Control.Lens.Setter

A Setter s t a b is a generalization of fmap from Functor. It allows you to map into a structure and change out the contents, but it isn't strong enough to allow you to enumerate those contents. Starting with fmap :: Functor f => (a -> b) -> f a -> f b we monomorphize the type to obtain (a -> b) -> s -> t and then decorate it with Identity to obtain:

type Setter s t a b = (a -> Identity b) -> s -> Identity t

Every Traversal is a valid Setter, since Identity is Applicative.

Everything you can do with a Functor, you can do with a Setter. There are combinators that generalize fmap and (<$).

Setters

type Setter s t a b = forall f. Settable f => (a -> f b) -> s -> f t

The only LensLike law that can apply to a Setter l is that

set l y (set l x a) ≡ set l y a

You can't view a Setter in general, so the other two laws are irrelevant.

However, two Functor laws apply to a Setter:

over l id ≡ id
over l f . over l g ≡ over l (f . g)

These can be stated more directly:

l pure ≡ pure
l f . untainted . l g ≡ l (f . untainted . g)

You can compose a Setter with a Lens or a Traversal using (.) from the Prelude and the result is always only a Setter and nothing more.

>>> over traverse f [a,b,c,d]
[f a,f b,f c,f d]

>>> over _1 f (a,b)
(f a,b)

>>> over (traverse._1) f [(a,b),(c,d)]
[(f a,b),(f c,d)]

>>> over both f (a,b)
(f a,f b)

>>> over (traverse.both) f [(a,b),(c,d)]
[(f a,f b),(f c,f d)]

type Setter' s a = Setter s s a a

A Setter' is just a Setter that doesn't change the types.

These are particularly common when talking about monomorphic containers. e.g.

sets Data.Text.map :: Setter' Text Char

type Setter' = Simple Setter

type ASetter s t a b = (a -> Identity b) -> s -> Identity t

Running a Setter instantiates it to a concrete type.

When consuming a setter directly to perform a mapping, you can use this type, but most user code will not need to use this type.

type ASetter' s a = ASetter s s a a

This is a useful alias for use when consuming a Setter'.

Most user code will never have to use this type.

type ASetter' = Simple ASetter

type Setting p s t a b = p a (Identity b) -> s -> Identity t

This is a convenient alias when defining highly polymorphic code that takes both ASetter and AnIndexedSetter as appropriate. If a function takes this it is expecting one of those two things based on context.

type Setting' p s a = Setting p s s a a

This is a convenient alias when defining highly polymorphic code that takes both ASetter' and AnIndexedSetter' as appropriate. If a function takes this it is expecting one of those two things based on context.

Building Setters

sets :: (Profunctor p, Profunctor q, Settable f) => (p a b -> q s t) -> Optical p q f s t a b

Build a Setter, IndexedSetter or IndexPreservingSetter depending on your choice of Profunctor.

sets :: ((a -> b) -> s -> t) -> Setter s t a b

cloneSetter :: ASetter s t a b -> Setter s t a b

Restore ASetter to a full Setter.

Common Setters

mapped :: Functor f => Setter (f a) (f b) a b

This Setter can be used to map over all of the values in a Functor.

fmap ≡ over mapped
fmapDefault ≡ over traverse
(<$) ≡ set mapped

>>> over mapped f [a,b,c]
[f a,f b,f c]

>>> over mapped (+1) [1,2,3]
[2,3,4]

>>> set mapped x [a,b,c]
[x,x,x]

>>> [[a,b],[c]] & mapped.mapped +~ x
[[a + x,b + x],[c + x]]

>>> over (mapped._2) length [("hello","world"),("leaders","!!!")]
[("hello",5),("leaders",3)]

mapped :: Functor f => Setter (f a) (f b) a b

If you want an IndexPreservingSetter use setting fmap.

lifted :: Monad m => Setter (m a) (m b) a b

This setter can be used to modify all of the values in a Monad.

You sometimes have to use this rather than mapped -- due to temporary insanity Functor was not a superclass of Monad until GHC 7.10.

liftM ≡ over lifted

>>> over lifted f [a,b,c]
[f a,f b,f c]

>>> set lifted b (Just a)
Just b

If you want an IndexPreservingSetter use setting liftM.

contramapped :: Functor f => Setter (f b) (f a) a b

This Setter can be used to map over all of the inputs to a Functor.

gmap ≡ over contramapped

>>> getPredicate (over contramapped (*2) (Predicate even)) 5
True

>>> getOp (over contramapped (*5) (Op show)) 100
"500"

>>> Prelude.map ($ 1) $ over (mapped . _Unwrapping' Op . contramapped) (*12) [(*2),(+1),(^3)]
[24,13,1728]

argument :: Profunctor p => Setter (p b r) (p a r) a b

This Setter can be used to map over the input of a Profunctor.

