Portability | non-portable |
---|---|

Stability | experimental |

Maintainer | Edward Kmett <ekmett@gmail.com> |

Safe Haskell | None |

This module exists for users who like to work with qualified imports but want access to the operators from Lens.

import qualified Control.Lens as L import Control.Lens.Operators

- (&) :: a -> (a -> b) -> b
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- (??) :: Functor f => f (a -> b) -> a -> f b
- (^.) :: s -> Getting a s t a b -> a
- (^@.) :: s -> IndexedGetting i (i, a) s t a b -> (i, a)
- (^#) :: s -> ALens s t a b -> a
- (^!) :: Monad m => s -> Acting m a s t a b -> m a
- (^@!) :: Monad m => s -> IndexedActing i m (i, a) s t a b -> m (i, a)
- (^!!) :: Monad m => s -> Acting m [a] s t a b -> m [a]
- (^@!!) :: Monad m => s -> IndexedActing i m [(i, a)] s t a b -> m [(i, a)]
- (^!?) :: Monad m => s -> Acting m (Leftmost a) s t a b -> m (Maybe a)
- (^@!?) :: Monad m => s -> IndexedActing i m (Leftmost (i, a)) s t a b -> m (Maybe (i, a))
- (^..) :: s -> Getting (Endo [a]) s t a b -> [a]
- (^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s t a b -> [(i, a)]
- (^?) :: s -> Getting (First a) s t a b -> Maybe a
- (^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s t a b -> Maybe (i, a)
- (^?!) :: s -> Getting (Endo a) s t a b -> a
- (^@?!) :: s -> IndexedGetting i (Endo (i, a)) s t a b -> (i, a)
- (.~) :: ASetter s t a b -> b -> s -> t
- (.=) :: MonadState s m => ASetter s s a b -> b -> m ()
- (<.~) :: ASetter s t a b -> b -> s -> (b, t)
- (<.=) :: MonadState s m => ASetter s s a b -> b -> m b
- (<<.~) :: Overloading (->) q ((,) a) s t a b -> b -> q s (a, t)
- (<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a
- (#~) :: ALens s t a b -> b -> s -> t
- (#=) :: MonadState s m => ALens s s a b -> b -> m ()
- (<#~) :: ALens s t a b -> b -> s -> (b, t)
- (<#=) :: MonadState s m => ALens s s a b -> b -> m b
- (?~) :: ASetter s t a (Maybe b) -> b -> s -> t
- (?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()
- (<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)
- (<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b
- (%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t
- (%=) :: (Profunctor p, MonadState s m) => Setting p s s a b -> p a b -> m ()
- (<%~) :: Profunctor p => Overloading p q ((,) b) s t a b -> p a b -> q s (b, t)
- (<%=) :: (Profunctor p, MonadState s m) => Overloading p (->) ((,) b) s s a b -> p a b -> m b
- (<<%~) :: Strong p => Overloading p q ((,) a) s t a b -> p a b -> q s (a, t)
- (<<%=) :: (Strong p, MonadState s m) => Overloading p (->) ((,) a) s s a b -> p a b -> m a
- (#%~) :: ALens s t a b -> (a -> b) -> s -> t
- (#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()
- (<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t)
- (<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b
- (%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
- (%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()
- (<%@~) :: Overloading (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t)
- (<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b
- (%%~) :: Overloading p q f s t a b -> p a (f b) -> q s (f t)
- (%%=) :: MonadState s m => Overloading p (->) ((,) r) s s a b -> p a (r, b) -> m r
- (#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
- (#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
- (%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f t
- (%%@=) :: MonadState s m => IndexedLensLike i ((,) r) s s a b -> (i -> a -> (r, b)) -> m r
- (+~) :: Num a => ASetter s t a a -> a -> s -> t
- (+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (<+~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (-~) :: Num a => ASetter s t a a -> a -> s -> t
- (-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (<-~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (*~) :: Num a => ASetter s t a a -> a -> s -> t
- (*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (<*~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (//~) :: Fractional a => ASetter s t a a -> a -> s -> t
- (//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()
- (<//~) :: Fractional a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
- (^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t
- (^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()
- (<^~) :: (Num a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)
- (<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t
- (^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()
- (<^^~) :: (Fractional a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)
- (<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (**~) :: Floating a => ASetter s t a a -> a -> s -> t
- (**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()
- (<**~) :: Floating a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
- (||~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (<||~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)
- (<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (<&&~) :: Overloading (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)
- (<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
- (<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()
- (<<>~) :: Monoid m => Overloading (->) q ((,) m) s t m m -> m -> q s (m, t)
- (<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
- (<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r
- (<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
- (.>) :: (st -> r) -> (kab -> st) -> kab -> r
- (<~) :: MonadState s m => ASetter s s a b -> m b -> m ()
- (<<~) :: MonadState s m => ALens s s a b -> m b -> m b
- type family h :> p
- type :>> h a = Zipper h Int a
- (<|) :: Cons Reviewed Identity s s a a => a -> s -> s
- (|>) :: Snoc Reviewed Identity s s a a => s -> a -> s

