Diagrams.Prelude

A module to re-export most of the functionality of the diagrams core and standard library.

Diagrams library

Exports from this library for working with diagrams.

module Diagrams

Convenience re-exports from other packages

For working with default values. Diagrams also exports with, an alias for def.

module Data.Default.Class

For representing and operating on colors.

module Data.Colour

A large list of color names.

module Data.Colour.Names

Specify your own colours.

module Data.Colour.SRGB

Semigroups and monoids show up all over the place, so things from Data.Semigroup and Data.Monoid often come in handy.

module Data.Semigroup

For computing with vectors.

module Linear.Vector

For computing with points and vectors.

module Linear.Affine

For computing with dot products and norm.

module Linear.Metric

For working with Active (i.e. animated) things.

module Data.Active

Most of the lens package. The following functions are not exported from lens because they either conflict with diagrams or may conflict with other libraries:

• at
• contains
• .>
• <.>
• index
• indices
• none
• coerce
• indexed
• inside
• levels
• ...
• children
• transform
• outside
• argument
• beside
• singular

module Control.Lens

class Functor f => Applicative f where

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, (<*>)

Instances

Applicative []

Methods

pure :: a -> [a]

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

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

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

Applicative Maybe

Methods

pure :: a -> Maybe a

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

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

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

Applicative IO

Methods

pure :: a -> IO a

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

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

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

Applicative U1

Methods

pure :: a -> U1 a

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

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

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

Applicative Par1

Methods

pure :: a -> Par1 a

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

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

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

Applicative Q

Methods

pure :: a -> Q a

(<*>) :: Q (a -> b) -> Q a -> Q b

(*>) :: Q a -> Q b -> Q b

(<*) :: Q a -> Q b -> Q a

Applicative Active

Methods

pure :: a -> Active a

(<*>) :: Active (a -> b) -> Active a -> Active b

(*>) :: Active a -> Active b -> Active b

(<*) :: Active a -> Active b -> Active a

Applicative Duration

Methods

pure :: a -> Duration a

(<*>) :: Duration (a -> b) -> Duration a -> Duration b

(*>) :: Duration a -> Duration b -> Duration b

(<*) :: Duration a -> Duration b -> Duration a

Applicative Id

Methods

pure :: a -> Id a

(<*>) :: Id (a -> b) -> Id a -> Id b

(*>) :: Id a -> Id b -> Id b

(<*) :: Id a -> Id b -> Id a

Applicative P

Methods

pure :: a -> P a

(<*>) :: P (a -> b) -> P a -> P b

(*>) :: P a -> P b -> P b

(<*) :: P a -> P b -> P a

Applicative Identity

Methods

pure :: a -> Identity a

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

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

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

Applicative Min

Methods

pure :: a -> Min a

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

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

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

Applicative Max

Methods

pure :: a -> Max a

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

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

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

Applicative First

Methods

pure :: a -> First a

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

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

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

Applicative Last

Methods

pure :: a -> Last a

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

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

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

Applicative Option

Methods

pure :: a -> Option a

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

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

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

Applicative NonEmpty

Methods

pure :: a -> NonEmpty a

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

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

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

Applicative Complex

Methods

pure :: a -> Complex a

