Copyright	Conor McBride and Ross Paterson 2005
License	BSD-style (see the LICENSE file in the distribution)
Maintainer	libraries@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Control.Applicative

Contents

Applicative functors
Alternatives
Instances
Utility functions

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

class Functor f => Applicative f where
class Applicative f => Alternative f where
newtype Const a b = Const {
- getConst :: a
}
newtype WrappedMonad m a = WrapMonad {
- unwrapMonad :: m a
}
newtype WrappedArrow a b c = WrapArrow {
- unwrapArrow :: a b c
}
newtype ZipList a = ZipList {
- getZipList :: [a]
}
(<$>) :: Functor f => (a -> b) -> f a -> f b
(<$) :: Functor f => a -> f b -> f a
(<**>) :: Applicative f => f a -> f (a -> b) -> f b
liftA :: Applicative f => (a -> b) -> f a -> f b
liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d
optional :: Alternative f => f a -> f (Maybe a)

Applicative functors

class Functor f => Applicative f where 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

Applicative [] #	Since: 2.1
Instance details 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 #
Applicative Maybe #	Since: 2.1
Instance details 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 #
Applicative IO #	Since: 2.1
Instance details 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 #
Applicative Par1 #	Since: 4.9.0.0
Instance details 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 #
Applicative NonEmpty #	Since: 4.9.0.0
Instance details 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 #
Applicative ReadP #	Since: 4.6.0.0
Instance details 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 #
Applicative ReadPrec #	Since: 4.6.0.0
Instance details 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 #
Applicative Down #	Since: 4.11.0.0
Instance details Methods pure :: 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 #
Applicative Product #	Since: 4.8.0.0
Instance details 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 #
Applicative Sum #	Since: 4.8.0.0
Instance details 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 #
Applicative Dual #	Since: 4.8.0.0
Instance details 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 #
Applicative Last #
Instance details 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 #
Applicative First #
Instance details 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 #
Applicative STM #	Since: 4.8.0.0
Instance details 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 #
Applicative Identity #	Since: 4.8.0.0
Instance details 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 #
Applicative ZipList #	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: 2.1
Instance details 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 #
Applicative Option #	Since: 4.9.0.0
Instance details 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 #
Applicative Last #	Since: 4.9.0.0
Instance details 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 #
Applicative First #	Since: 4.9.0.0
Instance details 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 #
Applicative Max #	Since: 4.9.0.0
Instance details 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 #
Applicative Min #	Since: 4.9.0.0
Instance details 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 #
Applicative Complex #	Since: 4.9.0.0
Instance details 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 #
Applicative (Either e) #	Since: 3.0
Instance details 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 #
Applicative (U1 :: * -> *) #	Since: 4.9.0.0
Instance details 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) #	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <> ("world!", 2002) ("hello world!",2017) Since: 2.1*
Instance details Methods pure :: 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 #
Applicative (ST s) #	Since: 4.4.0.0
Instance details 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 (Proxy :: * -> *) #	Since: 4.7.0.0
Instance details 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) #	Since: 4.6.0.0
Instance details Methods pure :: a0 -> ArrowMonad a a0 Source # (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #
Monad m => Applicative (WrappedMonad m) #	Since: 2.1
Instance details 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 #
Applicative (ST s) #	Since: 2.1
Instance details 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) #	Since: 4.9.0.0
Instance details 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) #
Instance details 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 :: * -> *) #	Since: 2.0.1
Instance details 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) #	Since: 2.1
Instance details Methods pure :: a0 -> WrappedArrow a b a0 Source # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Applicative ((->) a :: * -> *) #	Since: 2.1
Instance details Methods pure :: 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 #
(Applicative f, Applicative g) => Applicative (f :*: g) #	Since: 4.9.0.0
Instance details 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) #	Since: 4.9.0.0
Instance details 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) #	Since: 4.9.0.0
Instance details 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 -> 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 #
(Applicative f, Applicative g) => Applicative (f :.: g) #	Since: 4.9.0.0
Instance details 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) #	Since: 4.9.0.0
Instance details 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

empty, (<|>)