The most common Profunctor to use this with is (->).

>>> (argument %~ f) g x
g (f x)

>>> (argument %~ show) length [1,2,3]
7

>>> (argument %~ f) h x y
h (f x) y

Map over the argument of the result of a function -- i.e., its second argument:

>>> (mapped.argument %~ f) h x y
h x (f y)

argument :: Setter (b -> r) (a -> r) a b

Functional Combinators

over :: ASetter s t a b -> (a -> b) -> s -> t

Modify the target of a Lens or all the targets of a Setter or Traversal with a function.

fmap ≡ over mapped
fmapDefault ≡ over traverse
sets . over ≡ id
over . sets ≡ id

Given any valid Setter l, you can also rely on the law:

over l f . over l g = over l (f . g)

e.g.

>>> over mapped f (over mapped g [a,b,c]) == over mapped (f . g) [a,b,c]
True

Another way to view over is to say that it transforms a Setter into a "semantic editor combinator".

>>> over mapped f (Just a)
Just (f a)

>>> over mapped (*10) [1,2,3]
[10,20,30]

>>> over _1 f (a,b)
(f a,b)

>>> over _1 show (10,20)
("10",20)

over :: Setter s t a b -> (a -> b) -> s -> t
over :: ASetter s t a b -> (a -> b) -> s -> t

set :: ASetter s t a b -> b -> s -> t

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

(<$) ≡ set mapped

>>> set _2 "hello" (1,())
(1,"hello")

>>> set mapped () [1,2,3,4]
[(),(),(),()]

Note: Attempting to set a Fold or Getter will fail at compile time with an relatively nice error message.

set :: Setter s t a b    -> b -> s -> t
set :: Iso s t a b       -> b -> s -> t
set :: Lens s t a b      -> b -> s -> t
set :: Traversal s t a b -> b -> s -> t

(.~) :: ASetter s t a b -> b -> s -> t infixr 4

Replace the target of a Lens or all of the targets of a Setter or Traversal with a constant value.

This is an infix version of set, provided for consistency with (.=).

f <$ a ≡ mapped .~ f $ a

>>> (a,b,c,d) & _4 .~ e
(a,b,c,e)

>>> (42,"world") & _1 .~ "hello"
("hello","world")

>>> (a,b) & both .~ c
(c,c)

(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

(%~) :: ASetter s t a b -> (a -> b) -> s -> t infixr 4

Modifies the target of a Lens or all of the targets of a Setter or Traversal with a user supplied function.

This is an infix version of over.

fmap f ≡ mapped %~ f
fmapDefault f ≡ traverse %~ f

>>> (a,b,c) & _3 %~ f
(a,b,f c)

>>> (a,b) & both %~ f
(f a,f b)

>>> _2 %~ length $ (1,"hello")
(1,5)

>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]

>>> traverse %~ even $ [1,2,3]
[False,True,False]

>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]

(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

(+~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4

Increment the target(s) of a numerically valued Lens, Setter or Traversal.

>>> (a,b) & _1 +~ c
(a + c,b)

>>> (a,b) & both +~ c
(a + c,b + c)

>>> (1,2) & _2 +~ 1
(1,3)

>>> [(a,b),(c,d)] & traverse.both +~ e
[(a + e,b + e),(c + e,d + e)]

(+~) :: Num a => Setter' s a    -> a -> s -> s
(+~) :: Num a => Iso' s a       -> a -> s -> s
(+~) :: Num a => Lens' s a      -> a -> s -> s
(+~) :: Num a => Traversal' s a -> a -> s -> s

(-~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4

Decrement the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 -~ c
(a - c,b)

>>> (a,b) & both -~ c
(a - c,b - c)

>>> _1 -~ 2 $ (1,2)
(-1,2)

>>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
[[3,4],[5,6]]

(-~) :: Num a => Setter' s a    -> a -> s -> s
(-~) :: Num a => Iso' s a       -> a -> s -> s
(-~) :: Num a => Lens' s a      -> a -> s -> s
(-~) :: Num a => Traversal' s a -> a -> s -> s

(*~) :: Num a => ASetter s t a a -> a -> s -> t infixr 4

Multiply the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 *~ c
(a * c,b)

>>> (a,b) & both *~ c
(a * c,b * c)

>>> (1,2) & _2 *~ 4
(1,8)

>>> Just 24 & mapped *~ 2
Just 48

(*~) :: Num a => Setter' s a    -> a -> s -> s
(*~) :: Num a => Iso' s a       -> a -> s -> s
(*~) :: Num a => Lens' s a      -> a -> s -> s
(*~) :: Num a => Traversal' s a -> a -> s -> s

(//~) :: Fractional a => ASetter s t a a -> a -> s -> t infixr 4

Divide the target(s) of a numerically valued Lens, Iso, Setter or Traversal.

