Safe Haskell	Safe
Language	Haskell98

Lens.Family2.Unchecked

Contents

Lenses
Traversals
Documentation
Types
Re-exports

Description

Caution: Improper use of this module can lead to unexpected behaviour if the preconditions of the functions are not met.

Synopsis

lens :: (a -> b) -> (a -> b' -> a') -> Lens a a' b b'
iso :: (a -> b) -> (b' -> a') -> Lens a a' b b'
setting :: ((b -> b') -> a -> a') -> Setter a a' b b'
type Lens a a' b b' = forall f. Functor f => LensLike f a a' b b'
type Lens' a b = forall f. Functor f => LensLike' f a b
type Traversal a a' b b' = forall f. Applicative f => LensLike f a a' b b'
type Traversal' a b = forall f. Applicative f => LensLike' f a b
type Setter a a' b b' = forall f. Identical f => LensLike f a a' b b'
type Setter' a b = forall f. Identical f => LensLike' f a b
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 Applicative f => Identical (f :: * -> *)
class Functor f => Applicative (f :: * -> *)

Lenses

A lens family is created by separating a substructure from the rest of its structure by a functor. How to create a lens family is best illustrated by the common example of a field of a record:

data MyRecord a = MyRecord { _myA :: a, _myB :: Int }

-- The use of type variables a and a' allow for polymorphic updates.
myA :: Lens (MyRecord a) (MyRecord a') a a'
myA f (MyRecord a b) = (\a' -> MyRecord a' b) `fmap` (f a)

-- The field _myB is monomorphic, so we can use a 'Lens'' type.
-- However, the structure of the function is exactly the same as for Lens.
myB :: Lens' (MyRecord a) Int
myB f (MyRecord a b) = (\b' -> MyRecord a b') `fmap` (f b)

By following this template you can safely build your own lenses. To use this template, you do not need anything from this module other than the type synonyms Lens and Lens', and even they are optional. See the lens-family-th package to generate this code using Template Haskell.

Note: It is possible to build lenses without even depending on lens-family by expanding away the type synonym.

-- A lens definition that only requires the Haskell "Prelude".
myA :: Functor f => (a -> f a') -> (MyRecord a) -> f (MyRecord a')
myA f (MyRecord a b) = (\a' -> MyRecord a' b) `fmap` (f a)

You can build lenses for more than just fields of records. Any value l :: Lens a a' b b' is well-defined when it satisfies the two van Laarhoven lens laws:

```
l Identity === Identity
```

l (Compose . fmap f . g) === Compose . fmap (l f) . (l g)

The functions lens and iso can also be used to construct lenses. The resulting lenses will be well-defined so long as their preconditions are satisfied.

Traversals

If you have zero or more fields of the same type of a record, a traversal can be used to refer to all of them in order. Multiple references are made by replacing the Functor constraint of lenses with an Applicative constraint. Consider the following example of a record with two Int fields.

data MyRecord = MyRecord { _myA :: Int, _myB :: Int }

-- myInts is a traversal over both fields of MyRecord.
myInts :: Traversal' MyRecord Int
myInts f (MyRecord a b) = MyRecord <$> f a <*> f b

If the record and the referenced fields are parametric, you can can build traversals with polymorphic updating. Consider the following example of a record with two Maybe fields.

data MyRecord a = MyRecord { _myA :: Maybe a, _myB :: Maybe a }

-- myInts is a traversal over both fields of MyRecord.
myMaybes :: Traversal (MyRecord a) (MyRecord a') (Maybe a) (Maybe a')
myMaybes f (MyRecord a b) = MyRecord <$> f a <*> f b

Note: As with lenses, is possible to build traversals without even depending on lens-family-core by expanding away the type synonym.

-- A traversal definition that only requires the Haskell "Prelude".
myMaybes :: Applicative f => (Maybe a -> f (Maybe a')) -> MyRecord a -> f (MyRecord a')
myMaybes f (MyRecord a b) = MyRecord <$> f a <*> f b

Unfortuantely, there are no helper functions for making traversals. You must make them by hand.

Any value t :: Traversal a a' b b' is well-defined when it satisfies the two van Laarhoven traversal laws:

```
t Identity === Identity
```

t (Compose . fmap f . g) === Compose . fmap (t f) . (t g)

traverse is the canonical traversal for various containers.

Documentation

lens Source #

Arguments

:: (a -> b)	getter
-> (a -> b' -> a')	setter
-> Lens a a' b b'

Build a lens from a getter and setter families.