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

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

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

Applicative ZipList

Methods

pure :: a -> ZipList a

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

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

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

Applicative STM

Methods

pure :: a -> STM a

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

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

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

Applicative Dual

Methods

pure :: a -> Dual a

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

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

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

Applicative Sum

Methods

pure :: a -> Sum a

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

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

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

Applicative Product

Methods

pure :: a -> Product a

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

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

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

Applicative First

Methods

pure :: a -> First a

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

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

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

Applicative Last

Methods

pure :: a -> Last a

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

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

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

Applicative ReadPrec

Methods

pure :: a -> ReadPrec a

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

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

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

Applicative ReadP

Methods

pure :: a -> ReadP a

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

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

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

Applicative Id

Methods

pure :: a -> Id a

(<*>) :: Id (a -> b) -> Id a -> Id b

(*>) :: Id a -> Id b -> Id b

(<*) :: Id a -> Id b -> Id a

Applicative Get

Methods

pure :: a -> Get a

(<*>) :: Get (a -> b) -> Get a -> Get b

(*>) :: Get a -> Get b -> Get b

(<*) :: Get a -> Get b -> Get a

Applicative Get

Methods

pure :: a -> Get a

(<*>) :: Get (a -> b) -> Get a -> Get b

(*>) :: Get a -> Get b -> Get b

(<*) :: Get a -> Get b -> Get a

Applicative RGB

Methods

pure :: a -> RGB a

(<*>) :: RGB (a -> b) -> RGB a -> RGB b

(*>) :: RGB a -> RGB b -> RGB b

(<*) :: RGB a -> RGB b -> RGB a

Applicative Tree

Methods

pure :: a -> Tree a

(<*>) :: Tree (a -> b) -> Tree a -> Tree b

(*>) :: Tree a -> Tree b -> Tree b

(<*) :: Tree a -> Tree b -> Tree a

Applicative Seq

Methods

pure :: a -> Seq a

(<*>) :: Seq (a -> b) -> Seq a -> Seq b

(*>) :: Seq a -> Seq b -> Seq b

(<*) :: Seq a -> Seq b -> Seq a

Applicative Interval

Methods

pure :: a -> Interval a

(<*>) :: Interval (a -> b) -> Interval a -> Interval b

(*>) :: Interval a -> Interval b -> Interval b

(<*) :: Interval a -> Interval b -> Interval a

Applicative Vector

Methods

pure :: a -> Vector a

(<*>) :: Vector (a -> b) -> Vector a -> Vector b

(*>) :: Vector a -> Vector b -> Vector b

(<*) :: Vector a -> Vector b -> Vector a

Applicative Quaternion

Methods

pure :: a -> Quaternion a

(<*>) :: Quaternion (a -> b) -> Quaternion a -> Quaternion b

(*>) :: Quaternion a -> Quaternion b -> Quaternion b

(<*) :: Quaternion a -> Quaternion b -> Quaternion a

Applicative Plucker

Methods

pure :: a -> Plucker a

(<*>) :: Plucker (a -> b) -> Plucker a -> Plucker b

(*>) :: Plucker a -> Plucker b -> Plucker b

(<*) :: Plucker a -> Plucker b -> Plucker a

Applicative V4

Methods

pure :: a -> V4 a

(<*>) :: V4 (a -> b) -> V4 a -> V4 b

(*>) :: V4 a -> V4 b -> V4 b

(<*) :: V4 a -> V4 b -> V4 a

Applicative V3

Methods

pure :: a -> V3 a

(<*>) :: V3 (a -> b) -> V3 a -> V3 b

(*>) :: V3 a -> V3 b -> V3 b

(<*) :: V3 a -> V3 b -> V3 a

Applicative V2

Methods

pure :: a -> V2 a

(<*>) :: V2 (a -> b) -> V2 a -> V2 b

(*>) :: V2 a -> V2 b -> V2 b

(<*) :: V2 a -> V2 b -> V2 a

Applicative V1

Methods

pure :: a -> V1 a

(<*>) :: V1 (a -> b) -> V1 a -> V1 b

(*>) :: V1 a -> V1 b -> V1 b

(<*) :: V1 a -> V1 b -> V1 a

Applicative V0

Methods

pure :: a -> V0 a

(<*>) :: V0 (a -> b) -> V0 a -> V0 b

(*>) :: V0 a -> V0 b -> V0 b

(<*) :: V0 a -> V0 b -> V0 a

Applicative ReadM

Methods

pure :: a -> ReadM a

(<*>) :: ReadM (a -> b) -> ReadM a -> ReadM b

(*>) :: ReadM a -> ReadM b -> ReadM b

(<*) :: ReadM a -> ReadM b -> ReadM a

Applicative Parser

Methods

pure :: a -> Parser a