>>> (a,b) & _1 //~ c
(a / c,b)

>>> (a,b) & both //~ c
(a / c,b / c)

>>> ("Hawaii",10) & _2 //~ 2
("Hawaii",5.0)

(//~) :: Fractional a => Setter' s a    -> a -> s -> s
(//~) :: Fractional a => Iso' s a       -> a -> s -> s
(//~) :: Fractional a => Lens' s a      -> a -> s -> s
(//~) :: Fractional a => Traversal' s a -> a -> s -> s

(^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

>>> (1,3) & _2 ^~ 2
(1,9)

(^~) :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
(^~) :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
(^~) :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
(^~) :: (Num a, Integral e) => Traversal' s a -> e -> s -> s

(^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t infixr 4

Raise the target(s) of a fractionally valued Lens, Setter or Traversal to an integral power.

>>> (1,2) & _2 ^^~ (-1)
(1,0.5)

(^^~) :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
(^^~) :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s

(**~) :: Floating a => ASetter s t a a -> a -> s -> t infixr 4

Raise the target(s) of a floating-point valued Lens, Setter or Traversal to an arbitrary power.

>>> (a,b) & _1 **~ c
(a**c,b)

>>> (a,b) & both **~ c
(a**c,b**c)

>>> _2 **~ 10 $ (3,2)
(3,1024.0)

(**~) :: Floating a => Setter' s a    -> a -> s -> s
(**~) :: Floating a => Iso' s a       -> a -> s -> s
(**~) :: Floating a => Lens' s a      -> a -> s -> s
(**~) :: Floating a => Traversal' s a -> a -> s -> s

(||~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4

Logically || the target(s) of a Bool-valued Lens or Setter.

>>> both ||~ True $ (False,True)
(True,True)

>>> both ||~ False $ (False,True)
(False,True)

(||~) :: Setter' s Bool    -> Bool -> s -> s
(||~) :: Iso' s Bool       -> Bool -> s -> s
(||~) :: Lens' s Bool      -> Bool -> s -> s
(||~) :: Traversal' s Bool -> Bool -> s -> s

(<>~) :: Semigroup a => ASetter s t a a -> a -> s -> t infixr 4

Modify the target of a Semigroup value by using (<>).

>>> (Sum a,b) & _1 <>~ Sum c
(Sum {getSum = a + c},b)

>>> (Sum a,Sum b) & both <>~ Sum c
(Sum {getSum = a + c},Sum {getSum = b + c})

>>> both <>~ "!!!" $ ("hello","world")
("hello!!!","world!!!")

(<>~) :: Semigroup a => Setter s t a a    -> a -> s -> t
(<>~) :: Semigroup a => Iso s t a a       -> a -> s -> t
(<>~) :: Semigroup a => Lens s t a a      -> a -> s -> t
(<>~) :: Semigroup a => Traversal s t a a -> a -> s -> t

(&&~) :: ASetter s t Bool Bool -> Bool -> s -> t infixr 4

Logically && the target(s) of a Bool-valued Lens or Setter.

>>> both &&~ True $ (False, True)
(False,True)

>>> both &&~ False $ (False, True)
(False,False)

(&&~) :: Setter' s Bool    -> Bool -> s -> s
(&&~) :: Iso' s Bool       -> Bool -> s -> s
(&&~) :: Lens' s Bool      -> Bool -> s -> s
(&&~) :: Traversal' s Bool -> Bool -> s -> s

(<.~) :: ASetter s t a b -> b -> s -> (b, t) infixr 4

Set with pass-through.

This is mostly present for consistency, but may be useful for chaining assignments.

If you do not need a copy of the intermediate result, then using l .~ t directly is a good idea.