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

Alternative [] #	Since: 2.1
Instance details Methods empty :: [a] Source # (<\|>) :: [a] -> [a] -> [a] Source # some :: [a] -> [[a]] Source # many :: [a] -> [[a]] Source #
Alternative Maybe #	Since: 2.1
Instance details Methods empty :: Maybe a Source # (<\|>) :: Maybe a -> Maybe a -> Maybe a Source # some :: Maybe a -> Maybe [a] Source # many :: Maybe a -> Maybe [a] Source #
Alternative IO #	Since: 4.9.0.0
Instance details Methods empty :: IO a Source # (<\|>) :: IO a -> IO a -> IO a Source # some :: IO a -> IO [a] Source # many :: IO a -> IO [a] Source #
Alternative ReadP #	Since: 4.6.0.0
Instance details Methods empty :: ReadP a Source # (<\|>) :: ReadP a -> ReadP a -> ReadP a Source # some :: ReadP a -> ReadP [a] Source # many :: ReadP a -> ReadP [a] Source #
Alternative ReadPrec #	Since: 4.6.0.0
Instance details Methods empty :: ReadPrec a Source # (<\|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source # some :: ReadPrec a -> ReadPrec [a] Source # many :: ReadPrec a -> ReadPrec [a] Source #
Alternative STM #	Since: 4.8.0.0
Instance details Methods empty :: STM a Source # (<\|>) :: STM a -> STM a -> STM a Source # some :: STM a -> STM [a] Source # many :: STM a -> STM [a] Source #
Alternative ZipList #	Since: 4.11.0.0
Instance details Methods empty :: ZipList a Source # (<\|>) :: ZipList a -> ZipList a -> ZipList a Source # some :: ZipList a -> ZipList [a] Source # many :: ZipList a -> ZipList [a] Source #
Alternative Option #	Since: 4.9.0.0
Instance details Methods empty :: Option a Source # (<\|>) :: Option a -> Option a -> Option a Source # some :: Option a -> Option [a] Source # many :: Option a -> Option [a] Source #
Alternative (U1 :: * -> *) #	Since: 4.9.0.0
Instance details Methods empty :: U1 a Source # (<\|>) :: U1 a -> U1 a -> U1 a Source # some :: U1 a -> U1 [a] Source # many :: U1 a -> U1 [a] Source #
Alternative (Proxy :: * -> *) #	Since: 4.9.0.0
Instance details Methods empty :: Proxy a Source # (<\|>) :: Proxy a -> Proxy a -> Proxy a Source # some :: Proxy a -> Proxy [a] Source # many :: Proxy a -> Proxy [a] Source #
ArrowPlus a => Alternative (ArrowMonad a) #	Since: 4.6.0.0
Instance details Methods empty :: 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 #
MonadPlus m => Alternative (WrappedMonad m) #	Since: 2.1
Instance details Methods empty :: WrappedMonad m a Source # (<\|>) :: 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 #
Alternative f => Alternative (Rec1 f) #	Since: 4.9.0.0
Instance details Methods empty :: 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 (Alt f) #
Instance details Methods empty :: 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 #
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) #	Since: 2.1
Instance details Methods empty :: WrappedArrow a b a0 Source # (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source # some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source # many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source #
(Alternative f, Alternative g) => Alternative (f :*: g) #	Since: 4.9.0.0
Instance details Methods empty :: (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 g) => Alternative (Product f g) #	Since: 4.9.0.0
Instance details Methods empty :: 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 (M1 i c f) #	Since: 4.9.0.0
Instance details Methods empty :: 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 #
(Alternative f, Applicative g) => Alternative (f :.: g) #	Since: 4.9.0.0
Instance details Methods empty :: (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) #	Since: 4.9.0.0
Instance details Methods empty :: 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 #

Instances

newtype Const a b Source #

The Const functor.