# General Purpose

(&) :: a -> (a -> b) -> bSource

Passes the result of the left side to the function on the right side (forward pipe operator).

This is the flipped version of (`$`

), which is more common in languages like F# as (`|>`

) where it is needed
for inference. Here it is supplied for notational convenience and given a precedence that allows it
to be nested inside uses of (`$`

).

`>>>`

f a`a & f`

`>>>`

6`"hello" & length & succ`

This combinator is commonly used when applying multiple `Lens`

operations in sequence.

`>>>`

("jelly","world")`("hello","world") & _1.element 0 .~ 'j' & _1.element 4 .~ 'y'`

This reads somewhat similar to:

`>>>`

("jelly","world")`flip execState ("hello","world") $ do _1.element 0 .= 'j'; _1.element 4 .= 'y'`

(??) :: Functor f => f (a -> b) -> a -> f bSource

This is convenient to `flip`

argument order of composite functions.

`>>>`

("hello",5)`over _2 ?? ("hello","world") $ length`

`>>>`

("hello",5)`over ?? length ?? ("hello","world") $ _2`

# Getting

(^.) :: s -> Getting a s t a b -> aSource

View the value pointed to by a `Getter`

or `Lens`

or the
result of folding over all the results of a `Fold`

or
`Traversal`

that points at a monoidal values.

This is the same operation as `view`

with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be
performed with (`.`

).

`>>>`

b`(a,b)^._2`

`>>>`

"world"`("hello","world")^._2`

`>>>`

`import Data.Complex`

`>>>`

2.23606797749979`((0, 1 :+ 2), 3)^._1._2.to magnitude`

(`^.`

) :: s ->`Getter`

s a -> a (`^.`

) ::`Monoid`

m => s ->`Fold`

s m -> m (`^.`

) :: s ->`Iso'`

s a -> a (`^.`

) :: s ->`Lens'`

s a -> a (`^.`

) ::`Monoid`

m => s ->`Traversal'`

s m -> m

(^@.) :: s -> IndexedGetting i (i, a) s t a b -> (i, a)Source

View the value pointed to by a `Getter`

or `Lens`

.

This is the same operation as `iview`

with the arguments flipped.

The fixity and semantics are such that subsequent field accesses can be
performed with (`.`

).

`>>>`

(1,b)`(a,b,c,d)^@._2`

`>>>`

(1,"world")`("hello","world","!!!")^@._2`

(`^@.`

) :: s ->`IndexedGetter`

i s a -> (i, a) (`^@.`

) :: s ->`IndexedLens'`

i s a -> (i, a)

The result probably doesn't have much meaning when applied to an `IndexedFold`

.

## Loupes

## with Effects

(^!) :: Monad m => s -> Acting m a s t a b -> m aSource

Perform an `Action`

.

`>>>`

hello world`["hello","world"]^!folded.act putStrLn`

(^@!) :: Monad m => s -> IndexedActing i m (i, a) s t a b -> m (i, a)Source

Perform an `IndexedAction`

.

(^!!) :: Monad m => s -> Acting m [a] s t a b -> m [a]Source

Perform a `MonadicFold`

and collect all of the results in a list.

(^@!!) :: Monad m => s -> IndexedActing i m [(i, a)] s t a b -> m [(i, a)]Source

Obtain a list of all of the results of an `IndexedMonadicFold`

.