>>> (a,b) & _1 <.~ c
(c,(c,b))

>>> ("good","morning","vietnam") & _3 <.~ "world"
("world",("good","morning","world"))

>>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
(Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<.~) :: Setter s t a b    -> b -> s -> (b, t)
(<.~) :: Iso s t a b       -> b -> s -> (b, t)
(<.~) :: Lens s t a b      -> b -> s -> (b, t)
(<.~) :: Traversal s t a b -> b -> s -> (b, t)

(?~) :: ASetter s t a (Maybe b) -> b -> s -> t infixr 4

Set the target of a Lens, Traversal or Setter to Just a value.

l ?~ t ≡ set l (Just t)

>>> Nothing & id ?~ a
Just a

>>> Map.empty & at 3 ?~ x
fromList [(3,x)]

?~ can be used type-changily:

>>> ('a', ('b', 'c')) & _2.both ?~ 'x'
('a',(Just 'x',Just 'x'))

(?~) :: Setter s t a (Maybe b)    -> b -> s -> t
(?~) :: Iso s t a (Maybe b)       -> b -> s -> t
(?~) :: Lens s t a (Maybe b)      -> b -> s -> t
(?~) :: Traversal s t a (Maybe b) -> b -> s -> t

(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t) infixr 4

Set to Just a value with pass-through.

This is mostly present for consistency, but may be useful for for chaining assignments.

If you do not need a copy of the intermediate result, then using l ?~ d directly is a good idea.

>>> import Data.Map as Map
>>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
("world",(42,fromList [("goodnight","gracie"),("hello","world")]))

(<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
(<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
(<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
(<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)

State Combinators

assign :: MonadState s m => ASetter s s a b -> b -> m ()

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an alias for (.=).

>>> execState (do assign _1 c; assign _2 d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

assign :: MonadState s m => Iso' s a       -> a -> m ()
assign :: MonadState s m => Lens' s a      -> a -> m ()
assign :: MonadState s m => Traversal' s a -> a -> m ()
assign :: MonadState s m => Setter' s a    -> a -> m ()

modifying :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()

This is an alias for (%=).

(.=) :: MonadState s m => ASetter s s a b -> b -> m () infix 4

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with a new value, irrespective of the old.

This is an infix version of assign.

>>> execState (do _1 .= c; _2 .= d) (a,b)
(c,d)

>>> execState (both .= c) (a,b)
(c,c)

(.=) :: MonadState s m => Iso' s a       -> a -> m ()
(.=) :: MonadState s m => Lens' s a      -> a -> m ()
(.=) :: MonadState s m => Traversal' s a -> a -> m ()
(.=) :: MonadState s m => Setter' s a    -> a -> m ()

It puts the state in the monad or it gets the hose again.

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m () infix 4

Map over the target of a Lens or all of the targets of a Setter or Traversal in our monadic state.

>>> execState (do _1 %= f;_2 %= g) (a,b)
(f a,g b)

>>> execState (do both %= f) (a,b)
(f a,f b)

(%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
(%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
(%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
(%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()

(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()

(+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by adding a value.

Example:

fresh :: MonadState Int m => m Int
fresh = do
  id += 1
  use id

>>> execState (do _1 += c; _2 += d) (a,b)
(a + c,b + d)

>>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
(fromList [(1,10),(2,100)],"hello")

(+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by subtracting a value.

>>> execState (do _1 -= c; _2 -= d) (a,b)
(a - c,b - d)

(-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by multiplying by value.

>>> execState (do _1 *= c; _2 *= d) (a,b)
(a * c,b * d)

(*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

(//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by dividing by a value.

>>> execState (do _1 //= c; _2 //= d) (a,b)
(a / c,b / d)

(//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()

(^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m () infix 4

Raise the target(s) of a numerically valued Lens, Setter or Traversal to a non-negative integral power.

(^=) ::  (MonadState s m, Num a, Integral e) => Setter' s a    -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Iso' s a       -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Lens' s a      -> e -> m ()
(^=) ::  (MonadState s m, Num a, Integral e) => Traversal' s a -> e -> m ()

(^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m () infix 4

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an integral power.

(^^=) ::  (MonadState s m, Fractional a, Integral e) => Setter' s a    -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Iso' s a       -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Lens' s a      -> e -> m ()
(^^=) ::  (MonadState s m, Fractional a, Integral e) => Traversal' s a -> e -> m ()

(**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m () infix 4

Raise the target(s) of a numerically valued Lens, Setter or Traversal to an arbitrary power

>>> execState (do _1 **= c; _2 **= d) (a,b)
(a**c,b**d)

(**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()

(||=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4

Modify the target(s) of a Lens', 'Iso, Setter or Traversal by taking their logical || with a value.

>>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
(True,True,True,False)

(||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(<>=) :: (MonadState s m, Semigroup a) => ASetter' s a -> a -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by using (<>).