Constructors

Const
Fields getConst :: a

Instances

Generic1 (Const a :: k -> *) #
Instance details Associated Types type Rep1 (Const a) :: k -> * Source # Methods from1 :: Const a a0 -> Rep1 (Const a) a0 Source # to1 :: Rep1 (Const a) a0 -> Const a a0 Source #
Show2 (Const :: * -> * -> *) #	Since: 4.9.0.0
Instance details Methods liftShowsPrec2 :: (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 #
Read2 (Const :: * -> * -> *) #	Since: 4.9.0.0
Instance details Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b) Source # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b] Source #
Ord2 (Const :: * -> * -> *) #	Since: 4.9.0.0
Instance details Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering Source #
Eq2 (Const :: * -> * -> *) #	Since: 4.9.0.0
Instance details Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool Source #
Bifunctor (Const :: * -> * -> *) #	Since: 4.8.0.0
Instance details Methods bimap :: (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 #
Bifoldable (Const :: * -> * -> *) #	Since: 4.10.0.0
Instance details Methods bifold :: 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 #
Bitraversable (Const :: * -> * -> *) #	Since: 4.10.0.0
Instance details Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Const a b -> f (Const c d) Source #
Functor (Const m :: * -> *) #	Since: 2.1
Instance details Methods fmap :: (a -> b) -> Const m a -> Const m b Source # (<$) :: a -> Const m b -> Const m a Source #
Monoid m => Applicative (Const m :: * -> *) #	Since: 2.0.1
Instance details 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 #
Foldable (Const m :: * -> *) #	Since: 4.7.0.0
Instance details Methods fold :: Monoid m0 => Const m m0 -> 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 #
Traversable (Const m :: * -> *) #	Since: 4.7.0.0
Instance details Methods traverse :: 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 #
Show a => Show1 (Const a :: * -> *) #	Since: 4.9.0.0
Instance details Methods liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS Source # liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS Source #
Read a => Read1 (Const a :: * -> *) #	Since: 4.9.0.0
Instance details Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0) Source # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0] Source #
Ord a => Ord1 (Const a :: * -> *) #	Since: 4.9.0.0
Instance details Methods liftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering Source #
Eq a => Eq1 (Const a :: * -> *) #	Since: 4.9.0.0
Instance details Methods liftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool Source #
Bounded a => Bounded (Const a b) #
Instance details Methods minBound :: Const a b Source # maxBound :: Const a b Source #
Enum a => Enum (Const a b) #
Instance details Methods succ :: Const a b -> Const a b Source # pred :: Const a b -> Const a b Source # toEnum :: Int -> Const a b Source # fromEnum :: Const a b -> Int Source # enumFrom :: Const a b -> [Const a b] Source # enumFromThen :: Const a b -> Const a b -> [Const a b] Source # enumFromTo :: Const a b -> Const a b -> [Const a b] Source # enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] Source #
Eq a => Eq (Const a b) #
Instance details Methods (==) :: Const a b -> Const a b -> Bool Source # (/=) :: Const a b -> Const a b -> Bool Source #
Floating a => Floating (Const a b) #
Instance details Methods pi :: 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 #
Fractional a => Fractional (Const a b) #
Instance details Methods (/) :: Const a b -> Const a b -> Const a b Source # recip :: Const a b -> Const a b Source # fromRational :: Rational -> Const a b Source #
Integral a => Integral (Const a b) #
Instance details Methods quot :: Const a b -> Const a b -> Const a b Source # rem :: Const a b -> Const a b -> Const a b Source # div :: Const a b -> Const a b -> Const a b Source # mod :: Const a b -> Const a b -> Const a b Source # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source # divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source # toInteger :: Const a b -> Integer Source #
(Typeable k, Data a, Typeable b) => Data (Const a b) #	Since: 4.10.0.0
Instance details Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Const a b -> c (Const a b) 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 :: (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 #
Num a => Num (Const a b) #
Instance details 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 # fromInteger :: Integer -> Const a b Source #
Ord a => Ord (Const a b) #
Instance details Methods compare :: 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 #
Read a => Read (Const a b) #	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: 4.8.0.0
Instance details Methods readsPrec :: Int -> ReadS (Const a b) Source # readList :: ReadS [Const a b] Source # readPrec :: ReadPrec (Const a b) Source # readListPrec :: ReadPrec [Const a b] Source #
Real a => Real (Const a b) #
Instance details Methods toRational :: Const a b -> Rational Source #
RealFloat a => RealFloat (Const a b) #
Instance details Methods floatRadix :: Const a b -> Integer Source # floatDigits :: Const a b -> Int Source # floatRange :: Const a b -> (Int, Int) Source # decodeFloat :: Const a b -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Const a b Source # exponent :: Const a b -> Int Source # significand :: Const a b -> Const a b Source # scaleFloat :: Int -> Const a b -> Const a b Source # isNaN :: Const a b -> Bool Source # isInfinite :: Const a b -> Bool Source # isDenormalized :: Const a b -> Bool Source # isNegativeZero :: Const a b -> Bool Source # isIEEE :: Const a b -> Bool Source # atan2 :: Const a b -> Const a b -> Const a b Source #
RealFrac a => RealFrac (Const a b) #
Instance details Methods properFraction :: 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) #	This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed Since: 4.8.0.0
Instance details Methods showsPrec :: Int -> Const a b -> ShowS Source # show :: Const a b -> String Source # showList :: [Const a b] -> ShowS Source #
Ix a => Ix (Const a b) #
Instance details Methods range :: (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 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
IsString a => IsString (Const a b) #	Since: 4.9.0.0
Instance details Methods fromString :: String -> Const a b Source #
Generic (Const a b) #
Instance details Associated Types type Rep (Const a b) :: * -> * Source # Methods from :: Const a b -> Rep (Const a b) x Source # to :: Rep (Const a b) x -> Const a b Source #
Semigroup a => Semigroup (Const a b) #
Instance details 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 #
Monoid a => Monoid (Const a b) #
Instance details Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
FiniteBits a => FiniteBits (Const a b) #
Instance details Methods finiteBitSize :: Const a b -> Int Source # countLeadingZeros :: Const a b -> Int Source # countTrailingZeros :: Const a b -> Int Source #
Bits a => Bits (Const a b) #
Instance details 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 #
Storable a => Storable (Const a b) #
Instance details Methods sizeOf :: Const a b -> Int Source # alignment :: Const a b -> Int Source # peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b) Source # pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO () Source # peekByteOff :: Ptr b0 -> Int -> IO (Const a b) Source # pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO () Source # peek :: Ptr (Const a b) -> IO (Const a b) Source # poke :: Ptr (Const a b) -> Const a b -> IO () Source #
type Rep1 (Const a :: k -> *) #
Instance details type Rep1 (Const a :: k -> *) = 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) #
Instance details 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