(<*>) :: Parser (a -> b) -> Parser a -> Parser b

(*>) :: Parser a -> Parser b -> Parser b

(<*) :: Parser a -> Parser b -> Parser a

Applicative ParserM

Methods

pure :: a -> ParserM a

(<*>) :: ParserM (a -> b) -> ParserM a -> ParserM b

(*>) :: ParserM a -> ParserM b -> ParserM b

(<*) :: ParserM a -> ParserM b -> ParserM a

Applicative ParserResult

Methods

pure :: a -> ParserResult a

(<*>) :: ParserResult (a -> b) -> ParserResult a -> ParserResult b

(*>) :: ParserResult a -> ParserResult b -> ParserResult b

(<*) :: ParserResult a -> ParserResult b -> ParserResult a

Applicative Id

Methods

pure :: a -> Id a

(<*>) :: Id (a -> b) -> Id a -> Id b

(*>) :: Id a -> Id b -> Id b

(<*) :: Id a -> Id b -> Id a

Applicative Box

Methods

pure :: a -> Box a

(<*>) :: Box (a -> b) -> Box a -> Box b

(*>) :: Box a -> Box b -> Box b

(<*) :: Box a -> Box b -> Box a

Applicative Stream

Methods

pure :: a -> Stream a

(<*>) :: Stream (a -> b) -> Stream a -> Stream b

(*>) :: Stream a -> Stream b -> Stream b

(<*) :: Stream a -> Stream b -> Stream a

Applicative Angle

Methods

pure :: a -> Angle a

(<*>) :: Angle (a -> b) -> Angle a -> Angle b

(*>) :: Angle a -> Angle b -> Angle b

(<*) :: Angle a -> Angle b -> Angle a

Applicative ((->) a)

Methods

pure :: a -> a -> a

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

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

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

Applicative (Either e)

Methods

pure :: a -> Either e a

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

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

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

Applicative f => Applicative (Rec1 f)

Methods

pure :: a -> Rec1 f a

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

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

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

Monoid a => Applicative ((,) a)

Methods

pure :: a -> (a, a)

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

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

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

Representable f => Applicative (Co f)

Methods

pure :: a -> Co f a

(<*>) :: Co f (a -> b) -> Co f a -> Co f b

(*>) :: Co f a -> Co f b -> Co f b

(<*) :: Co f a -> Co f b -> Co f a

Applicative (ST s)

Methods

pure :: a -> ST s a

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

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

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

Applicative (StateL s)

Methods

pure :: a -> StateL s a

(<*>) :: StateL s (a -> b) -> StateL s a -> StateL s b

(*>) :: StateL s a -> StateL s b -> StateL s b

(<*) :: StateL s a -> StateL s b -> StateL s a

Applicative (StateR s)

Methods

pure :: a -> StateR s a

(<*>) :: StateR s (a -> b) -> StateR s a -> StateR s b

(*>) :: StateR s a -> StateR s b -> StateR s b

(<*) :: StateR s a -> StateR s b -> StateR s a

Applicative (ST s)

Methods

pure :: a -> ST s a

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

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

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

Monad m => Applicative (WrappedMonad m)

Methods

pure :: a -> WrappedMonad m a

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

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

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

Arrow a => Applicative (ArrowMonad a)

Methods

pure :: a -> ArrowMonad a a

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

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

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

Applicative (Proxy *)

Methods

pure :: a -> Proxy * a

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

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

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

Applicative (StateL s)

Methods

pure :: a -> StateL s a

(<*>) :: StateL s (a -> b) -> StateL s a -> StateL s b

(*>) :: StateL s a -> StateL s b -> StateL s b

(<*) :: StateL s a -> StateL s b -> StateL s a

Applicative (StateR s)

Methods

pure :: a -> StateR s a

(<*>) :: StateR s (a -> b) -> StateR s a -> StateR s b

(*>) :: StateR s a -> StateR s b -> StateR s b

(<*) :: StateR s a -> StateR s b -> StateR s a

Applicative (State s)

Methods

pure :: a -> State s a

(<*>) :: State s (a -> b) -> State s a -> State s b

(*>) :: State s a -> State s b -> State s b

(<*) :: State s a -> State s b -> State s a

Applicative (Measured n)

Methods

pure :: a -> Measured n a

(<*>) :: Measured n (a -> b) -> Measured n a -> Measured n b

(*>) :: Measured n a -> Measured n b -> Measured n b

(<*) :: Measured n a -> Measured n b -> Measured n a

Applicative f => Applicative (Point f)