>>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
(Sum {getSum = a + c},Product {getProduct = b * d})

>>> execState (both <>= "!!!") ("hello","world")
("hello!!!","world!!!")

(<>=) :: (MonadState s m, Semigroup a) => Setter' s a -> a -> m ()
(<>=) :: (MonadState s m, Semigroup a) => Iso' s a -> a -> m ()
(<>=) :: (MonadState s m, Semigroup a) => Lens' s a -> a -> m ()
(<>=) :: (MonadState s m, Semigroup a) => Traversal' s a -> a -> m ()

(&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m () infix 4

Modify the target(s) of a Lens', Iso, Setter or Traversal by taking their logical && with a value.

>>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
(True,False,False,False)

(&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(<.=) :: MonadState s m => ASetter s s a b -> b -> m b infix 4

Set with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- _2 <.= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l .= d will avoid unused binding warnings.

(<.=) :: MonadState s m => Setter s s a b    -> b -> m b
(<.=) :: MonadState s m => Iso s s a b       -> b -> m b
(<.=) :: MonadState s m => Lens s s a b      -> b -> m b
(<.=) :: MonadState s m => Traversal s s a b -> b -> m b

(?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m () infix 4

Replace the target of a Lens or all of the targets of a Setter or Traversal in our monadic state with Just a new value, irrespective of the old.

>>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
fromList [(1,a),(2,b)]

>>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
(Just b,Just c)

(?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
(?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
(?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
(?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()

(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b infix 4

Set Just a value with pass-through

This is useful for chaining assignment without round-tripping through your Monad stack.

do x <- at "foo" <?= ninety_nine_bottles_of_beer_on_the_wall

If you do not need a copy of the intermediate result, then using l ?= d will avoid unused binding warnings.

(<?=) :: MonadState s m => Setter s s a (Maybe b)    -> b -> m b
(<?=) :: MonadState s m => Iso s s a (Maybe b)       -> b -> m b
(<?=) :: MonadState s m => Lens s s a (Maybe b)      -> b -> m b
(<?=) :: MonadState s m => Traversal s s a (Maybe b) -> b -> m b

(<~) :: MonadState s m => ASetter s s a b -> m b -> m () infixr 2

Run a monadic action, and set all of the targets of a Lens, Setter or Traversal to its result.

(<~) :: MonadState s m => Iso s s a b       -> m b -> m ()
(<~) :: MonadState s m => Lens s s a b      -> m b -> m ()
(<~) :: MonadState s m => Traversal s s a b -> m b -> m ()
(<~) :: MonadState s m => Setter s s a b    -> m b -> m ()

As a reasonable mnemonic, this lets you store the result of a monadic action in a Lens rather than in a local variable.

do foo <- bar
   ...

will store the result in a variable, while

do foo <~ bar
   ...

will store the result in a Lens, Setter, or Traversal.

Writer Combinators

scribe :: (MonadWriter t m, Monoid s) => ASetter s t a b -> b -> m ()

Write to a fragment of a larger Writer format.

passing :: MonadWriter w m => Setter w w u v -> m (a, u -> v) -> m a

This is a generalization of pass that allows you to modify just a portion of the resulting MonadWriter.

censoring :: MonadWriter w m => Setter w w u v -> (u -> v) -> m a -> m a

This is a generalization of censor that allows you to censor just a portion of the resulting MonadWriter.

Reader Combinators

locally :: MonadReader s m => ASetter s s a b -> (a -> b) -> m r -> m r

Modify the value of the Reader environment associated with the target of a Setter, Lens, or Traversal.

locally l id a ≡ a
locally l f . locally l g ≡ locally l (f . g)

>>> (1,1) & locally _1 (+1) (uncurry (+))
3

>>> "," & locally ($) ("Hello" <>) (<> " world!")
"Hello, world!"

locally :: MonadReader s m => Iso s s a b       -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Lens s s a b      -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Traversal s s a b -> (a -> b) -> m r -> m r
locally :: MonadReader s m => Setter s s a b    -> (a -> b) -> m r -> m r

Simplified State Setting

set' :: ASetter' s a -> a -> s -> s

Replace the target of a Lens or all of the targets of a Setter' or Traversal with a constant value, without changing its type.

This is a type restricted version of set, which retains the type of the original.