(^!?) :: Monad m => s -> Acting m (Leftmost a) s t a b -> m (Maybe a)Source

Perform a `MonadicFold`

and collect the leftmost result.

*Note:* this still causes all effects for all elements.

(^@!?) :: Monad m => s -> IndexedActing i m (Leftmost (i, a)) s t a b -> m (Maybe (i, a))Source

Perform an `IndexedMonadicFold`

and collect the `Leftmost`

result.

*Note:* this still causes all effects for all elements.

## from Folds

(^..) :: s -> Getting (Endo [a]) s t a b -> [a]Source

A convenient infix (flipped) version of `toListOf`

.

`>>>`

[1,2,3]`[[1,2],[3]]^..traverse.traverse`

`>>>`

[1,2]`(1,2)^..both`

`toList`

xs ≡ xs`^..`

`folded`

(`^..`

) ≡`flip`

`toListOf`

(`^..`

) :: s ->`Getter`

s a -> [a] (`^..`

) :: s ->`Fold`

s a -> [a] (`^..`

) :: s ->`Lens'`

s a -> [a] (`^..`

) :: s ->`Iso'`

s a -> [a] (`^..`

) :: s ->`Traversal'`

s a -> [a] (`^..`

) :: s ->`Prism'`

s a -> [a]

(^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s t a b -> [(i, a)]Source

An infix version of `itoListOf`

.

(^?) :: s -> Getting (First a) s t a b -> Maybe aSource

Perform a safe `head`

of a `Fold`

or `Traversal`

or retrieve `Just`

the result
from a `Getter`

or `Lens`

.

When using a `Traversal`

as a partial `Lens`

, or a `Fold`

as a partial `Getter`

this can be a convenient
way to extract the optional value.

Note: if you get stack overflows due to this, you may want to use `firstOf`

instead, which can deal
more gracefully with heavily left-biased trees.

`>>>`

Just 4`Left 4 ^?_Left`

`>>>`

Nothing`Right 4 ^?_Left`

`>>>`

Just 'l'`"world" ^? ix 3`

`>>>`

Nothing`"world" ^? ix 20`

(`^?`

) ≡`flip`

`preview`

(`^?`

) :: s ->`Getter`

s a ->`Maybe`

a (`^?`

) :: s ->`Fold`

s a ->`Maybe`

a (`^?`

) :: s ->`Lens'`

s a ->`Maybe`

a (`^?`

) :: s ->`Iso'`

s a ->`Maybe`

a (`^?`

) :: s ->`Traversal'`

s a ->`Maybe`

a

(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s t a b -> Maybe (i, a)Source

Perform a safe `head`

(with index) of an `IndexedFold`

or `IndexedTraversal`

or retrieve `Just`

the index and result
from an `IndexedGetter`

or `IndexedLens`

.

When using a `IndexedTraversal`

as a partial `IndexedLens`

, or an `IndexedFold`

as a partial `IndexedGetter`

this can be a convenient
way to extract the optional value.

(`^@?`

) :: s ->`IndexedGetter`

i s a ->`Maybe`

(i, a) (`^@?`

) :: s ->`IndexedFold`

i s a ->`Maybe`

(i, a) (`^@?`

) :: s ->`IndexedLens'`

i s a ->`Maybe`

(i, a) (`^@?`

) :: s ->`Iso'`

i s a ->`Maybe`

(i, a) (`^@?`

) :: s ->`Traversal'`

i s a ->`Maybe`

(i, a)

(^@?!) :: s -> IndexedGetting i (Endo (i, a)) s t a b -> (i, a)Source

Perform an *UNSAFE* `head`

(with index) of an `IndexedFold`

or `IndexedTraversal`

assuming that it is there.

(`^@?!`

) :: s ->`IndexedGetter`

i s a -> (i, a) (`^@?!`

) :: s ->`IndexedFold`

i s a -> (i, a) (`^@?!`

) :: s ->`Lens'`

i s a -> (i, a) (`^@?!`

) :: s ->`Iso'`

i s a -> (i, a) (`^@?!`

) :: s ->`Traversal'`

i s a -> (i, a)

# Common Operators

## Setting

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

`>>>`

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

`>>>`

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

(.=) :: 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`

.

