base-4.18.0.0: Basic libraries

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 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

# Applicative functors

class Functor f => Applicative f where Source #

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 • m1 <*> m2 = m1 >>= (\x1 -> m2 >>= (\x2 -> return (x1 x2))) • (*>) = (>>) (which implies that pure and <*> satisfy the applicative functor laws). Minimal complete definition pure, ((<*>) | liftA2) Methods pure :: a -> f a Source # 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 Expand 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 <$> produceFoo <*> produceBar <*> produceBaz  liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source # Lift a binary function to actions. Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>. This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap. #### Example Expand >>> liftA2 (,) (Just 3) (Just 5) Just (3,5)  (*>) :: f a -> f b -> f b infixl 4 Source # Sequence actions, discarding the value of the first argument. #### Examples Expand If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing. >>> Just 2 *> Just 3 Just 3  >>> Nothing *> Just 3 Nothing  Of course a more interesting use case would be to have effectful computations instead of just returning pure values. >>> import Data.Char >>> import Text.ParserCombinators.ReadP >>> let p = string "my name is " *> munch1 isAlpha <* eof >>> readP_to_S p "my name is Simon" [("Simon","")]  (<*) :: f a -> f b -> f a infixl 4 Source # Sequence actions, discarding the value of the second argument. #### Instances Instances details  Source # f <$> 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: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: a -> ZipList a Source #(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source #liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source #(*>) :: ZipList a -> ZipList b -> ZipList b Source #(<*) :: ZipList a -> ZipList b -> ZipList a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Complex Methodspure :: a -> Complex a Source #(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source #liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source #(*>) :: Complex a -> Complex b -> Complex b Source #(<*) :: Complex a -> Complex b -> Complex a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Functor.Identity Methodspure :: a -> Identity a Source #(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source #liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source #(*>) :: Identity a -> Identity b -> Identity b Source #(<*) :: Identity a -> Identity b -> Identity a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodspure :: a -> First a Source #(<*>) :: First (a -> b) -> First a -> First b Source #liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #(*>) :: First a -> First b -> First b Source #(<*) :: First a -> First b -> First a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodspure :: a -> Last a Source #(<*>) :: Last (a -> b) -> Last a -> Last b Source #liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #(*>) :: Last a -> Last b -> Last b Source #(<*) :: Last a -> Last b -> Last a Source # Source # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methodspure :: a -> Down a Source #(<*>) :: Down (a -> b) -> Down a -> Down b Source #liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source #(*>) :: Down a -> Down b -> Down b Source #(<*) :: Down a -> Down b -> Down a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> First a Source #(<*>) :: First (a -> b) -> First a -> First b Source #liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #(*>) :: First a -> First b -> First b Source #(<*) :: First a -> First b -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Last a Source #(<*>) :: Last (a -> b) -> Last a -> Last b Source #liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #(*>) :: Last a -> Last b -> Last b Source #(<*) :: Last a -> Last b -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Max a Source #(<*>) :: Max (a -> b) -> Max a -> Max b Source #liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source #(*>) :: Max a -> Max b -> Max b Source #(<*) :: Max a -> Max b -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Min a Source #(<*>) :: Min (a -> b) -> Min a -> Min b Source #liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source #(*>) :: Min a -> Min b -> Min b Source #(<*) :: Min a -> Min b -> Min a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Dual a Source #(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source #liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #(*>) :: Dual a -> Dual b -> Dual b Source #(<*) :: Dual a -> Dual b -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Product a Source #(<*>) :: Product (a -> b) -> Product a -> Product b Source #liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #(*>) :: Product a -> Product b -> Product b Source #(<*) :: Product a -> Product b -> Product a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Sum a Source #(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source #liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #(*>) :: Sum a -> Sum b -> Sum b Source #(<*) :: Sum a -> Sum b -> Sum a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodspure :: a -> NonEmpty a Source #(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source #liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source #(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.Conc.Sync Methodspure :: a -> STM a Source #(<*>) :: STM (a -> b) -> STM a -> STM b Source #liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source #(*>) :: STM a -> STM b -> STM b Source #(<*) :: STM a -> STM b -> STM a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in GHC.GHCi Methodspure :: a -> NoIO a Source #(<*>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source #liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source #(*>) :: NoIO a -> NoIO b -> NoIO b Source #(<*) :: NoIO a -> NoIO b -> NoIO a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> Par1 a Source #(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source #liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source #(*>) :: Par1 a -> Par1 b -> Par1 b Source #(<*) :: Par1 a -> Par1 b -> Par1 a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methodspure :: a -> ReadP a Source #(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source #liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source #(*>) :: ReadP a -> ReadP b -> ReadP b Source #(<*) :: ReadP a -> ReadP b -> ReadP a Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methodspure :: a -> ReadPrec a Source #(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source #liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source #(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> IO a Source #(<*>) :: IO (a -> b) -> IO a -> IO b Source #liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source #(*>) :: IO a -> IO b -> IO b Source #(<*) :: IO a -> IO b -> IO a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> Maybe a Source #(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source #liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #(*>) :: Maybe a -> Maybe b -> Maybe b Source #(<*) :: Maybe a -> Maybe b -> Maybe a Source # Source # Since: base-4.15 