Lens.Family.Stock

This module contains lenses and traversals for common structures in Haskell. It also contains the combinators for lenses and traversals.

Lens Combinators

choosing :: Functor f => LensLike f a a' c c' -> LensLike f b b' c c' -> LensLike f (Either a b) (Either a' b') c c'

choosing :: Lens a a' c c' -> Lens b b' c c' -> Lens (Either a b) (Either a' b') c c'

choosing :: Traversal a a' c c' -> Traversal b b' c c' -> Traversal (Either a b) (Either a' b') c c'

choosing :: Getter a a' c c' -> Getter b b' c c' -> Getter (Either a b) (Either a' b') c c'

choosing :: Fold a a' c c' -> Fold b b' c c' -> Fold (Either a b) (Either a' b') c c'

choosing :: Setter a a' c c' -> Setter b b' c c' -> Setter (Either a b) (Either a' b') c c'

Given two lens/traversal/getter/fold/setter families with the same substructure, make a new lens/traversal/getter/fold/setter on Either.

alongside :: Functor f => LensLike (AlongsideLeft f b2') a1 a1' b1 b1' -> LensLike (AlongsideRight f a1') a2 a2' b2 b2' -> LensLike f (a1, a2) (a1', a2') (b1, b2) (b1', b2')

alongside :: Lens a1 a1' b1 b1' -> Lens a2 a2' b2 b2' -> Lens (a1, a2) (a1', a2') (b1, b2) (b1', b2')

alongside :: Getter a1 a1' b1 b1' -> Getter a2 a2' b2 b2' -> Getter (a1, a2) (a1', a2') (b1, b2) (b1', b2')

Given two lens/getter families, make a new lens/getter on their product.

beside :: Applicative f => LensLike f a a' c c' -> LensLike f b b' c c' -> LensLike f (a, b) (a', b') c c'

beside :: Traversal a a' c c' -> Traversal b' b' c c' -> Traversal (a,b) (a',b') c c'

beside :: Fold a a' c c' -> Fold b' b' c c' -> Fold (a,b) (a',b') c c'

beside :: Setter a a' c c' -> Setter b' b' c c' -> Setter (a,b) (a',b') c c'

Given two traversals/folds/setters referencing a type c, create a traversal/fold/setter on the pair referencing c.

Stock Lenses

_1 :: Functor f => LensLike f (a, b) (a', b) a a'

_1 :: Lens (a, b) (a', b) a a'

Lens on the first element of a pair.

_2 :: Functor f => LensLike f (a, b) (a, b') b b'

_2 :: Lens (a, b) (a, b') b b'

Lens on the second element of a pair.

chosen :: Functor f => LensLike f (Either a a) (Either b b) a b

chosen :: Lens (Either a a) (Either b b) a b

Lens on the Left or Right element of an (Either a a).

ix :: (Eq k, Functor f) => k -> LensLike' f (k -> v) v

ix :: Eq k => k -> Lens' (k -> v) v

Lens on a given point of a function.

at :: (Ord k, Functor f) => k -> LensLike' f (Map k v) (Maybe v)

at :: Ord k => k -> Lens' (Map.Map k v) (Maybe v)

Lens on a given point of a Map.

intAt :: Functor f => Int -> LensLike' f (IntMap v) (Maybe v)

intAt :: Int -> Lens (IntMap.IntMap v) (Maybe v)

Lens on a given point of a IntMap.

at' :: (Ord k, Functor f) => k -> LensLike' f (Map k v) (Maybe v)

at :: Ord k => k -> Lens' (Map.Map k v) (Maybe v)

Lens providing strict access to a given point of a Map.

intAt' :: Functor f => Int -> LensLike' f (IntMap v) (Maybe v)

intAt :: Int -> Lens (IntMap.IntMap v) (Maybe v)

Lens providing strict access to a given point of a IntMap.

contains :: (Ord k, Functor f) => k -> LensLike' f (Set k) Bool

contains :: Ord => k -> Lens' (Set.Set k) Bool

Lens on a given point of a Set.

intContains :: Functor f => Int -> LensLike' f IntSet Bool

intContains :: Int -> Lens' IntSet.IntSet Bool

Lens on a given point of a IntSet.