WrapMonad
Fields unwrapMonad :: m a

Instances

Monad m => Monad (WrappedMonad m) #
Instance details 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 # fail :: String -> WrappedMonad m a Source #
Monad m => Functor (WrappedMonad m) #	Since: 2.1
Instance details Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source #
Monad m => Applicative (WrappedMonad m) #	Since: 2.1
Instance details 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 #
MonadPlus m => Alternative (WrappedMonad m) #	Since: 2.1
Instance details Methods empty :: WrappedMonad m a Source # (<\|>) :: 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 #
Generic1 (WrappedMonad m :: * -> *) #
Instance details Associated Types type Rep1 (WrappedMonad m) :: k -> * Source # Methods from1 :: WrappedMonad m a -> Rep1 (WrappedMonad m) a Source # to1 :: Rep1 (WrappedMonad m) a -> WrappedMonad m a Source #
Generic (WrappedMonad m a) #
Instance details Associated Types type Rep (WrappedMonad m a) :: * -> * Source # Methods from :: WrappedMonad m a -> Rep (WrappedMonad m a) x Source # to :: Rep (WrappedMonad m a) x -> WrappedMonad m a Source #
type Rep1 (WrappedMonad m :: * -> *) #
Instance details type Rep1 (WrappedMonad m :: * -> *) = 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) #
Instance details 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
Fields unwrapArrow :: a b c

