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

A minimal complete definition must include implementations of these functions satisfying the following laws:

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 = pure  (const  id ) <*>  u <*>  v

```
u <*  v = pure  const  <*>  u <*>  v
```

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

```
fmap  f x = pure  f <*>  x
```

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, (<*>)

Methods

pure :: a -> f a Source #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #

Sequential application.

(*>) :: 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 [] Source #

Methods

pure :: a -> [a] Source #

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

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

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

Applicative Maybe Source #

Methods

pure :: a -> Maybe a Source #

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

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

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

Applicative IO Source #

Methods

pure :: a -> IO a Source #

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

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

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

Applicative U1 Source #

Methods

pure :: a -> U1 a Source #

(<*>) :: U1 (a -> b) -> U1 a -> U1 b Source #

(*>) :: U1 a -> U1 b -> U1 b Source #

(<*) :: U1 a -> U1 b -> U1 a Source #

Applicative Par1 Source #

Methods

pure :: a -> Par1 a Source #

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source #

(*>) :: Par1 a -> Par1 b -> Par1 b Source #

(<*) :: Par1 a -> Par1 b -> Par1 a Source #

Applicative ReadP Source #

Methods

pure :: a -> ReadP a Source #

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source #

(*>) :: ReadP a -> ReadP b -> ReadP b Source #

(<*) :: ReadP a -> ReadP b -> ReadP a Source #

Applicative ReadPrec Source #

Methods

pure :: a -> ReadPrec a Source #

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source #

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source #

Applicative Last Source #

Methods

pure :: a -> Last a Source #

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

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

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

Applicative First Source #

Methods

pure :: a -> First a Source #

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

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

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

Applicative Product Source #

Methods

pure :: a -> Product a Source #

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

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

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

Applicative Sum Source #

Methods

pure :: a -> Sum a Source #

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

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

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

Applicative Dual Source #

Methods

pure :: a -> Dual a Source #

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

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

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

Applicative STM Source #

Methods

pure :: a -> STM a Source #

(<*>) :: STM (a -> b) -> STM a -> STM b Source #

(*>) :: STM a -> STM b -> STM b Source #

(<*) :: STM a -> STM b -> STM a Source #

Applicative ZipList Source #

Methods

pure :: a -> ZipList a Source #

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

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

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

Applicative Complex Source #

Methods

pure :: a -> Complex a Source #

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source #

(*>) :: Complex a -> Complex b -> Complex b Source #

(<*) :: Complex a -> Complex b -> Complex a Source #

Applicative NonEmpty Source #

Methods

pure :: a -> NonEmpty a Source #

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

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

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

Applicative Option Source #

Methods

pure :: a -> Option a Source #

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

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

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

Applicative Last Source #

Methods

pure :: a -> Last a Source #

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

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

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

Applicative First Source #

Methods

pure :: a -> First a Source #

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

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

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

Applicative Max Source #

Methods

pure :: a -> Max a Source #

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

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

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

Applicative Min Source #

Methods

pure :: a -> Min a Source #

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

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

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

Applicative Identity Source #

Methods

pure :: a -> Identity a Source #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source #

(*>) :: Identity a -> Identity b -> Identity b Source #

(<*) :: Identity a -> Identity b -> Identity a Source #

Applicative ((->) a) Source #

Methods

pure :: a -> a -> a Source #

(<*>) :: (a -> a -> b) -> (a -> a) -> a -> b Source #

(*>) :: (a -> a) -> (a -> b) -> a -> b Source #

(<*) :: (a -> a) -> (a -> b) -> a -> a Source #

Applicative (Either e) Source #

Methods

pure :: a -> Either e a Source #

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

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

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

Applicative f => Applicative (Rec1 f) Source #

Methods

pure :: a -> Rec1 f a Source #

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source #

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source #

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source #

Monoid a => Applicative ((,) a) Source #

Methods

pure :: a -> (a, a) Source #

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

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

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

Applicative (ST s) Source #

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

Applicative (Proxy *) Source #

Methods

pure :: a -> Proxy * a Source #

(<*>) :: Proxy * (a -> b) -> Proxy * a -> Proxy * b Source #

(*>) :: Proxy * a -> Proxy * b -> Proxy * b Source #

(<*) :: Proxy * a -> Proxy * b -> Proxy * a Source #

Arrow a => Applicative (ArrowMonad a) Source #

Methods

pure :: a -> ArrowMonad a a Source #

(<*>) :: ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b 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 #

Methods

pure :: a -> WrappedMonad m a Source #

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source #

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #

Applicative (ST s) Source #

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

(Applicative f, Applicative g) => Applicative ((:*:) f g) Source #

Methods

pure :: a -> (f :*: g) a Source #

(<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b 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 ((:.:) f g) Source #

Methods

pure :: a -> (f :.: g) a Source #

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b Source #

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source #

(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) 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 #

(*>) :: 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 #

Methods

pure :: a -> Const * m a Source #

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

Methods

pure :: a -> WrappedArrow a b a Source #

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

Applicative f => Applicative (M1 i c f) Source #

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 #

(*>) :: 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 (Product * f g) Source #

Methods

pure :: a -> Product * f g a Source #

(<*>) :: Product * f g (a -> b) -> Product * f g a -> Product * f g b 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 (Compose * * f g) Source #

Methods

pure :: a -> Compose * * f g a Source #

(<*>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b 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 [] Source #