Instance detailsDefined in GHC.Base Methodspure :: a -> Solo a Source #(<*>) :: Solo (a -> b) -> Solo a -> Solo b Source #liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c Source #(*>) :: Solo a -> Solo b -> Solo b Source #(<*) :: Solo a -> Solo b -> Solo a Source # Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> [a] Source #(<*>) :: [a -> b] -> [a] -> [b] Source #liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source #(*>) :: [a] -> [b] -> [b] Source #(<*) :: [a] -> [b] -> [a] Source # Monad m => Applicative (WrappedMonad m) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: 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) Source # Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodspure :: 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 # Source # Since: base-2.1 Instance detailsDefined in Control.Monad.ST.Lazy.Imp Methodspure :: a -> ST s a Source #(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #(*>) :: ST s a -> ST s b -> ST s b Source #(<*) :: ST s a -> ST s b -> ST s a Source # Source # Since: base-3.0 Instance detailsDefined in Data.Either Methodspure :: a -> Either e a Source #(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source #liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source #(*>) :: Either e a -> Either e b -> Either e b Source #(<*) :: Either e a -> Either e b -> Either e a Source # Applicative (Proxy :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodspure :: a -> Proxy a Source #(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source #liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source #(*>) :: Proxy a -> Proxy b -> Proxy b Source #(<*) :: Proxy a -> Proxy b -> Proxy a Source # Applicative (U1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> U1 a Source #(<*>) :: U1 (a -> b) -> U1 a -> U1 b Source #liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source #(*>) :: U1 a -> U1 b -> U1 b Source #(<*) :: U1 a -> U1 b -> U1 a Source # Source # Since: base-4.4.0.0 Instance detailsDefined in GHC.ST Methodspure :: a -> ST s a Source #(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #(*>) :: ST s a -> ST s b -> ST s b Source #(<*) :: ST s a -> ST s b -> ST s a Source # Monoid a => Applicative ((,) a) Source # 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: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a0 -> (a, a0) Source #(<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source #liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source #(*>) :: (a, a0) -> (a, b) -> (a, b) Source #(<*) :: (a, a0) -> (a, b) -> (a, a0) Source # Arrow a => Applicative (WrappedArrow a b) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: 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) Source # Since: base-4.14.0.0 Instance detailsDefined in Control.Arrow Methodspure :: 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) Source # Since: base-2.0.1 Instance detailsDefined in Data.Functor.Const Methodspure :: a -> Const m a Source #(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source #liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source #(*>) :: Const m a -> Const m b -> Const m b Source #(<*) :: Const m a -> Const m b -> Const m a Source # Applicative f => Applicative (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodspure :: a -> Ap f a Source #(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source #liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source #(*>) :: Ap f a -> Ap f b -> Ap f b Source #(<*) :: Ap f a -> Ap f b -> Ap f a Source # Applicative f => Applicative (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Alt f a Source #(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source #liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source #(*>) :: Alt f a -> Alt f b -> Alt f b Source #(<*) :: Alt f a -> Alt f b -> Alt f a Source # (Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source # Since: base-4.17.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> Generically1 f a Source #(<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source #liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source #(*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source #(<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source # Applicative f => Applicative (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> Rec1 f a Source #(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source #liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source #(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source #(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source # (Monoid a, Monoid b) => Applicative ((,,) a b) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Base Methodspure :: a0 -> (a, b, a0) Source #(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source #liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source #(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source #(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source # (Applicative f, Applicative g) => Applicative (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodspure :: 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) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> (f :*: g) a Source #(<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b Source #liftA2 :: (a -> b -> c) -> (f :*: g) a -> (f :*: g) b -> (f :*: g) c Source #(*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b Source #(<*) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a Source # Monoid c => Applicative (K1 i c :: Type -> Type) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> K1 i c a Source #(<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source #liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source #(*>) :: K1 i c a -> K1 i c b -> K1 i c b Source #(<*) :: K1 i c a -> K1 i c b -> K1 i c a Source # (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source # Since: base-4.14.0.0 Instance detailsDefined in GHC.Base Methodspure :: 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) Source # Since: base-2.1 Instance detailsDefined in GHC.Base Methodspure :: a -> r -> a Source #(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source #liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source #(*>) :: (r -> a) -> (r -> b) -> r -> b Source #(<*) :: (r -> a) -> (r -> b) -> r -> a Source # (Applicative f, Applicative g) => Applicative (Compose f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Compose Methodspure :: 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) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> (f :.: g) a Source #(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source #liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c Source #(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source #(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a Source # Applicative f => Applicative (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodspure :: a -> M1 i c f a Source #(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source #liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source #(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source #(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source # # 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: • some v = (:) <$> v <*> many v
• many v = some v <|> pure []