Methods

pure :: a -> Point f a

(<*>) :: Point f (a -> b) -> Point f a -> Point f b

(*>) :: Point f a -> Point f b -> Point f b

(<*) :: Point f a -> Point f b -> Point f a

Alternative f => Applicative (Cofree f)

Methods

pure :: a -> Cofree f a

(<*>) :: Cofree f (a -> b) -> Cofree f a -> Cofree f b

(*>) :: Cofree f a -> Cofree f b -> Cofree f b

(<*) :: Cofree f a -> Cofree f b -> Cofree f a

Applicative f => Applicative (Yoneda f)

Methods

pure :: a -> Yoneda f a

(<*>) :: Yoneda f (a -> b) -> Yoneda f a -> Yoneda f b

(*>) :: Yoneda f a -> Yoneda f b -> Yoneda f b

(<*) :: Yoneda f a -> Yoneda f b -> Yoneda f a

Applicative (ReifiedGetter s)

Methods

pure :: a -> ReifiedGetter s a

(<*>) :: ReifiedGetter s (a -> b) -> ReifiedGetter s a -> ReifiedGetter s b

(*>) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s b

(<*) :: ReifiedGetter s a -> ReifiedGetter s b -> ReifiedGetter s a

Applicative (ReifiedFold s)

Methods

pure :: a -> ReifiedFold s a

(<*>) :: ReifiedFold s (a -> b) -> ReifiedFold s a -> ReifiedFold s b

(*>) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s b

(<*) :: ReifiedFold s a -> ReifiedFold s b -> ReifiedFold s a

Applicative f => Applicative (Indexing f)

Methods

pure :: a -> Indexing f a

(<*>) :: Indexing f (a -> b) -> Indexing f a -> Indexing f b

(*>) :: Indexing f a -> Indexing f b -> Indexing f b

(<*) :: Indexing f a -> Indexing f b -> Indexing f a

Applicative f => Applicative (Indexing64 f)

Methods

pure :: a -> Indexing64 f a

(<*>) :: Indexing64 f (a -> b) -> Indexing64 f a -> Indexing64 f b

(*>) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f b

(<*) :: Indexing64 f a -> Indexing64 f b -> Indexing64 f a

Applicative m => Applicative (ListT m)

Methods

pure :: a -> ListT m a

(<*>) :: ListT m (a -> b) -> ListT m a -> ListT m b

(*>) :: ListT m a -> ListT m b -> ListT m b

(<*) :: ListT m a -> ListT m b -> ListT m a

(Applicative (Rep p), Representable p) => Applicative (Prep p)

Methods

pure :: a -> Prep p a

(<*>) :: Prep p (a -> b) -> Prep p a -> Prep p b

(*>) :: Prep p a -> Prep p b -> Prep p b

(<*) :: Prep p a -> Prep p b -> Prep p a

Applicative f => Applicative (WrappedApplicative f)

Methods

pure :: a -> WrappedApplicative f a

(<*>) :: WrappedApplicative f (a -> b) -> WrappedApplicative f a -> WrappedApplicative f b

(*>) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f b

(<*) :: WrappedApplicative f a -> WrappedApplicative f b -> WrappedApplicative f a

Apply f => Applicative (MaybeApply f)

Methods

pure :: a -> MaybeApply f a

(<*>) :: MaybeApply f (a -> b) -> MaybeApply f a -> MaybeApply f b

(*>) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f b

(<*) :: MaybeApply f a -> MaybeApply f b -> MaybeApply f a

(Functor m, Monad m) => Applicative (MaybeT m)

Methods

pure :: a -> MaybeT m a

(<*>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b

(*>) :: MaybeT m a -> MaybeT m b -> MaybeT m b

(<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a

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

Methods

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

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

(*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b

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

(Applicative f, Applicative g) => Applicative ((:.:) f g)

Methods

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

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

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

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

Arrow a => Applicative (WrappedArrow a b)

Methods

pure :: a -> WrappedArrow a b a

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

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

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

Monoid m => Applicative (Const * m)

Methods

pure :: a -> Const * m a

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

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

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

Applicative f => Applicative (Alt * f)