Methods

empty :: [a] Source #

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

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

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

Alternative Maybe Source #

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 Source #

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 U1 Source #

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 ReadP Source #

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 Source #

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 Source #

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 Option Source #

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 f => Alternative (Rec1 f) Source #

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 (Proxy *) Source #

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) Source #

Methods

empty :: ArrowMonad a a Source #

(<|>) :: ArrowMonad a a -> ArrowMonad a a -> ArrowMonad a a Source #

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

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

MonadPlus m => Alternative (WrappedMonad m) Source #

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 g) => Alternative ((:*:) f g) Source #

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 ((:.:) f g) Source #

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 (Alt * f) Source #

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) Source #

Methods

empty :: 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 #

Alternative f => Alternative (M1 i c f) Source #

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, Alternative g) => Alternative (Product * f g) Source #

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, Applicative g) => Alternative (Compose * * f g) Source #

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

Bifunctor (Const *) Source #

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 #

Show2 (Const *) Source #

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 *) Source #

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 #

Ord2 (Const *) Source #

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering Source #

Eq2 (Const *) Source #

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool Source #

Functor (Const * m) Source #

Methods

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

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

Monoid m => Applicative (Const * m) Source #

Methods

pure :: a -> Const * m a Source #

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

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

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

Foldable (Const * m) Source #

Methods

fold :: 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 #

Traversable (Const * m) Source #

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 m => (a -> m b) -> Const * m a -> m (Const * m b) Source #

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

Generic1 (Const * a) Source #

Associated Types

type Rep1 (Const * a :: * -> *) :: * -> * Source #

Methods

from1 :: Const * a a -> Rep1 (Const * a) a Source #

to1 :: Rep1 (Const * a) a -> Const * a a Source #

Show a => Show1 (Const * a) Source #

Methods

liftShowsPrec :: (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 #

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Const * a a) Source #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Const * a a] Source #

Ord a => Ord1 (Const * a) Source #

Methods

liftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering Source #

Eq a => Eq1 (Const * a) Source #

Methods

liftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool Source #

Bounded a => Bounded (Const k a b) Source #

Methods

minBound :: Const k a b Source #

maxBound :: Const k a b Source #

Enum a => Enum (Const k a b) Source #

Methods

succ :: 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 #

Methods

pi :: 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 #

Methods

quot :: 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 #

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 #

Methods

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

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

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

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

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

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

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

Read a => Read (Const k a b) Source #

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

Methods

readsPrec :: 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 #

Methods

toRational :: Const k a b -> Rational Source #

RealFloat a => RealFloat (Const k a b) Source #

Methods

floatRadix :: 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 #

Methods

properFraction :: 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 removed

Methods

showsPrec :: 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 #

Methods

range :: (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 -> Int

inRange :: (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 #

Methods

fromString :: String -> Const * a b Source #

Generic (Const k a b) Source #

Associated Types

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

Methods

from :: 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 #

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 #

Methods

mempty :: 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 #

Methods

finiteBitSize :: 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 #

Methods

sizeOf :: 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 (Const * a) Source #

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

Fields

unwrapMonad :: 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 #

fail :: String -> WrappedMonad m a Source #

Monad m => Functor (WrappedMonad m) Source #

Methods

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

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

Monad m => Applicative (WrappedMonad m) Source #

Methods

pure :: a -> WrappedMonad m a Source #

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source #

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source #

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source #

Generic1 (WrappedMonad m) Source #

Associated Types

type Rep1 (WrappedMonad m :: * -> *) :: * -> * Source #

Methods

from1 :: WrappedMonad m a -> Rep1 (WrappedMonad m) a Source #

to1 :: Rep1 (WrappedMonad m) a -> WrappedMonad m a Source #

MonadPlus m => Alternative (WrappedMonad m) Source #

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 #

Generic (WrappedMonad m a) Source #

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) 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

Fields

unwrapArrow :: a b c

Instances

Arrow a => Functor (WrappedArrow a b) Source #

Methods

fmap :: (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 #

Methods

pure :: a -> WrappedArrow a b a Source #

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

Generic1 (WrappedArrow a b) Source #

Associated Types

type Rep1 (WrappedArrow a b :: * -> *) :: * -> * Source #

Methods

from1 :: WrappedArrow a b a -> Rep1 (WrappedArrow a b) a Source #

to1 :: Rep1 (WrappedArrow a b) a -> WrappedArrow a b a Source #

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

Methods

empty :: 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 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) 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, so that

f <$>  ZipList  xs1 <*>  ... <*>  ZipList  xsn = ZipList  (zipWithn f xs1 ... xsn)

Constructors

ZipList

Fields

getZipList :: [a]

Instances

Functor ZipList Source #

Methods

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

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

Applicative ZipList Source #

Methods

pure :: a -> ZipList a Source #

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

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

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

Foldable ZipList 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 #

Traversable ZipList Source #

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 #

Generic1 ZipList Source #

Associated Types

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

Methods

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

to1 :: Rep1 ZipList a -> 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 #

Read a => Read (ZipList a) Source #

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) Source #

Methods

showsPrec :: Int -> ZipList a -> ShowS Source #

show :: ZipList a -> String Source #

showList :: [ZipList a] -> ShowS Source #

Generic (ZipList a) 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 #

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 [])))

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])))

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 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.

liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c Source #

Lift a binary function to actions.

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.