Caution: In order for the generated lens family to be well-defined, you must ensure that the three lens laws hold:

```
getter (setter a b) === b
```
```
setter a (getter a) === a
```

setter (setter a b1) b2) === setter a b2

iso Source #

Arguments

:: (a -> b)	yin
-> (b' -> a')	yang
-> Lens a a' b b'

Build a lens from isomorphism families.

Caution: In order for the generated lens family to be well-defined, you must ensure that the two isomorphism laws hold:

```
yin . yang === id
```
```
yang . yin === id
```

setting Source #

Arguments

:: ((b -> b') -> a -> a')	sec (semantic editor combinator)
-> Setter a a' b b'

setting promotes a "semantic editor combinator" to a modify-only lens. To demote a lens to a semantic edit combinator, use the section (l %~) or over l from Lens.Family2.

>>> setting map . fstL %~ length $ [("The",0),("quick",1),("brown",1),("fox",2)]
[(3,0),(5,1),(5,1),(3,2)]

Caution: In order for the generated setter family to be well-defined, you must ensure that the two functors laws hold:

```
sec id === id
```
```
sec f . sec g === sec (f . g)
```

Types

type Lens a a' b b' = forall f. Functor f => LensLike f a a' b b' Source #

type Lens' a b = forall f. Functor f => LensLike' f a b Source #

type Traversal a a' b b' = forall f. Applicative f => LensLike f a a' b b' Source #

type Traversal' a b = forall f. Applicative f => LensLike' f a b Source #

type Setter a a' b b' = forall f. Identical f => LensLike f a a' b b' Source #

type Setter' a b = forall f. Identical f => LensLike' f a b Source #

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 Applicative f => Identical (f :: * -> *) #

Minimal complete definition

extract

Instances

Identical Identity
Instance details Defined in Lens.Family.Identical Methods extract :: Identity a -> a
Identical f => Identical (Backwards f)
Instance details Defined in Lens.Family.Identical Methods extract :: Backwards f a -> a
(Identical f, Identical g) => Identical (Compose f g)
Instance details Defined in Lens.Family.Identical Methods extract :: Compose f g a -> a

Re-exports

class Functor f => Applicative (f :: * -> *) #

A functor with application, providing operations to

embed pure expressions (pure), and
sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id

liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

identity

pure id <*> v = v

composition

pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

pure f <*> pure x = pure (f x)

interchange

u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

```
u *> v = (id <$ u) <*> v
```
```
u <* v = liftA2 const u v
```

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

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

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

```
pure = return
```
```
(<*>) = ap
```
```
(*>) = (>>)
```