Minimal complete definition

Methods

empty :: f a Source #

The identity of <|>

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

An associative binary operation

some :: f a -> f [a] Source #

One or more.

many :: f a -> f [a] Source #

Zero or more.

#### Instances

Instances details
 Source # Since: base-4.11.0.0 Instance detailsDefined in Control.Applicative Methods(<|>) :: ZipList a -> ZipList a -> ZipList a Source #some :: ZipList a -> ZipList [a] Source #many :: ZipList a -> ZipList [a] Source # Source # Takes the first non-retrying STM action.Since: base-4.8.0.0 Instance detailsDefined in GHC.Conc.Sync Methods(<|>) :: STM a -> STM a -> STM a Source #some :: STM a -> STM [a] Source #many :: STM a -> STM [a] Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methods(<|>) :: ReadP a -> ReadP a -> ReadP a Source #some :: ReadP a -> ReadP [a] Source #many :: ReadP a -> ReadP [a] Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Text.ParserCombinators.ReadPrec Methods(<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source #some :: ReadPrec a -> ReadPrec [a] Source #many :: ReadPrec a -> ReadPrec [a] Source # Source # Takes the first non-throwing IO action's result. empty throws an exception.Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<|>) :: IO a -> IO a -> IO a Source #some :: IO a -> IO [a] Source #many :: IO a -> IO [a] Source # Source # Picks the leftmost Just value, or, alternatively, Nothing.Since: base-2.1 Instance detailsDefined in GHC.Base Methods(<|>) :: Maybe a -> Maybe a -> Maybe a Source #some :: Maybe a -> Maybe [a] Source #many :: Maybe a -> Maybe [a] Source # Source # Combines lists by concatenation, starting from the empty list.Since: base-2.1 Instance detailsDefined in GHC.Base Methodsempty :: [a] Source #(<|>) :: [a] -> [a] -> [a] Source #some :: [a] -> [[a]] Source #many :: [a] -> [[a]] Source # Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methods(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source #some :: WrappedMonad m a -> WrappedMonad m [a] Source #many :: WrappedMonad m a -> WrappedMonad m [a] Source # Source # Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodsempty :: ArrowMonad a a0 Source #(<|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source #many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source # Alternative (Proxy :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Proxy Methods(<|>) :: Proxy a -> Proxy a -> Proxy a Source #some :: Proxy a -> Proxy [a] Source #many :: Proxy a -> Proxy [a] Source # Alternative (U1 :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(<|>) :: U1 a -> U1 a -> U1 a Source #some :: U1 a -> U1 [a] Source #many :: U1 a -> U1 [a] Source # (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsempty :: 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 # Alternative m => Alternative (Kleisli m a) Source # Since: base-4.14.0.0 Instance detailsDefined in Control.Arrow Methodsempty :: Kleisli m a a0 Source #(<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source #some :: Kleisli m a a0 -> Kleisli m a [a0] Source #many :: Kleisli m a a0 -> Kleisli m a [a0] Source # Alternative f => Alternative (Ap f) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsempty :: Ap f a Source #(<|>) :: Ap f a -> Ap f a -> Ap f a Source #some :: Ap f a -> Ap f [a] Source #many :: Ap f a -> Ap f [a] Source # Alternative f => Alternative (Alt f) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsempty :: Alt f a Source #(<|>) :: Alt f a -> Alt f a -> Alt f a Source #some :: Alt f a -> Alt f [a] Source #many :: Alt f a -> Alt f [a] Source # (Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f) Source # Since: base-4.17.0.0 Instance detailsDefined in GHC.Generics Methods(<|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a Source #some :: Generically1 f a -> Generically1 f [a] Source #many :: Generically1 f a -> Generically1 f [a] Source # Alternative f => Alternative (Rec1 f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsempty :: Rec1 f a Source #(<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source #some :: Rec1 f a -> Rec1 f [a] Source #many :: Rec1 f a -> Rec1 f [a] Source # (Alternative f, Alternative g) => Alternative (Product f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Product Methodsempty :: Product f g a Source #(<|>) :: Product f g a -> Product f g a -> Product f g a Source #some :: Product f g a -> Product f g [a] Source #many :: Product f g a -> Product f g [a] Source # (Alternative f, Alternative g) => Alternative (f :*: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsempty :: (f :*: g) a Source #(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source #some :: (f :*: g) a -> (f :*: g) [a] Source #many :: (f :*: g) a -> (f :*: g) [a] Source # (Alternative f, Applicative g) => Alternative (Compose f g) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Compose Methodsempty :: Compose f g a Source #(<|>) :: Compose f g a -> Compose f g a -> Compose f g a Source #some :: Compose f g a -> Compose f g [a] Source #many :: Compose f g a -> Compose f g [a] Source # (Alternative f, Applicative g) => Alternative (f :.: g) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsempty :: (f :.: g) a Source #(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source #some :: (f :.: g) a -> (f :.: g) [a] Source #many :: (f :.: g) a -> (f :.: g) [a] Source # Alternative f => Alternative (M1 i c f) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsempty :: M1 i c f a Source #(<|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source #some :: M1 i c f a -> M1 i c f [a] Source #many :: M1 i c f a -> M1 i c f [a] Source #

# Instances

newtype Const a b Source #

The Const functor.