>>> set' mapped x [a,b,c,d]
[x,x,x,x]

>>> set' _2 "hello" (1,"world")
(1,"hello")

>>> set' mapped 0 [1,2,3,4]
[0,0,0,0]

Note: Attempting to adjust set' a Fold or Getter will fail at compile time with an relatively nice error message.

set' :: Setter' s a    -> a -> s -> s
set' :: Iso' s a       -> a -> s -> s
set' :: Lens' s a      -> a -> s -> s
set' :: Traversal' s a -> a -> s -> s

Arrow operators

assignA :: Arrow p => ASetter s t a b -> p s b -> p s t

Run an arrow command and use the output to set all the targets of a Lens, Setter or Traversal to the result.

assignA can be used very similarly to (<~), except that the type of the object being modified can change; for example:

runKleisli action ((), (), ()) where
  action =      assignA _1 (Kleisli (const getVal1))
           >>> assignA _2 (Kleisli (const getVal2))
           >>> assignA _3 (Kleisli (const getVal3))
  getVal1 :: Either String Int
  getVal1 = ...
  getVal2 :: Either String Bool
  getVal2 = ...
  getVal3 :: Either String Char
  getVal3 = ...

has the type Either String (Int, Bool, Char)

assignA :: Arrow p => Iso s t a b       -> p s b -> p s t
assignA :: Arrow p => Lens s t a b      -> p s b -> p s t
assignA :: Arrow p => Traversal s t a b -> p s b -> p s t
assignA :: Arrow p => Setter s t a b    -> p s b -> p s t

Exported for legible error messages

class (Applicative f, Cotraversable f, Traversable f) => Settable f

Anything Settable must be isomorphic to the Identity Functor.

Minimal complete definition

untainted

Instances

Settable Identity

So you can pass our Setter into combinators from other lens libraries.

Defined in Control.Lens.Internal.Setter

Methods

untainted :: Identity a -> a

untaintedDot :: Profunctor p => p a (Identity b) -> p a b

taintedDot :: Profunctor p => p a b -> p a (Identity b)

Settable f => Settable (Backwards f)

backwards

Defined in Control.Lens.Internal.Setter

Methods

untainted :: Backwards f a -> a

untaintedDot :: Profunctor p => p a (Backwards f b) -> p a b

taintedDot :: Profunctor p => p a b -> p a (Backwards f b)

(Settable f, Settable g) => Settable (Compose f g)

Defined in Control.Lens.Internal.Setter

Methods

untainted :: Compose f g a -> a

untaintedDot :: Profunctor p => p a (Compose f g b) -> p a b

taintedDot :: Profunctor p => p a b -> p a (Compose f g b)

newtype Identity a

Identity functor and monad. (a non-strict monad)

Since: base-4.8.0.0

Constructors

Identity

Fields

• runIdentity :: a

Instances

Monad Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

return :: a -> Identity a

fail :: String -> Identity a

Functor Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

MonadFix Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

mfix :: (a -> Identity a) -> Identity a

Applicative Identity

Since: base-4.8.0.0

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

Foldable Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

fold :: Monoid m => Identity m -> m

foldMap :: Monoid m => (a -> m) -> Identity a -> m

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

foldr' :: (a -> b -> b) -> b -> Identity a -> b

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

foldl' :: (b -> a -> b) -> b -> Identity a -> b

foldr1 :: (a -> a -> a) -> Identity a -> a

foldl1 :: (a -> a -> a) -> Identity a -> a

toList :: Identity a -> [a]

null :: Identity a -> Bool

length :: Identity a -> Int

elem :: Eq a => a -> Identity a -> Bool

maximum :: Ord a => Identity a -> a

minimum :: Ord a => Identity a -> a

sum :: Num a => Identity a -> a

product :: Num a => Identity a -> a

Traversable Identity

Since: base-4.9.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b)

sequenceA :: Applicative f => Identity (f a) -> f (Identity a)

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b)

sequence :: Monad m => Identity (m a) -> m (Identity a)

Eq1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Identity a -> Identity b -> Bool

Ord1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Identity a -> Identity b -> Ordering

Read1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Identity a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Identity a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Identity a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Identity a]

Show1 Identity

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Identity a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Identity a] -> ShowS

Foldable1 Identity

Defined in Data.Foldable1

Methods

fold1 :: Semigroup a => Identity a -> a

foldMap1 :: Semigroup b => (a -> b) -> Identity a -> b

foldr1 :: (a -> a -> a) -> Identity a -> a

foldl1 :: (a -> a -> a) -> Identity a -> a

foldr1' :: (a -> a -> a) -> Identity a -> a

foldl1' :: (a -> a -> a) -> Identity a -> a

toNonEmpty :: Identity a -> NonEmpty a

maximum :: Ord a => Identity a -> a

minimum :: Ord a => Identity a -> a

Cotraversable Identity

Defined in Data.Cotraversable

Methods

collect :: Functor g => (a -> Identity b) -> g a -> Identity (g b)

cosequence :: Functor g => g (Identity a) -> Identity (g a)

cotraverse :: Functor g => (g a -> b) -> g (Identity a) -> Identity b

Comonad Identity

Defined in Control.Comonad

Methods

copure :: Identity a -> a

cut :: Identity a -> Identity (Identity a)

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

Settable Identity

So you can pass our Setter into combinators from other lens libraries.