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Instances

Applicative []	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] # (<>) :: [a -> b] -> [a] -> [b] # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] # (>) :: [a] -> [b] -> [b] # (<*) :: [a] -> [b] -> [a] #
Applicative Maybe	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a # (<>) :: Maybe (a -> b) -> Maybe a -> Maybe b # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c # (>) :: Maybe a -> Maybe b -> Maybe b # (<*) :: Maybe a -> Maybe b -> Maybe a #
Applicative IO	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a # (<>) :: IO (a -> b) -> IO a -> IO b # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c # (>) :: IO a -> IO b -> IO b # (<*) :: IO a -> IO b -> IO a #
Applicative Par1	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Par1 a # (<>) :: Par1 (a -> b) -> Par1 a -> Par1 b # liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c # (>) :: Par1 a -> Par1 b -> Par1 b # (<*) :: Par1 a -> Par1 b -> Par1 a #
Applicative ZipList	f '<$>' 'ZipList' xs1 '<>' ... '<>' 'ZipList' xsN = 'ZipList' (zipWithN f xs1 ... xsN) where `zipWithN` refers to the `zipWith` function of the appropriate arity (`zipWith`, `zipWith3`, `zipWith4`, ...). For example: (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <> ZipList "567" <> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> ZipList a # (<>) :: ZipList (a -> b) -> ZipList a -> ZipList b # liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c # (>) :: ZipList a -> ZipList b -> ZipList b # (<*) :: ZipList a -> ZipList b -> ZipList a #
Applicative Identity	Since: base-4.8.0.0
Instance details Defined in Data.Functor.Identity Methods pure :: a -> Identity a # (<>) :: Identity (a -> b) -> Identity a -> Identity b # liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c # (>) :: Identity a -> Identity b -> Identity b # (<*) :: Identity a -> Identity b -> Identity a #
Applicative First
Instance details Defined in Data.Monoid Methods pure :: a -> First a # (<>) :: First (a -> b) -> First a -> First b # liftA2 :: (a -> b -> c) -> First a -> First b -> First c # (>) :: First a -> First b -> First b # (<*) :: First a -> First b -> First a #
Applicative Last
Instance details Defined in Data.Monoid Methods pure :: a -> Last a # (<>) :: Last (a -> b) -> Last a -> Last b # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c # (>) :: Last a -> Last b -> Last b # (<*) :: Last a -> Last b -> Last a #
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a # (<>) :: Dual (a -> b) -> Dual a -> Dual b # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c # (>) :: Dual a -> Dual b -> Dual b # (<*) :: Dual a -> Dual b -> Dual a #
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Applicative ReadP	Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a # (<>) :: ReadP (a -> b) -> ReadP a -> ReadP b # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c # (>) :: ReadP a -> ReadP b -> ReadP b # (<*) :: ReadP a -> ReadP b -> ReadP a #
Applicative NonEmpty	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a # (<>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c # (>) :: NonEmpty a -> NonEmpty b -> NonEmpty b # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a #
Applicative P	Since: base-4.5.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> P a # (<>) :: P (a -> b) -> P a -> P b # liftA2 :: (a -> b -> c) -> P a -> P b -> P c # (>) :: P a -> P b -> P b # (<*) :: P a -> P b -> P a #
Applicative (Either e)	Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a # (<>) :: Either e (a -> b) -> Either e a -> Either e b # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c # (>) :: Either e a -> Either e b -> Either e b # (<*) :: Either e a -> Either e b -> Either e a #
Applicative (U1 :: * -> *)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> U1 a # (<>) :: U1 (a -> b) -> U1 a -> U1 b # liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c # (>) :: U1 a -> U1 b -> U1 b # (<*) :: U1 a -> U1 b -> U1 a #
Monoid a => Applicative ((,) a)	For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate: ("hello ", (+15)) <> ("world!", 2002) ("hello world!",2017) Since: base-2.1*
Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) # (<>) :: (a, a0 -> b) -> (a, a0) -> (a, b) # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) # (>) :: (a, a0) -> (a, b) -> (a, b) # (<*) :: (a, a0) -> (a, b) -> (a, a0) #
Monad m => Applicative (WrappedMonad m)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #
Arrow a => Applicative (ArrowMonad a)	Since: base-4.6.0.0
Instance details Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 #
Applicative (Proxy :: * -> *)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods pure :: a -> Proxy a # (<>) :: Proxy (a -> b) -> Proxy a -> Proxy b # liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c # (>) :: Proxy a -> Proxy b -> Proxy b # (<*) :: Proxy a -> Proxy b -> Proxy a #
Applicative m => Applicative (ListT m)
Instance details Defined in Control.Monad.Trans.List Methods pure :: a -> ListT m a # (<>) :: ListT m (a -> b) -> ListT m a -> ListT m b # liftA2 :: (a -> b -> c) -> ListT m a -> ListT m b -> ListT m c # (>) :: ListT m a -> ListT m b -> ListT m b # (<*) :: ListT m a -> ListT m b -> ListT m a #
(Functor m, Monad m) => Applicative (MaybeT m)
Instance details Defined in Control.Monad.Trans.Maybe Methods pure :: a -> MaybeT m a # (<>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b # liftA2 :: (a -> b -> c) -> MaybeT m a -> MaybeT m b -> MaybeT m c # (>) :: MaybeT m a -> MaybeT m b -> MaybeT m b # (<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #
Applicative f => Applicative (Rec1 f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> Rec1 f a # (<>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b # liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c # (>) :: Rec1 f a -> Rec1 f b -> Rec1 f b # (<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #
Arrow a => Applicative (WrappedArrow a b)	Since: base-2.1
Instance details Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #
Monoid m => Applicative (Const m :: * -> *)	Since: base-2.0.1
Instance details Defined in Data.Functor.Const Methods pure :: a -> Const m a # (<>) :: Const m (a -> b) -> Const m a -> Const m b # liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c # (>) :: Const m a -> Const m b -> Const m b # (<*) :: Const m a -> Const m b -> Const m a #
