base-4.9.1.0: Basic libraries

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 [] # |
Methods pure :: a -> [a] Source # (<*>) :: [a -> b] -> [a] -> [b] Source # (*>) :: [a] -> [b] -> [b] Source # (<*) :: [a] -> [b] -> [a] Source #
Applicative Maybe # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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) # |
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) # |
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) # |
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) # |
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) # |
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 *) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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 [] # |
Methods empty :: [a] Source # (<|>) :: [a] -> [a] -> [a] Source # some :: [a] -> [[a]] Source # many :: [a] -> [[a]] Source #
Alternative Maybe # |
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 # |
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 # |
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 # |
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 # |
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 # |
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 # |
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) # |
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 *) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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 *) # |
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 *) # |
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 *) # |
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 *) # |
Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const * a c -> Const * b d -> Ordering Source #
Eq2 (Const *) # |
Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const * a c -> Const * b d -> Bool Source #
Functor (Const * m) # |
Methods fmap :: (a -> b) -> Const * m a -> Const * m b Source # (<$) :: a -> Const * m b -> Const * m a Source #
Monoid m => Applicative (Const * m) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
Methods liftCompare :: (a -> b -> Ordering) -> Const * a a -> Const * a b -> Ordering Source #
Eq a => Eq1 (Const * a) # |
Methods liftEq :: (a -> b -> Bool) -> Const * a a -> Const * a b -> Bool Source #
Bounded a => Bounded (Const k a b) # |
Methods minBound :: Const k a b Source # maxBound :: Const k a b Source #
Enum a => Enum (Const k a b) # |
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) # |
Methods (==) :: Const k a b -> Const k a b -> Bool Source # (/=) :: Const k a b -> Const k a b -> Bool Source #
Floating a => Floating (Const k a b) # |
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) # |
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) # |
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) # |
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) # |
Methods compare :: Const k a b -> Const k a b -> Ordering Source # (<) :: Const k a b -> Const k a b -> Bool Source # (<=) :: Const k a b -> Const k a b -> Bool Source # (>) :: Const k a b -> Const k a b -> Bool Source # (>=) :: Const k a b -> Const k a b -> Bool Source # max :: Const k a b -> Const k a b -> Const k a b Source # min :: Const k a b -> Const k a b -> Const k a b Source #
Read a => Read (Const k a b) # | This instance would be equivalent to the derived instances of the `Const` newtype if the `runConst` field were removed
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) # |
Methods toRational :: Const k a b -> Rational Source #
RealFloat a => RealFloat (Const k a b) # |
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) # |
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) # | 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) # |
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) # |
Methods fromString :: String -> Const * a b Source #
Generic (Const k a b) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
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) # |
Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source #
Monad m => Applicative (WrappedMonad m) # |
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) # |
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) # |
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) # |
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) # |
type Rep1 (WrappedMonad m) = D1 (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 (MetaCons "WrapMonad" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 m)))
type Rep (WrappedMonad m a) # |
type Rep (WrappedMonad m a) = D1 (MetaData "WrappedMonad" "Control.Applicative" "base" True) (C1 (MetaCons "WrapMonad" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapMonad") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (m a))))

newtype WrappedArrow a b c Source #

Constructors

WrapArrow |
Fields unwrapArrow :: a b c

Instances

Arrow a => Functor (WrappedArrow a b) # |
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) # |
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) # |
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) # |
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) # |
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) # |
type Rep1 (WrappedArrow a b) = D1 (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 (MetaCons "WrapArrow" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (a b))))
type Rep (WrappedArrow a b c) # |
type Rep (WrappedArrow a b c) = D1 (MetaData "WrappedArrow" "Control.Applicative" "base" True) (C1 (MetaCons "WrapArrow" PrefixI True) (S1 (MetaSel (Just Symbol "unwrapArrow") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a b c))))

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 # |
Methods fmap :: (a -> b) -> ZipList a -> ZipList b Source # (<$) :: a -> ZipList b -> ZipList a Source #
Applicative ZipList # |
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 # |
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 # |
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 # |
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) # |
Methods (==) :: ZipList a -> ZipList a -> Bool Source # (/=) :: ZipList a -> ZipList a -> Bool Source #
Ord a => Ord (ZipList a) # |
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) # |
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) # |
Methods showsPrec :: Int -> ZipList a -> ShowS Source # show :: ZipList a -> String Source # showList :: [ZipList a] -> ShowS Source #
Generic (ZipList a) # |
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 # |
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) # |
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.