base-4.10.1.0: 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 • (<*>) = ap (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. 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 <*>. (*>) :: f a -> f b -> f b infixl 4 Source # Sequence actions, discarding the value of the first argument. (<*) :: f a -> f b -> f a infixl 4 Source # Sequence actions, discarding the value of the second argument. Instances Source # Since: 2.1 Methods pure :: a -> [a] Source # (<*>) :: [a -> b] -> [a] -> [b] Source # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source # (*>) :: [a] -> [b] -> [b] Source # (<*) :: [a] -> [b] -> [a] Source # Source # Since: 2.1 Methods pure :: 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: 2.1 Methods pure :: 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: 4.9.0.0 Methods pure :: 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: 4.6.0.0 Methods pure :: 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: 4.6.0.0 Methods pure :: 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 # Methods pure :: 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 # Methods pure :: 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: 4.8.0.0 Methods pure :: 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: 4.8.0.0 Methods pure :: 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: 4.8.0.0 Methods pure :: 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: 4.8.0.0 Methods pure :: 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: 4.8.0.0 Methods pure :: 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 # 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 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: 4.9.0.0 Methods pure :: 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: 4.9.0.0 Methods pure :: a -> Option a Source # (<*>) :: Option (a -> b) -> Option a -> Option b Source # liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c Source # (*>) :: Option a -> Option b -> Option b Source # (<*) :: Option a -> Option b -> Option a Source # Source # Since: 4.9.0.0 Methods pure :: 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: 4.9.0.0 Methods pure :: 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: 4.9.0.0 Methods pure :: 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: 4.9.0.0 Methods pure :: 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: 4.9.0.0 Methods pure :: 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: 3.0 Methods pure :: 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 # Source # Since: 4.9.0.0 Methods pure :: 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 # 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: 2.1 Methods pure :: a -> (a, a) Source # (<*>) :: (a, a -> b) -> (a, a) -> (a, b) Source # liftA2 :: (a -> b -> c) -> (a, a) -> (a, b) -> (a, c) Source # (*>) :: (a, a) -> (a, b) -> (a, b) Source # (<*) :: (a, a) -> (a, b) -> (a, a) Source # Source # Since: 4.4.0.0 Methods pure :: 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: 4.7.0.0 Methods pure :: 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 # Arrow a => Applicative (ArrowMonad a) Source # Since: 4.6.0.0 Methods pure :: a -> ArrowMonad a a Source # (<*>) :: ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b Source # liftA2 :: (a -> b -> c) -> ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a a Source # Monad m => Applicative (WrappedMonad m) Source # Since: 2.1 Methods 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 # Source # Since: 2.1 Methods pure :: 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 # Applicative f => Applicative (Rec1 * f) Source # Since: 4.9.0.0 Methods pure :: 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 # Applicative f => Applicative (Alt * f) Source # Methods pure :: 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 # Monoid m => Applicative (Const * m) Source # Since: 2.0.1 Methods pure :: 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 # Arrow a => Applicative (WrappedArrow a b) Source # Since: 2.1 Methods pure :: a -> WrappedArrow a b a Source # (<*>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source # liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source # (<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source # Source # Since: 2.1 Methods pure :: a -> (LiftedRep -> LiftedRep) a a Source # (<*>) :: (LiftedRep -> LiftedRep) a (a -> b) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b Source # liftA2 :: (a -> b -> c) -> (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a c Source # (*>) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a b Source # (<*) :: (LiftedRep -> LiftedRep) a a -> (LiftedRep -> LiftedRep) a b -> (LiftedRep -> LiftedRep) a a Source # (Applicative f, Applicative g) => Applicative ((:*:) * f g) Source # Since: 4.9.0.0 Methods pure :: 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 g) => Applicative (Product * f g) Source # Since: 4.9.0.0 Methods 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 (M1 * i c f) Source # Since: 4.9.0.0 Methods pure :: 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 -> c) -> M1 * i c f a -> M1 * i c f b -> M1 * i c f c 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 # (Applicative f, Applicative g) => Applicative ((:.:) * * f g) Source # Since: 4.9.0.0 Methods pure :: 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 g) => Applicative (Compose * * f g) Source # Since: 4.9.0.0 Methods 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 # # 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

newtype Const a b Source #

The Const functor.