Applicative f => Applicative (Alt f)
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a # (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b # liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # (>) :: 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))`. Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a #
(Monoid c, Monad m) => Applicative (Zooming m c)
Instance details Defined in Lens.Family.State.Zoom Methods pure :: a -> Zooming m c a # (<>) :: Zooming m c (a -> b) -> Zooming m c a -> Zooming m c b # liftA2 :: (a -> b -> c0) -> Zooming m c a -> Zooming m c b -> Zooming m c c0 # (>) :: 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 f => Applicative (Backwards f)	Apply `f`-actions in the reverse order.
Instance details Defined in Control.Applicative.Backwards Methods pure :: a -> Backwards f a # (<>) :: Backwards f (a -> b) -> Backwards f a -> Backwards f b # liftA2 :: (a -> b -> c) -> Backwards f a -> Backwards f b -> Backwards f c # (>) :: Backwards f a -> Backwards f b -> Backwards f b # (<*) :: Backwards f a -> Backwards f b -> Backwards f a #
(Functor m, Monad m) => Applicative (StateT s m)
Instance details Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: 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)
Instance details Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a # (<>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c # (>) :: 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 :: * -> *)
Instance details Defined in Data.Functor.Constant Methods pure :: a0 -> Constant a a0 # (<>) :: Constant a (a0 -> b) -> Constant a a0 -> Constant a b # liftA2 :: (a0 -> b -> c) -> Constant a a0 -> Constant a b -> Constant a c # (>) :: Constant a a0 -> Constant a b -> Constant a b # (<*) :: Constant a a0 -> Constant a b -> Constant a a0 #
Applicative m => Applicative (IdentityT m)
Instance details Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a # (<>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c # (>) :: IdentityT m a -> IdentityT m b -> IdentityT m b # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a #
(Functor m, Monad m) => Applicative (ErrorT e m)
Instance details Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a # (<>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c # (>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #
(Functor m, Monad m) => Applicative (ExceptT e m)
Instance details Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a # (<>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c # (>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #
(Monoid w, Applicative m) => Applicative (WriterT w m)
Instance details Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: 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)
Instance details Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a # (<>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c # (>) :: WriterT w m a -> WriterT w m b -> WriterT w m b # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #
Applicative ((->) a :: * -> *)	Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a0 -> a -> a0 # (<>) :: (a -> a0 -> b) -> (a -> a0) -> a -> b # liftA2 :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> c # (>) :: (a -> a0) -> (a -> b) -> a -> b # (<*) :: (a -> a0) -> (a -> b) -> a -> a0 #
(Applicative f, Applicative g) => Applicative (f :*: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :: g) a # (<>) :: (f :: g) (a -> b) -> (f :: g) a -> (f :: g) b # liftA2 :: (a -> b -> c) -> (f :: g) a -> (f :: g) b -> (f :: g) c # (>) :: (f :: g) a -> (f :: g) b -> (f :: g) b # (<) :: (f :: g) a -> (f :: g) b -> (f :: g) a #
(Monad f, Applicative f) => Applicative (WhenMatched f x y)	Equivalent to `ReaderT Key (ReaderT x (ReaderT y (MaybeT f)))` Since: containers-0.5.9
Instance details Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (>) :: 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))` . Since: containers-0.5.9
Instance details Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (>) :: 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 (ContT r m)
Instance details Defined in Control.Monad.Trans.Cont Methods pure :: a -> ContT r m a # (<>) :: ContT r m (a -> b) -> ContT r m a -> ContT r m b # liftA2 :: (a -> b -> c) -> ContT r m a -> ContT r m b -> ContT r m c # (>) :: ContT r m a -> ContT r m b -> ContT r m b # (<*) :: ContT r m a -> ContT r m b -> ContT r m a #
Applicative m => Applicative (ReaderT r m)
Instance details Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a # (<>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c # (>) :: 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 (M1 i c f)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> M1 i c f a # (<>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b # liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 # (>) :: 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 (f :.: g)	Since: base-4.9.0.0
Instance details Defined in GHC.Generics Methods pure :: a -> (f :.: g) a # (<>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b # liftA2 :: (a -> b -> c) -> (f :.: g) a -> (f :.: g) b -> (f :.: g) c # (>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b # (<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #
(Applicative f, Applicative g) => Applicative (Compose f g)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a # (<>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c # (>) :: 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)))` Since: containers-0.5.9
Instance details Defined in Data.Map.Internal 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 # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (>) :: 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 #
(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m)
Instance details Defined in Control.Monad.Trans.RWS.Lazy 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 # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: 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)
Instance details Defined in Control.Monad.Trans.RWS.Strict 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 # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c # (>) :: 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 #