Methods

pure :: a -> Alt * f a

(<*>) :: Alt * f (a -> b) -> Alt * f a -> Alt * f b

(*>) :: Alt * f a -> Alt * f b -> Alt * f b

(<*) :: Alt * f a -> Alt * f b -> Alt * f a

Biapplicative p => Applicative (Join * p)

Methods

pure :: a -> Join * p a

(<*>) :: Join * p (a -> b) -> Join * p a -> Join * p b

(*>) :: Join * p a -> Join * p b -> Join * p b

(<*) :: Join * p a -> Join * p b -> Join * p a

Applicative w => Applicative (TracedT m w)

Methods

pure :: a -> TracedT m w a

(<*>) :: TracedT m w (a -> b) -> TracedT m w a -> TracedT m w b

(*>) :: TracedT m w a -> TracedT m w b -> TracedT m w b

(<*) :: TracedT m w a -> TracedT m w b -> TracedT m w a

Applicative (Cokleisli w a)

Methods

pure :: a -> Cokleisli w a a

(<*>) :: Cokleisli w a (a -> b) -> Cokleisli w a a -> Cokleisli w a b

(*>) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a b

(<*) :: Cokleisli w a a -> Cokleisli w a b -> Cokleisli w a a

Applicative m => Applicative (IdentityT * m)

Methods

pure :: a -> IdentityT * m a

(<*>) :: IdentityT * m (a -> b) -> IdentityT * m a -> IdentityT * m b

(*>) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m b

(<*) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m a

Applicative (Query v n)

Methods

pure :: a -> Query v n a

(<*>) :: Query v n (a -> b) -> Query v n a -> Query v n b

(*>) :: Query v n a -> Query v n b -> Query v n b

(<*) :: Query v n a -> Query v n b -> Query v n a

(Functor f, Monad m) => Applicative (FreeT f m)

Methods

pure :: a -> FreeT f m a

(<*>) :: FreeT f m (a -> b) -> FreeT f m a -> FreeT f m b

(*>) :: FreeT f m a -> FreeT f m b -> FreeT f m b

(<*) :: FreeT f m a -> FreeT f m b -> FreeT f m a

(Applicative f, Applicative g) => Applicative (Day f g)

Methods

pure :: a -> Day f g a

(<*>) :: Day f g (a -> b) -> Day f g a -> Day f g b

(*>) :: Day f g a -> Day f g b -> Day f g b

(<*) :: Day f g a -> Day f g b -> Day f g a

Applicative f => Applicative (Backwards * f)

Apply f-actions in the reverse order.

Methods

pure :: a -> Backwards * f a

(<*>) :: Backwards * f (a -> b) -> Backwards * f a -> Backwards * f b

(*>) :: Backwards * f a -> Backwards * f b -> Backwards * f b

(<*) :: Backwards * f a -> Backwards * f b -> Backwards * f a

(Functor m, Monad m) => Applicative (ErrorT e m)

Methods

pure :: a -> ErrorT e m a

(<*>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b

(*>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b

(<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a

Applicative (Indexed i a)

Methods

pure :: a -> Indexed i a a

(<*>) :: Indexed i a (a -> b) -> Indexed i a a -> Indexed i a b

(*>) :: Indexed i a a -> Indexed i a b -> Indexed i a b

(<*) :: Indexed i a a -> Indexed i a b -> Indexed i a a

(Monad m, Monoid s) => Applicative (Focusing m s)

Methods

pure :: a -> Focusing m s a

(<*>) :: Focusing m s (a -> b) -> Focusing m s a -> Focusing m s b

(*>) :: Focusing m s a -> Focusing m s b -> Focusing m s b

(<*) :: Focusing m s a -> Focusing m s b -> Focusing m s a

Applicative (k (May s)) => Applicative (FocusingMay k s)

Methods

pure :: a -> FocusingMay k s a

(<*>) :: FocusingMay k s (a -> b) -> FocusingMay k s a -> FocusingMay k s b

(*>) :: FocusingMay k s a -> FocusingMay k s b -> FocusingMay k s b

(<*) :: FocusingMay k s a -> FocusingMay k s b -> FocusingMay k s a

(Monad m, Monoid r) => Applicative (Effect m r)