Constructors

 Const FieldsgetConst :: a

Instances

 Generic1 k (Const k a) Source # Associated Typestype Rep1 (Const k a) (f :: Const k a -> *) :: k -> * Source # Methodsfrom1 :: f a -> Rep1 (Const k a) f a Source #to1 :: Rep1 (Const k a) f a -> f a Source # Source # Since: 4.9.0.0 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 # Source # Since: 4.9.0.0 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 # Source # Since: 4.9.0.0 MethodsliftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering Source # Source # Since: 4.9.0.0 MethodsliftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool Source # Source # Since: 4.8.0.0 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 # Source # Since: 4.10.0.0 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 # Source # Since: 4.10.0.0 Methodsbitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const * a b -> f (Const * c d) Source # Source # Since: 2.1 Methodsfmap :: (a -> b) -> Const * m a -> Const * m b Source #(<) :: a -> Const * m b -> Const * m a Source # Monoid m => Applicative (Const * m) Source # Since: 2.0.1 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 # Source # Since: 4.7.0.0 Methodsfold :: Monoid m => Const * m m -> m Source #foldMap :: Monoid m => (a -> m) -> Const * m a -> m 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 # Source # Since: 4.7.0.0 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 m => (a -> m b) -> Const * m a -> m (Const * m b) Source #sequence :: Monad m => Const * m (m a) -> m (Const * m a) Source # Show a => Show1 (Const * a) Source # Since: 4.9.0.0 MethodsliftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Const * a a -> ShowS Source #liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Const * a a] -> ShowS Source # Read a => Read1 (Const * a) Source # Since: 4.9.0.0 MethodsliftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Const * a a) Source #liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Const * a a] Source #liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Const * a a) Source #liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Const * a a] Source # Ord a => Ord1 (Const * a) Source # Since: 4.9.0.0 MethodsliftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering Source # Eq a => Eq1 (Const * a) Source # Since: 4.9.0.0 MethodsliftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool Source # Bounded a => Bounded (Const k a b) Source # MethodsminBound :: Const k a b Source #maxBound :: Const k a b Source # Enum a => Enum (Const k a b) Source # Methodssucc :: Const k a b -> Const k a b Source #pred :: Const k a b -> Const k a b Source #toEnum :: Int -> Const k a b Source #fromEnum :: Const k a b -> Int Source #enumFrom :: Const k a b -> [Const k a b] Source #enumFromThen :: Const k a b -> Const k a b -> [Const k a b] Source #enumFromTo :: Const k a b -> Const k a b -> [Const k a b] Source #enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b] Source # Eq a => Eq (Const k a b) Source # 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) Source # Methodspi :: Const k a b Source #exp :: Const k a b -> Const k a b Source #log :: Const k a b -> Const k a b Source #sqrt :: Const k a b -> Const k a b Source #(**) :: Const k a b -> Const k a b -> Const k a b Source #logBase :: Const k a b -> Const k a b -> Const k a b Source #sin :: Const k a b -> Const k a b Source #cos :: Const k a b -> Const k a b Source #tan :: Const k a b -> Const k a b Source #asin :: Const k a b -> Const k a b Source #acos :: Const k a b -> Const k a b Source #atan :: Const k a b -> Const k a b Source #sinh :: Const k a b -> Const k a b Source #cosh :: Const k a b -> Const k a b Source #tanh :: Const k a b -> Const k a b Source #asinh :: Const k a b -> Const k a b Source #acosh :: Const k a b -> Const k a b Source #atanh :: Const k a b -> Const k a b Source #log1p :: Const k a b -> Const k a b Source #expm1 :: Const k a b -> Const k a b Source #log1pexp :: Const k a b -> Const k a b Source #log1mexp :: Const k a b -> Const k a b Source # Fractional a => Fractional (Const k a b) Source # Methods(/) :: Const k a b -> Const k a b -> Const k a b Source #recip :: Const k a b -> Const k a b Source #fromRational :: Rational -> Const k a b Source # Integral a => Integral (Const k a b) Source # Methodsquot :: Const k a b -> Const k a b -> Const k a b Source #rem :: Const k a b -> Const k a b -> Const k a b Source #div :: Const k a b -> Const k a b -> Const k a b Source #mod :: Const k a b -> Const k a b -> Const k a b Source #quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source #divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b) Source #toInteger :: Const k a b -> Integer Source # (Typeable * k3, Data a, Typeable k3 b) => Data (Const k3 a b) Source # Since: 4.10.0.0 Methodsgfoldl :: (forall d c. Data d => c (d -> c) -> d -> c c) -> (forall g. g -> c g) -> Const k3 a b -> c (Const k3 a b) Source #gunfold :: (forall c r. Data c => c (c -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Const k3 a b) Source #toConstr :: Const k3 a b -> Constr Source #dataTypeOf :: Const k3 a b -> DataType Source #dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Const k3 a b)) Source #dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Const k3 a b)) Source #gmapT :: (forall c. Data c => c -> c) -> Const k3 a b -> Const k3 a b Source #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Const k3 a b -> r Source #gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Const k3 a b -> r Source #gmapQ :: (forall d. Data d => d -> u) -> Const k3 a b -> [u] Source #gmapQi :: Int -> (forall d. Data d => d -> u) -> Const k3 a b -> u Source #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Const k3 a b -> m (Const k3 a b) Source # Num a => Num (Const k a b) Source # Methods(+) :: Const k a b -> Const k a b -> Const k a b Source #(-) :: Const k a b -> Const k a b -> Const k a b Source #(*) :: Const k a b -> Const k a b -> Const k a b Source #negate :: Const k a b -> Const k a b Source #abs :: Const k a b -> Const k a b Source #signum :: Const k a b -> Const k a b Source #fromInteger :: Integer -> Const k a b Source # Ord a => Ord (Const k a b) Source # Methodscompare :: 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) Source # This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removedSince: 4.8.0.0 MethodsreadsPrec :: Int -> ReadS (Const k a b) Source #readList :: ReadS [Const k a b] Source #readPrec :: ReadPrec (Const k a b) Source #readListPrec :: ReadPrec [Const k a b] Source # Real a => Real (Const k a b) Source # MethodstoRational :: Const k a b -> Rational Source # RealFloat a => RealFloat (Const k a b) Source # MethodsfloatRadix :: Const k a b -> Integer Source #floatDigits :: Const k a b -> Int Source #floatRange :: Const k a b -> (Int, Int) Source #decodeFloat :: Const k a b -> (Integer, Int) Source #encodeFloat :: Integer -> Int -> Const k a b Source #exponent :: Const k a b -> Int Source #significand :: Const k a b -> Const k a b Source #scaleFloat :: Int -> Const k a b -> Const k a b Source #isNaN :: Const k a b -> Bool Source #isInfinite :: Const k a b -> Bool Source #isDenormalized :: Const k a b -> Bool Source #isNegativeZero :: Const k a b -> Bool Source #isIEEE :: Const k a b -> Bool Source #atan2 :: Const k a b -> Const k a b -> Const k a b Source # RealFrac a => RealFrac (Const k a b) Source # MethodsproperFraction :: Integral b => Const k a b -> (b, Const k a b) Source #truncate :: Integral b => Const k a b -> b Source #round :: Integral b => Const k a b -> b Source #ceiling :: Integral b => Const k a b -> b Source #floor :: Integral b => Const k a b -> b Source # Show a => Show (Const k a b) Source # This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removedSince: 4.8.0.0 MethodsshowsPrec :: Int -> Const k a b -> ShowS Source #show :: Const k a b -> String Source #showList :: [Const k a b] -> ShowS Source # Ix a => Ix (Const k a b) Source # Methodsrange :: (Const k a b, Const k a b) -> [Const k a b] Source #index :: (Const k a b, Const k a b) -> Const k a b -> Int Source #unsafeIndex :: (Const k a b, Const k a b) -> Const k a b -> IntinRange :: (Const k a b, Const k a b) -> Const k a b -> Bool Source #rangeSize :: (Const k a b, Const k a b) -> Int Source #unsafeRangeSize :: (Const k a b, Const k a b) -> Int IsString a => IsString (Const * a b) Source # Since: 4.9.0.0 Methods Generic (Const k a b) Source # Associated Typestype Rep (Const k a b) :: * -> * Source # Methodsfrom :: Const k a b -> Rep (Const k a b) x Source #to :: Rep (Const k a b) x -> Const k a b Source # Semigroup a => Semigroup (Const k a b) Source # Since: 4.9.0.0 Methods(<>) :: Const k a b -> Const k a b -> Const k a b Source #sconcat :: NonEmpty (Const k a b) -> Const k a b Source #stimes :: Integral b => b -> Const k a b -> Const k a b Source # Monoid a => Monoid (Const k a b) Source # Methodsmempty :: Const k a b Source #mappend :: Const k a b -> Const k a b -> Const k a b Source #mconcat :: [Const k a b] -> Const k a b Source # FiniteBits a => FiniteBits (Const k a b) Source # MethodsfiniteBitSize :: Const k a b -> Int Source #countLeadingZeros :: Const k a b -> Int Source #countTrailingZeros :: Const k a b -> Int Source # Bits a => Bits (Const k a b) Source # Methods(.&.) :: Const k a b -> Const k a b -> Const k a b Source #(.|.) :: Const k a b -> Const k a b -> Const k a b Source #xor :: Const k a b -> Const k a b -> Const k a b Source #complement :: Const k a b -> Const k a b Source #shift :: Const k a b -> Int -> Const k a b Source #rotate :: Const k a b -> Int -> Const k a b Source #zeroBits :: Const k a b Source #bit :: Int -> Const k a b Source #setBit :: Const k a b -> Int -> Const k a b Source #clearBit :: Const k a b -> Int -> Const k a b Source #complementBit :: Const k a b -> Int -> Const k a b Source #testBit :: Const k a b -> Int -> Bool Source #bitSizeMaybe :: Const k a b -> Maybe Int Source #bitSize :: Const k a b -> Int Source #isSigned :: Const k a b -> Bool Source #shiftL :: Const k a b -> Int -> Const k a b Source #unsafeShiftL :: Const k a b -> Int -> Const k a b Source #shiftR :: Const k a b -> Int -> Const k a b Source #unsafeShiftR :: Const k a b -> Int -> Const k a b Source #rotateL :: Const k a b -> Int -> Const k a b Source #rotateR :: Const k a b -> Int -> Const k a b Source #popCount :: Const k a b -> Int Source # Storable a => Storable (Const k a b) Source # MethodssizeOf :: Const k a b -> Int Source #alignment :: Const k a b -> Int Source #peekElemOff :: Ptr (Const k a b) -> Int -> IO (Const k a b) Source #pokeElemOff :: Ptr (Const k a b) -> Int -> Const k a b -> IO () Source #peekByteOff :: Ptr b -> Int -> IO (Const k a b) Source #pokeByteOff :: Ptr b -> Int -> Const k a b -> IO () Source #peek :: Ptr (Const k a b) -> IO (Const k a b) Source #poke :: Ptr (Const k a b) -> Const k a b -> IO () Source # type Rep1 k (Const k a) Source # 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) Source # 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))) newtype WrappedMonad m a Source # Constructors  WrapMonad FieldsunwrapMonad :: m a Instances  Monad m => Monad (WrappedMonad m) Source # 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 # Monad m => Functor (WrappedMonad m) Source # Since: 2.1 Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #(<) :: a -> WrappedMonad m b -> WrappedMonad m a Source # Monad m => Applicative (WrappedMonad m) Source # Since: 2.1 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 # Source # Since: 2.1 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 # Associated Typestype Rep1 (WrappedMonad m) (f :: WrappedMonad m -> *) :: k -> * Source # Methodsfrom1 :: f a -> Rep1 (WrappedMonad m) f a Source #to1 :: Rep1 (WrappedMonad m) f a -> f a Source # Generic (WrappedMonad m a) Source # Associated Typestype Rep (WrappedMonad m a) :: * -> * 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) Source # 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) Source # 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))))

