const k a b -> Const k a b -> Const k a b

complement :: Const k a b -> Const k a b

shift :: Const k a b -> Int -> Const k a b

rotate :: Const k a b -> Int -> Const k a b

zeroBits :: Const k a b

bit :: Int -> Const k a b

setBit :: Const k a b -> Int -> Const k a b

clearBit :: Const k a b -> Int -> Const k a b

complementBit :: Const k a b -> Int -> Const k a b

testBit :: Const k a b -> Int -> Bool

bitSizeMaybe :: Const k a b -> Maybe Int

bitSize :: Const k a b -> Int

isSigned :: Const k a b -> Bool

shiftL :: Const k a b -> Int -> Const k a b

unsafeShiftL :: Const k a b -> Int -> Const k a b

shiftR :: Const k a b -> Int -> Const k a b

unsafeShiftR :: Const k a b -> Int -> Const k a b

rotateL :: Const k a b -> Int -> Const k a b

rotateR :: Const k a b -> Int -> Const k a b

popCount :: Const k a b -> Int

FiniteBits a => FiniteBits (Const k a b)

Methods

finiteBitSize :: Const k a b -> Int

countLeadingZeros :: Const k a b -> Int

countTrailingZeros :: Const k a b -> Int

type Rep1 k (Const k a)

type Rep1 k (Const k a) = D1 k (MetaData "Const" "Data.Functor.Const" "base" True) (C1 k (MetaCons "Const" PrefixI True) (S1 k (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 k a)))

type Rep (Const k a b)

type Rep (Const k a b) = D1 * (MetaData "Const" "Data.Functor.Const" "base" True) (C1 * (MetaCons "Const" PrefixI True) (S1 * (MetaSel (Just Symbol "getConst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))

data WrappedMonad (m :: * -> *) a :: (* -> *) -> * -> *

Instances

Monad m => Monad (WrappedMonad m)

Methods

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

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

return :: a -> WrappedMonad m a

fail :: String -> WrappedMonad m a

Monad m => Functor (WrappedMonad m)

Since: 2.1

Methods

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

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

Monad m => Applicative (WrappedMonad m)

Since: 2.1

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

MonadPlus m => Alternative (WrappedMonad m)

Since: 2.1

Methods

empty :: WrappedMonad m a

(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a

some :: WrappedMonad m a -> WrappedMonad m [a]

many :: WrappedMonad m a -> WrappedMonad m [a]

Generic1 * (WrappedMonad m)

Associated Types

type Rep1 (WrappedMonad m) (f :: WrappedMonad m -> *) :: k -> *

Methods

from1 :: f a -> Rep1 (WrappedMonad m) f a

to1 :: Rep1 (WrappedMonad m) f a -> f a

Generic (WrappedMonad m a)

Associated Types

type Rep (WrappedMonad m a) :: * -> *

Methods

from :: WrappedMonad m a -> Rep (WrappedMonad m a) x

to :: Rep (WrappedMonad m a) x -> WrappedMonad m a

type Rep1 * (WrappedMonad m)

type Rep1 * (WrappedMonad m) = D1 * (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapMonad" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * m)))

type Rep (WrappedMonad m a)

type Rep (WrappedMonad m a) = D1 * (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapMonad" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (m a))))

data WrappedArrow (a :: * -> * -> *) b c :: (* -> * -> *) -> * -> * -> *

Instances

Generic1 * (WrappedArrow a b)

Associated Types

type Rep1 (WrappedArrow a b) (f :: WrappedArrow a b -> *) :: k -> *

Methods

from1 :: f a -> Rep1 (WrappedArrow a b) f a

to1 :: Rep1 (WrappedArrow a b) f a -> f a

Arrow a => Functor (WrappedArrow a b)

Since: 2.1

Methods

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

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

Arrow a => Applicative (WrappedArrow a b)

Since: 2.1

Methods

pure :: a -> WrappedArrow a b a

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

liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c

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

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

(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b)

Since: 2.1

Methods

empty :: WrappedArrow a b a

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

some :: WrappedArrow a b a -> WrappedArrow a b [a]

many :: WrappedArrow a b a -> WrappedArrow a b [a]

Generic (WrappedArrow a b c)

Associated Types

type Rep (WrappedArrow a b c) :: * -> *

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 Rep1 * (WrappedArrow a b) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * (a b))))

type Rep (WrappedArrow a b c)

type Rep (WrappedArrow a b c) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a b c))))

data ZipList a :: * -> *

Lists, but with an Applicative functor based on zipping.

Instances

Functor ZipList

Methods

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

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

Applicative ZipList

f '<$>' 'ZipList' xs1 '<*>' ... '<*>' 'ZipList' xsN

ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\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: 2.1

Methods

pure :: a -> ZipList a

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

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c

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

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

Foldable ZipList

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

toList :: ZipList a -> [a]

null :: ZipList a -> Bool

length :: ZipList a -> Int

elem :: Eq a => a -> ZipList a -> Bool

maximum :: Ord a => ZipList a -> a

minimum :: Ord a => ZipList a -> a

sum :: Num a => ZipList a -> a

product :: Num a => ZipList a -> a

Traversable ZipList

Since: 4.9.0.0

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b)

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a)

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b)

sequence :: Monad m => ZipList (m a) -> m (ZipList a)

Eq a => Eq (ZipList a)

Methods

(==) :: ZipList a -> ZipList a -> Bool

(/=) :: ZipList a -> ZipList a -> Bool

Ord a => Ord (ZipList a)

Methods

compare :: ZipList a -> ZipList a -> Ordering

(<) :: ZipList a -> ZipList a -> Bool

(<=) :: ZipList a -> ZipList a -> Bool

(>) :: ZipList a -> ZipList a -> Bool

(>=) :: ZipList a -> ZipList a -> Bool

max :: ZipList a -> ZipList a -> ZipList a

min :: ZipList a -> ZipList a -> ZipList a

Read a => Read (ZipList a)

Methods

readsPrec :: Int -> ReadS (ZipList a)

readList :: ReadS [ZipList a]

readPrec :: ReadPrec (ZipList a)

readListPrec :: ReadPrec [ZipList a]

Show a => Show (ZipList a)

Methods

showsPrec :: Int -> ZipList a -> ShowS

show :: ZipList a -> String

showList :: [ZipList a] -> ShowS

Generic (ZipList a)

Associated Types

type Rep (ZipList a) :: * -> *

Methods

from :: ZipList a -> Rep (ZipList a) x

to :: Rep (ZipList a) x -> ZipList a

Generic1 * ZipList

Associated Types

type Rep1 ZipList (f :: ZipList -> *) :: k -> *

Methods

from1 :: f a -> Rep1 ZipList f a

to1 :: Rep1 ZipList f a -> f a

type Rep (ZipList a)

type Rep (ZipList a) = D1 * (MetaData "ZipList" "Control.Applicative" "base" True) (C1 * (MetaCons "ZipList" PrefixI True) (S1 * (MetaSel (Just Symbol "getZipList") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [a])))

type Rep1 * ZipList

type Rep1 * ZipList = D1 * (MetaData "ZipList" "Control.Applicative" "base" True) (C1 * (MetaCons "ZipList" PrefixI True) (S1 * (MetaSel (Just Symbol "getZipList") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * [])))

(<$>) :: 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 => forall a 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.

(<**>) :: 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

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

liftA2 :: Applicative f => forall a b c. (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 <*>.

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.