Methods

pure :: a -> Effect m r a

(<*>) :: Effect m r (a -> b) -> Effect m r a -> Effect m r b

(*>) :: Effect m r a -> Effect m r b -> Effect m r b

(<*) :: Effect m r a -> Effect m r b -> Effect m r a

Dim k n => Applicative (V k n)

Methods

pure :: a -> V k n a

(<*>) :: V k n (a -> b) -> V k n a -> V k n b

(*>) :: V k n a -> V k n b -> V k n b

(<*) :: V k n a -> V k n b -> V k n a

(Functor m, Monad m) => Applicative (ExceptT e m)

Methods

pure :: a -> ExceptT e m a

(<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b

(*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b

(<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a

(Functor m, Monad m) => Applicative (StateT s m)

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(*>) :: StateT s m a -> StateT s m b -> StateT s m b

(<*) :: StateT s m a -> StateT s m b -> StateT s m a

(Functor m, Monad m) => Applicative (StateT s m)

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

(*>) :: StateT s m a -> StateT s m b -> StateT s m b

(<*) :: StateT s m a -> StateT s m b -> StateT s m a

(Monoid w, Applicative m) => Applicative (WriterT w m)

Methods

pure :: a -> WriterT w m a

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a

(Monoid w, Applicative m) => Applicative (WriterT w m)

Methods

pure :: a -> WriterT w m a

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a

(Profunctor p, Arrow p) => Applicative (Tambara p a)

Methods

pure :: a -> Tambara p a a

(<*>) :: Tambara p a (a -> b) -> Tambara p a a -> Tambara p a b

(*>) :: Tambara p a a -> Tambara p a b -> Tambara p a b

(<*) :: Tambara p a a -> Tambara p a b -> Tambara p a a

Applicative f => Applicative (Star f a)

Methods

pure :: a -> Star f a a

(<*>) :: Star f a (a -> b) -> Star f a a -> Star f a b

(*>) :: Star f a a -> Star f a b -> Star f a b

(<*) :: Star f a a -> Star f a b -> Star f a a

Applicative (Costar f a)

Methods

pure :: a -> Costar f a a

(<*>) :: Costar f a (a -> b) -> Costar f a a -> Costar f a b

(*>) :: Costar f a a -> Costar f a b -> Costar f a b

(<*) :: Costar f a a -> Costar f a b -> Costar f a a

Applicative (Tagged k s)

Methods

pure :: a -> Tagged k s a

(<*>) :: Tagged k s (a -> b) -> Tagged k s a -> Tagged k s b

(*>) :: Tagged k s a -> Tagged k s b -> Tagged k s b

(<*) :: Tagged k s a -> Tagged k s b -> Tagged k s a

Applicative f => Applicative (Reverse * f)

Derived instance.

Methods

pure :: a -> Reverse * f a

(<*>) :: Reverse * f (a -> b) -> Reverse * f a -> Reverse * f b

(*>) :: Reverse * f a -> Reverse * f b -> Reverse * f b

(<*) :: Reverse * f a -> Reverse * f b -> Reverse * f a

Monoid a => Applicative (Constant * a)

Methods

pure :: a -> Constant * a a

(<*>) :: Constant * a (a -> b) -> Constant * a a -> Constant * a b

(*>) :: Constant * a a -> Constant * a b -> Constant * a b

(<*) :: Constant * a a -> Constant * a b -> Constant * a a

Applicative f => Applicative (M1 i c f)

Methods

pure :: a -> M1 i c f a

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a

(Applicative f, Applicative g) => Applicative (Product * f g)

Methods

pure :: a -> Product * f g a

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

(*>) :: Product * f g a -> Product * f g b -> Product * f g b

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

(Monad m, Monoid s, Monoid w) => Applicative (FocusingWith w m s)

Methods

pure :: a -> FocusingWith w m s a

(<*>) :: FocusingWith w m s (a -> b) -> FocusingWith w m s a -> FocusingWith w m s b