`>>>`

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

`>>>`

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

(`.=`

) ::`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 ()

(<.~) :: 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 `

directly is a good idea.
`.~`

t

`>>>`

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

`>>>`

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

`>>>`

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

(<.=) :: 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 `

will avoid unused binding warnings.
`.=`

d

(`<.=`

) ::`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

(<<.~) :: Overloading (->) q ((,) a) s t a b -> b -> q s (a, t)Source

(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m aSource

Modify the target of a `Lens`

into your 'Monad'\'s state by a user supplied
function and return the *old* value that was replaced.

When applied to a `Traversal`

, it this will return a monoidal summary of all of the old values
present.

When you do not need the result of the operation, (`%=`

) is more flexible.

(`<<%=`

) ::`MonadState`

s m =>`Lens'`

s a -> (a -> a) -> m a (`<<%=`

) ::`MonadState`

s m =>`Iso'`

s a -> (a -> a) -> m a (`<<%=`

) :: (`MonadState`

s m,`Monoid`

t) =>`Traversal'`

s a -> (a -> a) -> m a

### Just

(?~) :: 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)

`>>>`

Just a`Nothing & id ?~ a`

`>>>`

fromList [(3,x)]`Map.empty & at 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

(?=) :: 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.

`>>>`

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

`>>>`

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

(`?=`

) ::`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 ()

(<?~) :: 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 `

directly is a good idea.
`?~`

d

`>>>`

`import Data.Map as Map`

`>>>`

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

(`<?~`

) ::`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)

(<?=) :: 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 `

will avoid unused binding warnings.
`?=`

d

(`<?=`

) ::`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

## Modifying

(%~) :: 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,f c)`(a,b,c) & _3 %~ f`

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

(`%~`

) ::`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

(%=) :: (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.

`>>>`

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

`>>>`

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

(<%~) :: Profunctor p => Overloading p q ((,) b) s t a b -> p a b -> q s (b, t)Source

(<%=) :: (Profunctor p, MonadState s m) => Overloading p (->) ((,) b) s s a b -> p a b -> m bSource

Modify the target of a `Lens`

into your 'Monad'\'s state by a user supplied
function and return the result.

When applied to a `Traversal`

, it this will return a monoidal summary of all of the intermediate
results.

When you do not need the result of the operation, (`%=`

) is more flexible.

(`<%=`

) ::`MonadState`

s m =>`Lens'`

s a -> (a -> a) -> m a (`<%=`

) ::`MonadState`

s m =>`Iso'`

s a -> (a -> a) -> m a (`<%=`

) :: (`MonadState`

s m,`Monoid`

a) =>`Traversal'`

s a -> (a -> a) -> m a

(<<%~) :: Strong p => Overloading p q ((,) a) s t a b -> p a b -> q s (a, t)Source

(<<%=) :: (Strong p, MonadState s m) => Overloading p (->) ((,) a) s s a b -> p a b -> m aSource

Modify the target of a `Lens`

into your 'Monad'\'s state by a user supplied
function and return the *old* value that was replaced.

When applied to a `Traversal`

, it this will return a monoidal summary of all of the old values
present.

When you do not need the result of the operation, (`%=`

) is more flexible.

(`<<%=`

) ::`MonadState`

s m =>`Lens'`

s a -> (a -> a) -> m a (`<<%=`

) ::`MonadState`

s m =>`Iso'`

s a -> (a -> a) -> m a (`<<%=`

) :: (`MonadState`

s m,`Monoid`

b) =>`Traversal'`

s a -> (a -> a) -> m a

(`<<%=`

) ::`MonadState`

s m =>`LensLike`

((,)a) s s a b -> (a -> b) -> m a

### Loupes

(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m ()Source

(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m bSource

### with Indices

(%@~) :: 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 ()

(<%@~) :: Overloading (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t)Source

Adjust the target of an `IndexedLens`

returning the intermediate result, or
adjust all of the targets of an `IndexedTraversal`

and return a monoidal summary
along with the answer.

l`<%~`

f ≡ l`<%@~`

`const`

f

When you do not need access to the index then (`<%~`

) is more liberal in what it can accept.

If you do not need the intermediate result, you can use (`%@~`

) or even (`%~`

).