Constructors

 Const FieldsgetConst :: a

#### Instances

Instances details
 Generic1 (Const a :: k -> Type) Source # Instance detailsDefined in Data.Functor.Const Associated Typestype Rep1 (Const a) :: k -> Type Source # Methodsfrom1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0 Source #to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0 Source # Bifoldable (Const :: Type -> Type -> Type) Source # Since: base-4.10.0.0 Instance detailsDefined in Data.Bifoldable Methodsbifold :: Monoid m => Const m m -> m Source #bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Const a b -> m Source #bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Const a b -> c Source #bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Const a b -> c Source # Bifoldable1 (Const :: Type -> Type -> Type) Source # Instance detailsDefined in Data.Bifoldable1 Methodsbifold1 :: Semigroup m => Const m m -> m Source #bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Const a b -> m Source # Bifunctor (Const :: Type -> Type -> Type) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d Source #first :: (a -> b) -> Const a c -> Const b c Source #second :: (b -> c) -> Const a b -> Const a c Source # Bitraversable (Const :: Type -> Type -> Type) Source # Since: base-4.10.0.0 Instance detailsDefined in Data.Bitraversable Methodsbitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) Source # Eq2 (Const :: Type -> Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool Source # Ord2 (Const :: Type -> Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering Source # Read2 (Const :: Type -> Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftReadsPrec2 :: (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 -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS Source #liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS Source # Foldable (Const m :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Functor.Const Methodsfold :: 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 #sum :: Num a => Const m a -> a Source #product :: Num a => Const m a -> a Source # Eq a => Eq1 (Const a :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool Source # Ord a => Ord1 (Const a :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering Source # Read a => Read1 (Const a :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftReadsPrec :: (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 -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Classes MethodsliftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS Source #liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS Source # Contravariant (Const a :: Type -> Type) Source # Instance detailsDefined in Data.Functor.Contravariant Methodscontramap :: (a' -> a0) -> Const a a0 -> Const a a' Source #(>$) :: b -> Const a b -> Const a a0 Source # Traversable (Const m :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) Source #sequenceA :: Applicative f => Const m (f a) -> f (Const m a) Source #mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) Source #sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) Source # Monoid m => Applicative (Const m :: Type -> Type) Source # Since: base-2.0.1 Instance detailsDefined in Data.Functor.Const Methodspure :: a -> Const m a Source #(<*>) :: Const m (a -> b) -> Const m a -> Const m b Source #liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c Source #(*>) :: Const m a -> Const m b -> Const m b Source #(<*) :: Const m a -> Const m b -> Const m a Source # Functor (Const m :: Type -> Type) Source # Since: base-2.1 Instance detailsDefined in Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b Source #(<$) :: a -> Const m b -> Const m a Source # (Typeable k, Data a, Typeable b) => Data (Const a b) Source # Since: base-4.10.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (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) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.String MethodsfromString :: String -> Const a b Source # Storable a => Storable (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodssizeOf :: 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 #peek :: Ptr (Const a b) -> IO (Const a b) Source #poke :: Ptr (Const a b) -> Const a b -> IO () Source # Monoid a => Monoid (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodsmempty :: Const a b Source #mappend :: Const a b -> Const a b -> Const a b Source #mconcat :: [Const a b] -> Const a b Source # Semigroup a => Semigroup (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(<>) :: Const a b -> Const a b -> Const a b Source #sconcat :: NonEmpty (Const a b) -> Const a b Source #stimes :: Integral b0 => b0 -> Const a b -> Const a b Source # Bits a => Bits (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(.