(*>) :: FocusingWith w m s a -> FocusingWith w m s b -> FocusingWith w m s b

(<*) :: FocusingWith w m s a -> FocusingWith w m s b -> FocusingWith w m s a

Applicative (k (s, w)) => Applicative (FocusingPlus w k s)

Methods

pure :: a -> FocusingPlus w k s a

(<*>) :: FocusingPlus w k s (a -> b) -> FocusingPlus w k s a -> FocusingPlus w k s b

(*>) :: FocusingPlus w k s a -> FocusingPlus w k s b -> FocusingPlus w k s b

(<*) :: FocusingPlus w k s a -> FocusingPlus w k s b -> FocusingPlus w k s a

Applicative (k (f s)) => Applicative (FocusingOn f k s)

Methods

pure :: a -> FocusingOn f k s a

(<*>) :: FocusingOn f k s (a -> b) -> FocusingOn f k s a -> FocusingOn f k s b

(*>) :: FocusingOn f k s a -> FocusingOn f k s b -> FocusingOn f k s b

(<*) :: FocusingOn f k s a -> FocusingOn f k s b -> FocusingOn f k s a

Applicative (k (Err e s)) => Applicative (FocusingErr e k s)

Methods

pure :: a -> FocusingErr e k s a

(<*>) :: FocusingErr e k s (a -> b) -> FocusingErr e k s a -> FocusingErr e k s b

(*>) :: FocusingErr e k s a -> FocusingErr e k s b -> FocusingErr e k s b

(<*) :: FocusingErr e k s a -> FocusingErr e k s b -> FocusingErr e k s a

Applicative (ContT k r m)

Methods

pure :: a -> ContT k r m a

(<*>) :: ContT k r m (a -> b) -> ContT k r m a -> ContT k r m b

(*>) :: ContT k r m a -> ContT k r m b -> ContT k r m b

(<*) :: ContT k r m a -> ContT k r m b -> ContT k r m a

Applicative m => Applicative (ReaderT * r m)

Methods

pure :: a -> ReaderT * r m a

(<*>) :: ReaderT * r m (a -> b) -> ReaderT * r m a -> ReaderT * r m b

(*>) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m b

(<*) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m a

(Applicative f, Applicative g) => Applicative (Compose * * f g)

Methods

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

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

(*>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b

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

Applicative (k (Freed f m s)) => Applicative (FocusingFree f m k s)

Methods

pure :: a -> FocusingFree f m k s a

(<*>) :: FocusingFree f m k s (a -> b) -> FocusingFree f m k s a -> FocusingFree f m k s b

(*>) :: FocusingFree f m k s a -> FocusingFree f m k s b -> FocusingFree f m k s b

(<*) :: FocusingFree f m k s a -> FocusingFree f m k s b -> FocusingFree f m k s a

(Monoid s, Monoid w, Monad m) => Applicative (EffectRWS w st m s)

Methods

pure :: a -> EffectRWS w st m s a

(<*>) :: EffectRWS w st m s (a -> b) -> EffectRWS w st m s a -> EffectRWS w st m s b

(*>) :: EffectRWS w st m s a -> EffectRWS w st m s b -> EffectRWS w st m s b

(<*) :: EffectRWS w st m s a -> EffectRWS w st m s b -> EffectRWS w st m s a

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

Methods

pure :: a -> RWST r w s m a

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)

Methods

pure :: a -> RWST r w s m a

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a

Reifies k s (ReifiedApplicative f) => Applicative (ReflectedApplicative k * f s)

Methods

pure :: a -> ReflectedApplicative k * f s a

(<*>) :: ReflectedApplicative k * f s (a -> b) -> ReflectedApplicative k * f s a -> ReflectedApplicative k * f s b

(*>) :: ReflectedApplicative k * f s a -> ReflectedApplicative k * f s b -> ReflectedApplicative k * f s b

(<*) :: ReflectedApplicative k * f s a -> ReflectedApplicative k * f s b -> ReflectedApplicative k * f s a

(*>) :: Applicative f => forall a b. f a -> f b -> f b

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

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 => forall a b. a -> f b -> f a

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.

liftA :: Applicative f => (a -> b) -> f a -> f b

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

Lift a binary function to actions.

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Lift a ternary function to actions.