Instances

Generic1 (WrappedArrow a b :: * -> *) #
Instance details Associated Types type Rep1 (WrappedArrow a b) :: k -> * Source # Methods from1 :: WrappedArrow a b a0 -> Rep1 (WrappedArrow a b) a0 Source # to1 :: Rep1 (WrappedArrow a b) a0 -> WrappedArrow a b a0 Source #
Arrow a => Functor (WrappedArrow a b) #	Since: 2.1
Instance details Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
Arrow a => Applicative (WrappedArrow a b) #	Since: 2.1
Instance details Methods pure :: a0 -> WrappedArrow a b a0 Source # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source #
(ArrowZero a, ArrowPlus a) => Alternative (WrappedArrow a b) #	Since: 2.1
Instance details Methods empty :: WrappedArrow a b a0 Source # (<\|>) :: WrappedArrow a b a0 -> WrappedArrow a b a0 -> WrappedArrow a b a0 Source # some :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source # many :: WrappedArrow a b a0 -> WrappedArrow a b [a0] Source #
Generic (WrappedArrow a b c) #
Instance details Associated Types type Rep (WrappedArrow a b c) :: * -> * Source # Methods from :: WrappedArrow a b c -> Rep (WrappedArrow a b c) x Source # to :: Rep (WrappedArrow a b c) x -> WrappedArrow a b c Source #
type Rep1 (WrappedArrow a b :: * -> *) #
Instance details type Rep1 (WrappedArrow a b :: * -> *) = 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) #
Instance details 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
Fields getZipList :: [a]

Instances

Functor ZipList #
Instance details Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source # (<$) :: a -> ZipList b -> ZipList a Source #
Applicative ZipList #	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: 2.1
Instance details 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 #
Foldable ZipList #
Instance details 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 #
Traversable ZipList #	Since: 4.9.0.0
Instance details 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 #
Alternative ZipList #	Since: 4.11.0.0
Instance details Methods empty :: ZipList a Source # (<\|>) :: ZipList a -> ZipList a -> ZipList a Source # some :: ZipList a -> ZipList [a] Source # many :: ZipList a -> ZipList [a] Source #
Eq a => Eq (ZipList a) #
Instance details Methods (==) :: ZipList a -> ZipList a -> Bool Source # (/=) :: ZipList a -> ZipList a -> Bool Source #
Ord a => Ord (ZipList a) #
Instance details Methods compare :: 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 #
Read a => Read (ZipList a) #
Instance details Methods readsPrec :: Int -> ReadS (ZipList a) Source # readList :: ReadS [ZipList a] Source # readPrec :: ReadPrec (ZipList a) Source # readListPrec :: ReadPrec [ZipList a] Source #
Show a => Show (ZipList a) #
Instance details Methods showsPrec :: Int -> ZipList a -> ShowS Source # show :: ZipList a -> String Source # showList :: [ZipList a] -> ShowS Source #
Generic (ZipList a) #
Instance details Associated Types type Rep (ZipList a) :: * -> * Source # Methods from :: ZipList a -> Rep (ZipList a) x Source # to :: Rep (ZipList a) x -> ZipList a Source #
Generic1 ZipList #
Instance details Associated Types type Rep1 ZipList :: k -> * Source # Methods from1 :: ZipList a -> Rep1 ZipList a Source # to1 :: Rep1 ZipList a -> ZipList a Source #
type Rep (ZipList a) #
Instance details 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 Rep1 ZipList #
Instance details type Rep1 ZipList = D1 (MetaData "ZipList" "Control.Applicative" "base" True) (C1 (MetaCons "ZipList" PrefixI True) (S1 (MetaSel (Just "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

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.

(<**>) :: 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.