&.) :: 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 #rotateR :: Const a b -> Int -> Const a b Source #popCount :: Const a b -> Int Source # FiniteBits a => FiniteBits (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsfiniteBitSize :: Const a b -> Int Source #countLeadingZeros :: Const a b -> Int Source # Bounded a => Bounded (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsminBound :: Const a b Source #maxBound :: Const a b Source # Enum a => Enum (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodssucc :: 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) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodspi :: Const a b Source #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 #log1pexp :: Const a b -> Const a b Source #log1mexp :: Const a b -> Const a b Source # RealFloat a => RealFloat (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsfloatRadix :: 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 #isIEEE :: Const a b -> Bool Source #atan2 :: Const a b -> Const a b -> Const a b Source # Generic (Const a b) Source # Instance detailsDefined in Data.Functor.Const Associated Typestype Rep (Const a b) :: Type -> Type Source # Methodsfrom :: Const a b -> Rep (Const a b) x Source #to :: Rep (Const a b) x -> Const a b Source # Ix a => Ix (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodsrange :: (Const a b, Const a b) -> [Const a b] Source #index :: (Const a b, Const a b) -> Const a b -> Int Source #unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int Source #inRange :: (Const a b, Const a b) -> Const a b -> Bool Source #rangeSize :: (Const a b, Const a b) -> Int Source #unsafeRangeSize :: (Const a b, Const a b) -> Int Source # Num a => Num (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(+) :: 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 # Read a => Read (Const a b) Source # This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removedSince: base-4.8.0.0 Instance detailsDefined in Data.Functor.Const MethodsreadsPrec :: Int -> ReadS (Const a b) Source #readList :: ReadS [Const a b] Source #readPrec :: ReadPrec (Const a b) Source # Fractional a => Fractional (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(/) :: Const a b -> Const a b -> Const a b Source #recip :: Const a b -> Const a b Source # Integral a => Integral (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodsquot :: 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 #toInteger :: Const a b -> Integer Source # Real a => Real (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodstoRational :: Const a b -> Rational Source # RealFrac a => RealFrac (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsproperFraction :: Integral b0 => Const a b -> (b0, Const a b) Source #truncate :: Integral b0 => Const a b -> b0 Source #round :: Integral b0 => Const a b -> b0 Source #ceiling :: Integral b0 => Const a b -> b0 Source #floor :: Integral b0 => Const a b -> b0 Source # Show a => Show (Const a b) Source # This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removedSince: base-4.8.0.0 Instance detailsDefined in Data.Functor.Const MethodsshowsPrec :: Int -> Const a b -> ShowS Source #show :: Const a b -> String Source #showList :: [Const a b] -> ShowS Source # Eq a => Eq (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(==) :: Const a b -> Const a b -> Bool Source #(/=) :: Const a b -> Const a b -> Bool Source # Ord a => Ord (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodscompare :: Const a b -> Const a b -> Ordering Source #(<) :: Const a b -> Const a b -> Bool Source #(<=) :: Const a b -> Const a b -> Bool Source #(>) :: Const a b -> Const a b -> Bool Source #(>=) :: Const a b -> Const a b -> Bool Source #max :: Const a b -> Const a b -> Const a b Source #min :: Const a b -> Const a b -> Const a b Source # type Rep1 (Const a :: k -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) type Rep (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const type Rep (Const a b) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype WrappedMonad m a Source #

