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' = Setter'

type IndexedSetter i s t a b = forall f p. (Indexable i p, Settable f) => p a (f b) -> s -> f t

Every IndexedSetter is a valid Setter.

The Setter laws are still required to hold.

type IndexedSetter' i s a = IndexedSetter i s s a a

 type IndexedSetter' i = Simple (IndexedSetter i)

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 AnIndexedSetter i s t a b = Indexed i a (Identity b) -> s -> Identity t

Running an IndexedSetter 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 AnIndexedSetter' i s a = AnIndexedSetter i s s a a

 type AnIndexedSetter' i = Simple (AnIndexedSetter i)

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

setting :: ((a -> b) -> s -> t) -> IndexPreservingSetter s t a b

Build an index-preserving Setter from a map-like function.

Your supplied function f is required to satisfy:

 f id ≡ id
 f g . f h ≡ f (g . h)

Equational reasoning:

 setting . over ≡ id
 over . setting ≡ id

Another way to view sets is that it takes a "semantic editor combinator" and transforms it into a Setter.

 setting :: ((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.

cloneIndexPreservingSetter :: ASetter s t a b -> IndexPreservingSetter s t a b

Build an IndexPreservingSetter from any Setter.

cloneIndexedSetter :: AnIndexedSetter i s t a b -> IndexedSetter i s t a b

Clone an IndexedSetter.

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 is not a superclass of Monad.

 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 :: Contravariant f => Setter (f b) (f a) a b

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

 contramap ≡ 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 :: Profunctor p => Setting p s t a b -> p 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

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

(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t

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

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

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

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

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

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

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

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

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

(<>~) :: Monoid a => ASetter s t a a -> a -> s -> t

Modify the target of a monoidally valued by mappending another value.

>>> (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!!!")

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

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

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)

Set 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 .~ 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

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)]

 (?~) :: 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)

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 ()

(.=) :: 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 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.

(%=) :: (Profunctor p, MonadState s m) => Setting p s s a b -> p a b -> m ()

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 ()

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 ()

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 ()

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 ()

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 ()

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 ()

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 ()

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 ()

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, Monoid a) => ASetter' s a -> a -> m ()

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

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

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

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

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 ()

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

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 ()

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 alows you to modify just a portion of the resulting MonadWriter.

ipassing :: MonadWriter w m => IndexedSetter i w w u v -> m (a, i -> u -> v) -> m a

This is a generalization of pass that alows you to modify just a portion of the resulting MonadWriter with access to the index of an IndexedSetter.

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

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

icensoring :: MonadWriter w m => IndexedSetter i w w u v -> (i -> u -> v) -> m a -> m a

This is a generalization of censor that alows you to censor just a portion of the resulting MonadWriter, with access to the index of an IndexedSetter.

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

Indexed Setters

imapOf :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

Deprecated: Use iover

Map with index. (Deprecated alias for iover).

When you do not need access to the index, then mapOf is more liberal in what it can accept.

 mapOf l ≡ imapOf l . const

 imapOf :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
 imapOf :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
 imapOf :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

iover :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

Map with index. This is an alias for imapOf.

When you do not need access to the index, then over is more liberal in what it can accept.

 over l ≡ iover l . const
 iover l ≡ over l . Indexed

 iover :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
 iover :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
 iover :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

isets :: ((i -> a -> b) -> s -> t) -> IndexedSetter i s t a b

Build an IndexedSetter from an imap-like function.

Your supplied function f is required to satisfy:

 f id ≡ id
 f g . f h ≡ f (g . h)

Equational reasoning:

 isets . iover ≡ id
 iover . isets ≡ id

Another way to view sets is that it takes a "semantic editor combinator" and transforms it into a Setter.

(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t

Adjust every target of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

 (%@~) ≡ imapOf

When you do not need access to the index then (%@~) is more liberal in what it can accept.

 l %~ f ≡ l %@~ const f

 (%@~) :: IndexedSetter i s t a b    -> (i -> a -> b) -> s -> t
 (%@~) :: IndexedLens i s t a b      -> (i -> a -> b) -> s -> t
 (%@~) :: IndexedTraversal i s t a b -> (i -> a -> b) -> s -> t

(%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()

Adjust every target in the current state of an IndexedSetter, IndexedLens or IndexedTraversal with access to the index.

When you do not need access to the index then (%=) is more liberal in what it can accept.

 l %= f ≡ l %@= const f

 (%@=) :: MonadState s m => IndexedSetter i s s a b    -> (i -> a -> b) -> m ()
 (%@=) :: MonadState s m => IndexedLens i s s a b      -> (i -> a -> b) -> m ()
 (%@=) :: MonadState s m => IndexedTraversal i s t a b -> (i -> a -> b) -> m ()

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, Distributive f, Traversable f) => Settable f

Anything Settable must be isomorphic to the Identity Functor.

Instances

Settable Identity

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

Settable f => Settable (Backwards f)

backwards

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

newtype Identity a

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

Constructors

Identity

Fields

runIdentity :: a

Instances

Monad Identity

Functor Identity

MonadFix Identity

Applicative Identity

Foldable Identity

Traversable Identity

Comonad Identity

ComonadApply Identity

Distributive Identity

Traversable1 Identity

Foldable1 Identity

Apply Identity

Bind Identity

Extend Identity

Eq1 Identity

Ord1 Identity

Read1 Identity

Show1 Identity

Settable Identity

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

TraversableWithIndex () Identity

FoldableWithIndex () Identity

FunctorWithIndex () Identity

Effective Identity r (Const r)

Eq a => Eq (Identity a)

Ord a => Ord (Identity a)

Read a => Read (Identity a)

Show a => Show (Identity a)

Wrapped (Identity a)

Ixed (Identity a)

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

Field1 (Identity a) (Identity b) a b

Each (Identity a) (Identity b) a b

each :: Traversal (Identity a) (Identity b) a b

Deprecated

mapOf :: Profunctor p => Setting p s t a b -> p a b -> s -> t

Deprecated: Use over

mapOf is a deprecated alias for over.