Defined in Control.Lens.Internal.Setter

Methods

untainted :: Identity a -> a

untaintedDot :: Profunctor p => p a (Identity b) -> p a b

taintedDot :: Profunctor p => p a b -> p a (Identity b)

Bounded a => Bounded (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

minBound :: Identity a

maxBound :: Identity a

Enum a => Enum (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

succ :: Identity a -> Identity a

pred :: Identity a -> Identity a

toEnum :: Int -> Identity a

fromEnum :: Identity a -> Int

enumFrom :: Identity a -> [Identity a]

enumFromThen :: Identity a -> Identity a -> [Identity a]

enumFromTo :: Identity a -> Identity a -> [Identity a]

enumFromThenTo :: Identity a -> Identity a -> Identity a -> [Identity a]

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

(==) :: Identity a -> Identity a -> Bool

(/=) :: Identity a -> Identity a -> Bool

Floating a => Floating (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

pi :: Identity a

exp :: Identity a -> Identity a

log :: Identity a -> Identity a

sqrt :: Identity a -> Identity a

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

logBase :: Identity a -> Identity a -> Identity a

sin :: Identity a -> Identity a

cos :: Identity a -> Identity a

tan :: Identity a -> Identity a

asin :: Identity a -> Identity a

acos :: Identity a -> Identity a

atan :: Identity a -> Identity a

sinh :: Identity a -> Identity a

cosh :: Identity a -> Identity a

tanh :: Identity a -> Identity a

asinh :: Identity a -> Identity a

acosh :: Identity a -> Identity a

atanh :: Identity a -> Identity a

log1p :: Identity a -> Identity a

expm1 :: Identity a -> Identity a

log1pexp :: Identity a -> Identity a

log1mexp :: Identity a -> Identity a

Fractional a => Fractional (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(/) :: Identity a -> Identity a -> Identity a

recip :: Identity a -> Identity a

fromRational :: Rational -> Identity a

Integral a => Integral (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

quot :: Identity a -> Identity a -> Identity a

rem :: Identity a -> Identity a -> Identity a

div :: Identity a -> Identity a -> Identity a

mod :: Identity a -> Identity a -> Identity a

quotRem :: Identity a -> Identity a -> (Identity a, Identity a)

divMod :: Identity a -> Identity a -> (Identity a, Identity a)

toInteger :: Identity a -> Integer

Data a => Data (Identity a)

Since: base-4.9.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Identity a -> c (Identity a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Identity a)

toConstr :: Identity a -> Constr

dataTypeOf :: Identity a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Identity a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Identity a))

gmapT :: (forall b. Data b => b -> b) -> Identity a -> Identity a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Identity a -> r

gmapQ :: (forall d. Data d => d -> u) -> Identity a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Identity a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Identity a -> m (Identity a)

Num a => Num (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

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

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> Identity a

Ord a => Ord (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

compare :: Identity a -> Identity a -> Ordering

(<) :: Identity a -> Identity a -> Bool

(<=) :: Identity a -> Identity a -> Bool

(>) :: Identity a -> Identity a -> Bool

(>=) :: Identity a -> Identity a -> Bool

max :: Identity a -> Identity a -> Identity a

min :: Identity a -> Identity a -> Identity a

Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

readsPrec :: Int -> ReadS (Identity a)

readList :: ReadS [Identity a]

readPrec :: ReadPrec (Identity a)

readListPrec :: ReadPrec [Identity a]

Real a => Real (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

toRational :: Identity a -> Rational

RealFloat a => RealFloat (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

floatRadix :: Identity a -> Integer

floatDigits :: Identity a -> Int

floatRange :: Identity a -> (Int, Int)

decodeFloat :: Identity a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Identity a

exponent :: Identity a -> Int

significand :: Identity a -> Identity a

scaleFloat :: Int -> Identity a -> Identity a

isNaN :: Identity a -> Bool

isInfinite :: Identity a -> Bool

isDenormalized :: Identity a -> Bool

isNegativeZero :: Identity a -> Bool

isIEEE :: Identity a -> Bool

atan2 :: Identity a -> Identity a -> Identity a

RealFrac a => RealFrac (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

properFraction :: Integral b => Identity a -> (b, Identity a)