Constructors

#### Instances

Instances details
 Generic1 (WrappedMonad m :: Type -> Type) Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep1 (WrappedMonad m) :: k -> Type Source # Methodsfrom1 :: forall (a :: k). WrappedMonad m a -> Rep1 (WrappedMonad m) a Source #to1 :: forall (a :: k). Rep1 (WrappedMonad m) a -> WrappedMonad m a Source # Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methods(<|>) :: WrappedMonad m a -> WrappedMonad m a -> WrappedMonad m a Source #some :: WrappedMonad m a -> WrappedMonad m [a] Source #many :: WrappedMonad m a -> WrappedMonad m [a] Source # Monad m => Applicative (WrappedMonad m) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: 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 # Monad m => Functor (WrappedMonad m) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # Monad m => Monad (WrappedMonad m) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methods(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source #(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source #return :: a -> WrappedMonad m a Source # (Typeable m, Typeable a, Data (m a)) => Data (WrappedMonad m a) Source # Since: base-4.14.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonad m a -> c (WrappedMonad m a) Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonad m a) Source #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonad m a)) Source #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonad m a)) Source #gmapT :: (forall b. Data b => b -> b) -> WrappedMonad m a -> WrappedMonad m a Source #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonad m a -> r Source #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonad m a -> r Source #gmapQ :: (forall d. Data d => d -> u) -> WrappedMonad m a -> [u] Source #gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonad m a -> u Source #gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source #gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source #gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonad m a -> m0 (WrappedMonad m a) Source # Generic (WrappedMonad m a) Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep (WrappedMonad m a) :: Type -> Type Source # Methodsfrom :: WrappedMonad m a -> Rep (WrappedMonad m a) x Source #to :: Rep (WrappedMonad m a) x -> WrappedMonad m a Source # type Rep1 (WrappedMonad m :: Type -> Type) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep1 (WrappedMonad m :: Type -> Type) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 m))) type Rep (WrappedMonad m a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep (WrappedMonad m a) = D1 ('MetaData "WrappedMonad" "Control.Applicative" "base" 'True) (C1 ('MetaCons "WrapMonad" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonad") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (m a)))) newtype WrappedArrow a b c Source # Constructors  WrapArrow FieldsunwrapArrow :: a b c #### Instances Instances details  Generic1 (WrappedArrow a b :: Type -> Type) Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep1 (WrappedArrow a b) :: k -> Type Source # Methodsfrom1 :: 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) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsempty :: 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) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: 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) Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (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) Source # Since: base-4.14.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (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) Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep (WrappedArrow a b c) :: Type -> Type Source # Methodsfrom :: 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) Source # Since: base-4.7.0.0 Instance detailsDefined 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) Source # Since: base-4.7.0.0 Instance detailsDefined 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))))

newtype ZipList a Source #

Lists, but with an Applicative functor based on zipping.