(`<%@~`

) ::`IndexedLens`

i s t a b -> (i -> a -> b) -> s -> (b, t) (`<%@~`

) ::`Monoid`

b =>`IndexedTraversal`

i s t a b -> (i -> a -> b) -> s -> (b, t)

(<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m bSource

Adjust the target of an `IndexedLens`

returning the intermediate result, or
adjust all of the targets of an `IndexedTraversal`

within the current state, and
return a monoidal summary of the intermediate results.

(`<%@=`

) ::`MonadState`

s m`IndexedLens`

i s s a b -> (i -> a -> b) -> m b (`<%@=`

) :: (`MonadState`

s m,`Monoid`

b) =>`IndexedTraversal`

i s s a b -> (i -> a -> b) -> m b

## Traversing

(%%~) :: Overloading p q f s t a b -> p a (f b) -> q s (f t)Source

(`%%~`

) can be used in one of two scenarios:

When applied to a `Lens`

, it can edit the target of the `Lens`

in a
structure, extracting a functorial result.

When applied to a `Traversal`

, it can edit the
targets of the traversals, extracting an applicative summary of its
actions.

For all that the definition of this combinator is just:

(`%%~`

) ≡`id`

It may be beneficial to think about it as if it had these even more restricted types, however:

(`%%~`

) ::`Functor`

f =>`Iso`

s t a b -> (a -> f b) -> s -> f t (`%%~`

) ::`Functor`

f =>`Lens`

s t a b -> (a -> f b) -> s -> f t (`%%~`

) ::`Applicative`

f =>`Traversal`

s t a b -> (a -> f b) -> s -> f t

When applied to a `Traversal`

, it can edit the
targets of the traversals, extracting a supplemental monoidal summary
of its actions, by choosing `f = ((,) m)`

(`%%~`

) ::`Iso`

s t a b -> (a -> (r, b)) -> s -> (r, t) (`%%~`

) ::`Lens`

s t a b -> (a -> (r, b)) -> s -> (r, t) (`%%~`

) ::`Monoid`

m =>`Traversal`

s t a b -> (a -> (m, b)) -> s -> (m, t)

(%%=) :: MonadState s m => Overloading p (->) ((,) r) s s a b -> p a (r, b) -> m rSource

Modify the target of a `Lens`

in the current state returning some extra
information of type `r`

or modify all targets of a
`Traversal`

in the current state, extracting extra
information of type `r`

and return a monoidal summary of the changes.

`>>>`

(f a,(g a,b))`runState (_1 %%= \x -> (f x, g x)) (a,b)`

(`%%=`

) ≡ (`state`

`.`

)

It may be useful to think of (`%%=`

), instead, as having either of the
following more restricted type signatures:

(`%%=`

) ::`MonadState`

s m =>`Iso`

s s a b -> (a -> (r, b)) -> m r (`%%=`

) ::`MonadState`

s m =>`Lens`

s s a b -> (a -> (r, b)) -> m r (`%%=`

) :: (`MonadState`

s m,`Monoid`

r) =>`Traversal`

s s a b -> (a -> (r, b)) -> m r

(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m rSource

(%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f tSource

Adjust the target of an `IndexedLens`

returning a supplementary result, or
adjust all of the targets of an `IndexedTraversal`

and return a monoidal summary
of the supplementary results and the answer.

(`%%@~`

) ≡`withIndex`

(`%%@~`

) ::`Functor`

f =>`IndexedLens`

i s t a b -> (i -> a -> f b) -> s -> f t (`%%@~`

) ::`Functor`

f =>`IndexedTraversal`

i s t a b -> (i -> a -> f b) -> s -> f t

In particular, it is often useful to think of this function as having one of these even more restricted type signatures:

(`%%@~`

) ::`IndexedLens`

i s t a b -> (i -> a -> (r, b)) -> s -> (r, t) (`%%@~`

) ::`Monoid`

r =>`IndexedTraversal`

i s t a b -> (i -> a -> (r, b)) -> s -> (r, t)

(%%@=) :: MonadState s m => IndexedLensLike i ((,) r) s s a b -> (i -> a -> (r, b)) -> m rSource

