lens-4.3.3: Lenses, Folds and Traversals

PortabilityRank2Types
Stabilityprovisional
MaintainerEdward Kmett <ekmett@gmail.com>
Safe HaskellTrustworthy

Control.Lens.Setter

Contents

Description

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 (<$).

Synopsis

Setters

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

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

These can be stated more directly:

 l purepure
 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 aSource

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 tSource

Every IndexedSetter is a valid Setter.

The Setter laws are still required to hold.

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

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 aSource

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 tSource

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

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 aSource

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 bSource

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 bSource

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

Your supplied function f is required to satisfy:

 f idid
 f g . f h ≡ f (g . h)

Equational reasoning:

 setting . overid
 over . settingid

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 bSource

Restore ASetter to a full Setter.

Common Setters

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

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

 fmapover mapped
 fmapDefaultover 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 bSource

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.

 liftMover 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 bSource

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

 contramapover 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 bSource

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 -> tSource

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

 fmapover mapped
 fmapDefaultover traverse
 sets . overid
 over . setsid

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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 -> tSource

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)Source

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 -> tSource

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)Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 ()Source

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 bSource

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 ()Source

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 bSource

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 ()Source

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 ()Source

Write to a fragment of a larger Writer format.

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

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 aSource

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 aSource

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 aSource

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 -> sSource

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 -> tSource

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 -> tSource

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 bSource

Build an IndexedSetter from an imap-like function.

Your supplied function f is required to satisfy:

 f idid
 f g . f h ≡ f (g . h)

Equational reasoning:

 isets . ioverid
 iover . isetsid

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 -> tSource

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 ()Source

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 tSource

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 Source

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) 

Deprecated

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

Deprecated: Use over

mapOf is a deprecated alias for over.