Constructors

 ZipList FieldsgetZipList :: [a]

#### Instances

Instances details
 Source # Since: base-4.9.0.0 Instance detailsDefined in Control.Applicative Methodsfold :: 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 #sum :: Num a => ZipList a -> a Source #product :: Num a => ZipList a -> a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) Source #sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) Source #mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) Source #sequence :: Monad m => ZipList (m a) -> m (ZipList a) Source # Source # Since: base-4.11.0.0 Instance detailsDefined in Control.Applicative Methods(<|>) :: ZipList a -> ZipList a -> ZipList a Source #some :: ZipList a -> ZipList [a] Source #many :: ZipList a -> ZipList [a] Source # Source # 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: base-2.1 Instance detailsDefined in Control.Applicative Methodspure :: a -> ZipList a Source #(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source #liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source #(*>) :: ZipList a -> ZipList b -> ZipList b Source #(<*) :: ZipList a -> ZipList b -> ZipList a Source # Source # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> ZipList a -> ZipList b Source #(<$) :: a -> ZipList b -> ZipList a Source # Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep1 ZipList :: k -> Type Source # Methodsfrom1 :: forall (a :: k). ZipList a -> Rep1 ZipList a Source #to1 :: forall (a :: k). Rep1 ZipList a -> ZipList a Source # Data a => Data (ZipList a) Source # Since: base-4.14.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (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 #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 # Source # Instance detailsDefined in Control.Applicative Associated Typestype Rep (ZipList a) :: Type -> Type Source # Methodsfrom :: ZipList a -> Rep (ZipList a) x Source #to :: Rep (ZipList a) x -> ZipList a Source # Source # Since: base-4.15.0.0 Instance detailsDefined in GHC.IsList Associated Typestype Item (ZipList a) Source # MethodsfromList :: [Item (ZipList a)] -> ZipList a Source #fromListN :: Int -> [Item (ZipList a)] -> ZipList a Source #toList :: ZipList a -> [Item (ZipList a)] Source # Read a => Read (ZipList a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methods Show a => Show (ZipList a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative MethodsshowsPrec :: Int -> ZipList a -> ShowS Source #show :: ZipList a -> String Source #showList :: [ZipList a] -> ShowS Source # Eq a => Eq (ZipList a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methods(==) :: ZipList a -> ZipList a -> Bool Source #(/=) :: ZipList a -> ZipList a -> Bool Source # Ord a => Ord (ZipList a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methodscompare :: ZipList a -> ZipList a -> Ordering Source #(<) :: ZipList a -> ZipList a -> Bool Source #(<=) :: ZipList a -> ZipList a -> Bool Source #(>) :: ZipList a -> ZipList a -> Bool Source #(>=) :: ZipList a -> ZipList a -> Bool Source #max :: ZipList a -> ZipList a -> ZipList a Source #min :: ZipList a -> ZipList a -> ZipList a Source # type Rep1 ZipList Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep1 ZipList = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 List))) type Rep (ZipList a) Source # Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative type Rep (ZipList a) = D1 ('MetaData "ZipList" "Control.Applicative" "base" 'True) (C1 ('MetaCons "ZipList" 'PrefixI 'True) (S1 ('MetaSel ('Just "getZipList") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) type Item (ZipList a) Source # Instance detailsDefined in GHC.IsList type Item (ZipList a) = a # 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, <$> is function application lifted over a Functor. #### Examples Expand Convert from a Maybe Int to a Maybe String using show: >>> show <$> 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 => a -> f b -> f a infixl 4 Source #

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.

#### Examples

Expand

Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$Just 2 Just 'a' >>> 'a' <$ Nothing
Nothing


(<**>) :: 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.

#### Examples

Expand

Using the Applicative instance for Lists:

>>> liftA (+1) [1, 2]
[2,3]


Or the Applicative instance for Maybe

>>> liftA (+1) (Just 3)
Just 4


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

Expand

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 using (<|>), generalizing concat.

asum is just like msum, but generalised to Alternative.

#### Examples

Expand

Basic usage:

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"