Adjust the target of an `IndexedLens`

returning a supplementary result, or
adjust all of the targets of an `IndexedTraversal`

within the current state, and
return a monoidal summary of the supplementary results.

l`%%@=`

f ≡`state`

(l`%%@~`

f)

(`%%@=`

) ::`MonadState`

s m`IndexedLens`

i s s a b -> (i -> a -> (r, b)) -> s -> m r (`%%@=`

) :: (`MonadState`

s m,`Monoid`

r) =>`IndexedTraversal`

i s s a b -> (i -> a -> (r, b)) -> s -> m r

## Addition

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

Increment the target(s) of a numerically valued `Lens`

, `Setter`

or `Traversal`

.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

(+=) :: (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`

`>>>`

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

`>>>`

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

(<+~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)Source

(<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m aSource

Add to the target of a numerically valued `Lens`

into your 'Monad'\'s state
and return the result.

When you do not need the result of the addition, (`+=`

) is more
flexible.

(`<+=`

) :: (`MonadState`

s m,`Num`

a) =>`Lens'`

s a -> a -> m a (`<+=`

) :: (`MonadState`

s m,`Num`

a) =>`Iso'`

s a -> a -> m a

## Subtraction

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

Decrement the target(s) of a numerically valued `Lens`

, `Iso`

, `Setter`

or `Traversal`

.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

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

(`-~`

) ::`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

(-=) :: (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.

`>>>`

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

(`-=`

) :: (`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 ()

(<-~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)Source

(<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m aSource

Subtract from the target of a numerically valued `Lens`

into your 'Monad'\'s
state and return the result.

When you do not need the result of the subtraction, (`-=`

) is more
flexible.

(`<-=`

) :: (`MonadState`

s m,`Num`

a) =>`Lens'`

s a -> a -> m a (`<-=`

) :: (`MonadState`

s m,`Num`

a) =>`Iso'`

s a -> a -> m a

## Multiplication

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

Multiply the target(s) of a numerically valued `Lens`

, `Iso`

, `Setter`

or `Traversal`

.

`>>>`

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

`>>>`

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

`>>>`

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

`>>>`

Just 48`Just 24 & mapped *~ 2`

(`*~`

) ::`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

(*=) :: (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.

`>>>`

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

(`*=`

) :: (`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 ()

(<*~) :: Num a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)Source

(<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m aSource

Multiply the target of a numerically valued `Lens`

into your 'Monad'\'s
state and return the result.

When you do not need the result of the multiplication, (`*=`

) is more
flexible.

(`<*=`

) :: (`MonadState`

s m,`Num`

a) =>`Lens'`

s a -> a -> m a (`<*=`

) :: (`MonadState`

s m,`Num`

a) =>`Iso'`

s a -> a -> m a

## Division

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

Divide the target(s) of a numerically valued `Lens`

, `Iso`

, `Setter`

or `Traversal`

.

`>>>`

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

`>>>`

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

`>>>`

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

(`//~`

) ::`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

(//=) :: (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.

`>>>`

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

(`//=`

) :: (`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 ()

(<//~) :: Fractional a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)Source

Divide the target of a fractionally valued `Lens`

and return the result.

When you do not need the result of the division, (`//~`

) is more flexible.

(`<//~`

) ::`Fractional`

b =>`Lens'`

s a -> a -> a -> (s, a) (`<//~`

) ::`Fractional`

b =>`Iso'`

s a -> a -> a -> (s, a)

(<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m aSource

Divide the target of a fractionally valued `Lens`

into your 'Monad'\'s state
and return the result.

When you do not need the result of the division, (`//=`

) is more flexible.

(`<//=`

) :: (`MonadState`

s m,`Fractional`

a) =>`Lens'`

s a -> a -> m a (`<//=`

) :: (`MonadState`

s m,`Fractional`

a) =>`Iso'`

s a -> a -> m a

## Exponentiation

(^~) :: (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.

`>>>`

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

(`^~`

) :: (`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

(^=) :: (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, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m aSource

Raise the target of a numerically valued `Lens`

into your 'Monad'\'s state
to a non-negative `Integral`

power and return the result.

When you do not need the result of the operation, (`**=`

) is more flexible.