newtype WrappedArrow a b c Source #

Constructors

 WrapArrow FieldsunwrapArrow :: a b c

Instances

 Source # Associated Typestype Rep1 (WrappedArrow a b) (f :: WrappedArrow a b -> *) :: k -> * Source # Methodsfrom1 :: f a -> Rep1 (WrappedArrow a b) f a Source #to1 :: Rep1 (WrappedArrow a b) f a -> f a Source # Arrow a => Functor (WrappedArrow a b) Source # Since: 2.1 Methodsfmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source #(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a Source # Arrow a => Applicative (WrappedArrow a b) Source # Since: 2.1 Methodspure :: a -> WrappedArrow a b a Source #(<*>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b Source #liftA2 :: (a -> b -> c) -> WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b c Source #(*>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b Source #(<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a Source # (ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) Source # Since: 2.1 Methodsempty :: WrappedArrow a b a Source #(<|>) :: WrappedArrow a b a -> WrappedArrow a b a -> WrappedArrow a b a Source #some :: WrappedArrow a b a -> WrappedArrow a b [a] Source #many :: WrappedArrow a b a -> WrappedArrow a b [a] Source # Generic (WrappedArrow a b c) Source # Associated Typestype Rep (WrappedArrow a b c) :: * -> * Source # Methodsfrom :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x Source #to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c Source # type Rep1 * (WrappedArrow a b) Source # type Rep1 * (WrappedArrow a b) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * (a b)))) type Rep (WrappedArrow a b c) Source # type Rep (WrappedArrow a b c) = D1 * (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 * (MetaCons "WrapArrow" PrefixI True) (S1 * (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a b c)))) newtype ZipList a Source # Lists, but with an Applicative functor based on zipping. Constructors  ZipList FieldsgetZipList :: [a] Instances Source # Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source # (<$) :: a -> ZipList b -> 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: 2.1

Methods

pure :: 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 #

Methods

fold :: Monoid m => ZipList m -> 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: 4.9.0.0

Methods

traverse :: 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 #

Eq a => Eq (ZipList a) Source #

Methods

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

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

Ord a => Ord (ZipList a) Source #

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 #

Methods

Show a => Show (ZipList a) Source #
Source #

Associated Types

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

Methods

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

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

Source #

Associated Types

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

Methods

from1 :: f a -> Rep1 ZipList f a Source #

to1 :: Rep1 ZipList f a -> f a Source #

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

# 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 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.

(<**>) :: 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. This function may be used as a value for fmap in a Functor instance.

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.