Stock Traversals

both :: Applicative f => LensLike f (a, a) (b, b) a b

both :: Traversal (a,a) (b,b) a b

Traversals on both elements of a pair (a,a).

_Left :: Applicative f => LensLike f (Either a b) (Either a' b) a a'

_Left :: Traversal (Either a b) (Either a' b) a a'

Traversal on the Left element of an Either.

_Right :: Applicative f => LensLike f (Either a b) (Either a b') b b'

_Right :: Traversal (Either a b) (Either a b') b b'

Traversal on the Right element of an Either.

_Just :: Applicative f => LensLike f (Maybe a) (Maybe a') a a'

_Just :: Traversal (Maybe a) (Maybe a') a a'

Traversal on the Just element of a Maybe.

_Nothing :: Applicative f => LensLike' f (Maybe a) ()

_Nothing :: Traversal' (Maybe a) ()

Traversal on the Nothing element of a Maybe.

ignored :: Applicative f => null -> a -> f a

ignored :: Traversal a a b b'

The empty traversal on any type.

Stock SECs

mapped :: (Identical f, Functor g) => LensLike f (g a) (g a') a a'

mapped :: Functor g => Setter (g a) (g a') a a'

An SEC referencing the parameter of a functor.

Types

data AlongsideLeft f b a

Instances

Functor f => Functor (AlongsideLeft f a)

Methods

fmap :: (a -> b) -> AlongsideLeft f a a -> AlongsideLeft f a b

(<$) :: a -> AlongsideLeft f a b -> AlongsideLeft f a a

Phantom f => Phantom (AlongsideLeft f a)

Methods

coerce :: AlongsideLeft f a a -> AlongsideLeft f a b

data AlongsideRight f a b

Instances

Functor f => Functor (AlongsideRight f a)

Methods

fmap :: (a -> b) -> AlongsideRight f a a -> AlongsideRight f a b

(<$) :: a -> AlongsideRight f a b -> AlongsideRight f a a

Phantom f => Phantom (AlongsideRight f a)

Methods

coerce :: AlongsideRight f a a -> AlongsideRight f a b

Re-exports

type LensLike f a a' b b' = (b -> f b') -> a -> f a'

type LensLike' f a b = (b -> f b) -> a -> f a

class Functor f => Applicative f

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 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 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 ((->) 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)

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 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

(Applicative f, Monad f) => Applicative (WhenMissing f x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)).

Methods

pure :: a -> WhenMissing f x a

(<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b

(*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b

(<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x 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

(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

(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 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

(Monoid c, Monad m) => Applicative (Zooming m c)

Methods

pure :: a -> Zooming m c a

(<*>) :: Zooming m c (a -> b) -> Zooming m c a -> Zooming m c b

(*>) :: Zooming m c a -> Zooming m c b -> Zooming m c b

(<*) :: Zooming m c a -> Zooming m c b -> Zooming m c a

Applicative (IKleeneStore b b')

Methods

pure :: a -> IKleeneStore b b' a

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

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

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

(Monad f, Applicative f) => Applicative (WhenMatched f x y)

Equivalent to ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))

Methods

pure :: a -> WhenMatched f x y a

(<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b

(*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b

(<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a

(Applicative f, Monad f) => Applicative (WhenMissing f k x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)) .

Methods

pure :: a -> WhenMissing f k x a

(<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b

(*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b

(<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x 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

(Monad f, Applicative f) => Applicative (WhenMatched f k x y)

Equivalent to ReaderT k (ReaderT x (ReaderT y (MaybeT f)))

Methods

pure :: a -> WhenMatched f k x y a

(<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b

(*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b

(<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a

class Applicative f => Identical f

Minimal complete definition

extract

Instances

Identical Identity

Methods

extract :: Identity a -> a

Identical f => Identical (Backwards * f)

Methods

extract :: Backwards * f a -> a

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

Methods

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