(`<^=`

) :: (`MonadState`

s m,`Num`

a,`Integral`

e) =>`Lens'`

s a -> e -> m a (`<^=`

) :: (`MonadState`

s m,`Num`

a,`Integral`

e) =>`Iso'`

s a -> e -> m a

(^^~) :: (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.

`>>>`

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

(`^^~`

) :: (`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

(^^=) :: (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 ()

(<^^~) :: (Fractional a, Integral e) => Overloading (->) q ((,) a) s t a a -> e -> q s (a, t)Source

Raise the target of a fractionally valued `Lens`

to an `Integral`

power
and return the result.

When you do not need the result of the division, (`^^~`

) is more flexible.

(`<^^~`

) :: (`Fractional`

b,`Integral`

e) =>`Lens'`

s a -> e -> a -> (a, s) (`<^^~`

) :: (`Fractional`

b,`Integral`

e) =>`Iso'`

s a -> e -> a -> (a, s)

(<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m aSource

Raise the target of a fractionally valued `Lens`

into your 'Monad'\'s state
to an `Integral`

power and return the result.

When you do not need the result of the operation, (`^^=`

) is more flexible.

(`<^^=`

) :: (`MonadState`

s m,`Fractional`

b,`Integral`

e) =>`Lens'`

s a -> e -> m a (`<^^=`

) :: (`MonadState`

s m,`Fractional`

b,`Integral`

e) =>`Iso'`

s a -> e -> m a

(**~) :: 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**c,b)`(a,b) & _1 **~ c`

`>>>`

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

`>>>`

(1,31.54428070019754)`_2 **~ pi $ (1,3)`

(`**~`

) ::`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

(**=) :: (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

`>>>`

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

(`**=`

) :: (`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 ()

(<**~) :: Floating a => Overloading (->) q ((,) a) s t a a -> a -> q s (a, t)Source

(<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m aSource

Raise the target of a floating-point valued `Lens`

into your 'Monad'\'s
state to an arbitrary power and return the result.

When you do not need the result of the operation, (`**=`

) is more flexible.

(`<**=`

) :: (`MonadState`

s m,`Floating`

a) =>`Lens'`

s a -> a -> m a (`<**=`

) :: (`MonadState`

s m,`Floating`

a) =>`Iso'`

s a -> a -> m a

## Logical Or

(||~) :: ASetter s t Bool Bool -> Bool -> s -> tSource

Logically `||`

the target(s) of a `Bool`

-valued `Lens`

or `Setter`

.

`>>>`

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

`>>>`

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

(||=) :: 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.

`>>>`

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

## Logical And

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

Logically `&&`

the target(s) of a `Bool`

-valued `Lens`

or `Setter`

.

`>>>`

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

`>>>`

(False,False)`both &&~ False $ (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

(&&=) :: 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.

`>>>`

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

## Monoidal

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

Modify the target of a monoidally valued by `mappend`

ing another value.

`>>>`

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

`>>>`

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

`>>>`

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

(<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()Source

Modify the target(s) of a `Lens'`

, `Iso`

, `Setter`

or `Traversal`

by `mappend`

ing a value.

`>>>`

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

`>>>`

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

(<<>~) :: Monoid m => Overloading (->) q ((,) m) s t m m -> m -> q s (m, t)Source

# Composing Indices

(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> rSource

Composition of `Indexed`

functions.

Mnemonically, the `<`

and `>`

points to the fact that we want to preserve the indices.

(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> rSource

Compose an `Indexed`

function with a non-indexed function.

Mnemonically, the `<`

points to the indexing we want to preserve.

# Monadic Assignment

(<~) :: 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
...

(<<~) :: MonadState s m => ALens s s a b -> m b -> m bSource

Run a monadic action, and set the target of `Lens`

to its result.

(`<<~`

) ::`MonadState`

s m =>`Iso`

s s a b -> m b -> m b (`<<~`

) ::`MonadState`

s m =>`Lens`

s s a b -> m b -> m b

NB: This is limited to taking an actual `Lens`

than admitting a `Traversal`

because
there are potential loss of state issues otherwise.

# Zippers

type :>> h a = Zipper h Int aSource

Many zippers are indexed by Int keys. This type alias is convenient for reducing syntactic noise for talking about these boring indices.