truncate :: Integral b => Identity a -> b

round :: Integral b => Identity a -> b

ceiling :: Integral b => Identity a -> b

floor :: Integral b => Identity a -> b

Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

showsPrec :: Int -> Identity a -> ShowS

show :: Identity a -> String

showList :: [Identity a] -> ShowS

Ix a => Ix (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

range :: (Identity a, Identity a) -> [Identity a]

index :: (Identity a, Identity a) -> Identity a -> Int

unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int

inRange :: (Identity a, Identity a) -> Identity a -> Bool

rangeSize :: (Identity a, Identity a) -> Int

unsafeRangeSize :: (Identity a, Identity a) -> Int

Generic (Identity a)

Defined in Data.Functor.Identity

Associated Types

type Rep (Identity a) :: Type -> Type

Methods

from :: Identity a -> Rep (Identity a) x

to :: Rep (Identity a) x -> Identity a

Semigroup a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

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

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Storable a => Storable (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

sizeOf :: Identity a -> Int

alignment :: Identity a -> Int

peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a)

pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Identity a)

pokeByteOff :: Ptr b -> Int -> Identity a -> IO ()

peek :: Ptr (Identity a) -> IO (Identity a)

poke :: Ptr (Identity a) -> Identity a -> IO ()

Bits a => Bits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(.&.) :: Identity a -> Identity a -> Identity a

(.|.) :: Identity a -> Identity a -> Identity a

xor :: Identity a -> Identity a -> Identity a

complement :: Identity a -> Identity a

shift :: Identity a -> Int -> Identity a

rotate :: Identity a -> Int -> Identity a

zeroBits :: Identity a

bit :: Int -> Identity a

setBit :: Identity a -> Int -> Identity a

clearBit :: Identity a -> Int -> Identity a

complementBit :: Identity a -> Int -> Identity a

testBit :: Identity a -> Int -> Bool

bitSizeMaybe :: Identity a -> Maybe Int

bitSize :: Identity a -> Int

isSigned :: Identity a -> Bool

shiftL :: Identity a -> Int -> Identity a

unsafeShiftL :: Identity a -> Int -> Identity a

shiftR :: Identity a -> Int -> Identity a

unsafeShiftR :: Identity a -> Int -> Identity a

rotateL :: Identity a -> Int -> Identity a

rotateR :: Identity a -> Int -> Identity a

popCount :: Identity a -> Int

FiniteBits a => FiniteBits (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

finiteBitSize :: Identity a -> Int

countLeadingZeros :: Identity a -> Int

countTrailingZeros :: Identity a -> Int

Prim a => Prim (Identity a)

Since: primitive-0.6.5.0

Defined in Data.Primitive.Types

Methods

sizeOf# :: Identity a -> Int#

alignment# :: Identity a -> Int#

indexByteArray# :: ByteArray# -> Int# -> Identity a

readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (#State# s, Identity a#)

writeByteArray# :: MutableByteArray# s -> Int# -> Identity a -> State# s -> State# s

setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Identity a -> State# s -> State# s

indexOffAddr# :: Addr# -> Int# -> Identity a

readOffAddr# :: Addr# -> Int# -> State# s -> (#State# s, Identity a#)

writeOffAddr# :: Addr# -> Int# -> Identity a -> State# s -> State# s

setOffAddr# :: Addr# -> Int# -> Int# -> Identity a -> State# s -> State# s

Wrapped (Identity a)

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Identity a) :: Type

Methods

_Wrapped' :: Iso' (Identity a) (Unwrapped (Identity a))

Generic1 Identity

Defined in Data.Functor.Identity

Associated Types

type Rep1 Identity :: k -> Type

Methods

from1 :: Identity a -> Rep1 Identity a

to1 :: Rep1 Identity a -> Identity a

t ~ Identity b => Rewrapped (Identity a) t

Defined in Control.Lens.Wrapped

Field1 (Identity a) (Identity b) a b

Defined in Control.Lens.Tuple

Methods

_1 :: Lens (Identity a) (Identity b) a b

type Rep (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

type Rep (Identity a) = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

type Unwrapped (Identity a)

Defined in Control.Lens.Wrapped

type Unwrapped (Identity a) = a

type Rep1 Identity

Since: base-4.8.0.0

Defined in Data.Functor.Identity

type Rep1 Identity = D1 (MetaData "Identity" "Data.Functor.Identity" "base" True) (C1 (MetaCons "Identity" PrefixI True) (S1 (MetaSel (Just "runIdentity") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))