Copyright | (C) 2012-15 Edward Kmett |
---|---|

License | BSD-style (see the file LICENSE) |

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

Stability | experimental |

Portability | non-portable |

Safe Haskell | None |

Language | Haskell98 |

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

- (<|) :: Cons s s a a => a -> s -> s
- (|>) :: Snoc s s a a => s -> a -> s
- (^..) :: s -> Getting (Endo [a]) s a -> [a]
- (^?) :: s -> Getting (First a) s a -> Maybe a
- (^?!) :: s -> Getting (Endo a) s a -> a
- (^@..) :: s -> IndexedGetting i (Endo [(i, a)]) s a -> [(i, a)]
- (^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a)
- (^@?!) :: s -> IndexedGetting i (Endo (i, a)) s a -> (i, a)
- (^.) :: s -> Getting a s a -> a
- (^@.) :: s -> IndexedGetting i (i, a) s a -> (i, a)
- (<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
- (.>) :: (st -> r) -> (kab -> st) -> kab -> r
- (<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r
- (%%~) :: Optical p q f s t a b -> p a (f b) -> q s (f t)
- (%%=) :: MonadState s m => Over p ((,) r) s s a b -> p a (r, b) -> m r
- (&) :: a -> (a -> b) -> b
- (&~) :: s -> State s a -> s
- (<&>) :: Functor f => f a -> (a -> b) -> f b
- (??) :: Functor f => f (a -> b) -> a -> f b
- (<%~) :: Profunctor p => Optical p q ((,) b) s t a b -> p a b -> q s (b, t)
- (<+~) :: Num a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<-~) :: Num a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<*~) :: Num a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<//~) :: Fractional a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<^~) :: (Num a, Integral e) => Optical (->) q ((,) a) s t a a -> e -> q s (a, t)
- (<^^~) :: (Fractional a, Integral e) => Optical (->) q ((,) a) s t a a -> e -> q s (a, t)
- (<**~) :: Floating a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t)
- (<||~) :: Optical (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)
- (<&&~) :: Optical (->) q ((,) Bool) s t Bool Bool -> Bool -> q s (Bool, t)
- (<<%~) :: Strong p => Optical p q ((,) a) s t a b -> p a b -> q s (a, t)
- (<<.~) :: Optical (->) q ((,) a) s t a b -> b -> q s (a, t)
- (<<+~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s)
- (<<-~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s)
- (<<*~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s)
- (<<//~) :: Fractional a => Optical' (->) q ((,) a) s a -> a -> q s (a, s)
- (<<^~) :: (Num a, Integral e) => Optical' (->) q ((,) a) s a -> e -> q s (a, s)
- (<<^^~) :: (Fractional a, Integral e) => Optical' (->) q ((,) a) s a -> e -> q s (a, s)
- (<<**~) :: Floating a => Optical' (->) q ((,) a) s a -> a -> q s (a, s)
- (<<||~) :: Optical' (->) q ((,) Bool) s Bool -> Bool -> q s (Bool, s)
- (<<&&~) :: Optical' (->) q ((,) Bool) s Bool -> Bool -> q s (Bool, s)
- (<<<>~) :: Monoid r => Optical' (->) q ((,) r) s r -> r -> q s (r, s)
- (<%=) :: (Profunctor p, MonadState s m) => Over p ((,) b) s s a b -> p a b -> m b
- (<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
- (<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
- (<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a
- (<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a
- (<<+=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<<*=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a
- (<<//=) :: (MonadState s m, Fractional a) => LensLike' ((,) a) s a -> a -> m a
- (<<^=) :: (MonadState s m, Num a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<<^^=) :: (MonadState s m, Fractional a, Integral e) => LensLike' ((,) a) s a -> e -> m a
- (<<**=) :: (MonadState s m, Floating a) => LensLike' ((,) a) s a -> a -> m a
- (<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool
- (<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
- (<<~) :: MonadState s m => ALens s s a b -> m b -> m b
- (<<>~) :: Monoid m => Optical (->) q ((,) m) s t m m -> m -> q s (m, t)
- (<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r
- (<%@~) :: Optical (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t)
- (<<%@~) :: Optical (Indexed i) q ((,) a) s t a b -> (i -> a -> b) -> q s (a, t)
- (%%@~) :: 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
- (<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b
- (<<%@=) :: MonadState s m => IndexedLensLike i ((,) a) s s a b -> (i -> a -> b) -> m a
- (^#) :: s -> ALens s t a b -> a
- (#~) :: ALens s t a b -> b -> s -> t
- (#%~) :: ALens s t a b -> (a -> b) -> s -> t
- (#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t
- (#=) :: MonadState s m => ALens s s a b -> b -> m ()
- (#%=) :: 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
- (#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r
- (<#~) :: ALens s t a b -> b -> s -> (b, t)
- (<#=) :: MonadState s m => ALens s s a b -> b -> m b
- (...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b
- (#) :: AReview t b -> b -> t
- (%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t
- (.~) :: ASetter s t a b -> b -> s -> t
- (?~) :: ASetter s t a (Maybe b) -> b -> s -> t
- (<.~) :: ASetter s t a b -> b -> s -> (b, t)
- (<?~) :: ASetter s t a (Maybe b) -> b -> s -> (b, t)
- (+~) :: Num a => ASetter s t a a -> a -> s -> t
- (*~) :: Num a => ASetter s t a a -> a -> s -> t
- (-~) :: Num a => ASetter s t a a -> a -> s -> t
- (//~) :: Fractional a => ASetter s t a a -> a -> s -> t
- (^~) :: (Num a, Integral e) => ASetter s t a a -> e -> s -> t
- (^^~) :: (Fractional a, Integral e) => ASetter s t a a -> e -> s -> t
- (**~) :: Floating a => ASetter s t a a -> a -> s -> t
- (||~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (&&~) :: ASetter s t Bool Bool -> Bool -> s -> t
- (.=) :: MonadState s m => ASetter s s a b -> b -> m ()
- (%=) :: (Profunctor p, MonadState s m) => Setting p s s a b -> p a b -> m ()
- (?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m ()
- (+=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (-=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (*=) :: (MonadState s m, Num a) => ASetter' s a -> a -> m ()
- (//=) :: (MonadState s m, Fractional a) => ASetter' s a -> a -> m ()
- (^=) :: (MonadState s m, Num a, Integral e) => ASetter' s a -> e -> m ()
- (^^=) :: (MonadState s m, Fractional a, Integral e) => ASetter' s a -> e -> m ()
- (**=) :: (MonadState s m, Floating a) => ASetter' s a -> a -> m ()
- (&&=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (||=) :: MonadState s m => ASetter' s Bool -> Bool -> m ()
- (<~) :: MonadState s m => ASetter s s a b -> m b -> m ()
- (<.=) :: MonadState s m => ASetter s s a b -> b -> m b
- (<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m b
- (<>~) :: Monoid a => ASetter s t a a -> a -> s -> t
- (<>=) :: (MonadState s m, Monoid a) => ASetter' s a -> a -> m ()
- (%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t
- (%@=) :: MonadState s m => AnIndexedSetter i s s a b -> (i -> a -> b) -> m ()

# Control.Lens.Cons

# Control.Lens.Fold

(^..) :: s -> Getting (Endo [a]) s a -> [a] infixl 8 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 -> Getting (First a) s a -> Maybe a infixl 8 Source

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 [(i, a)]) s a -> [(i, a)] infixl 8 Source

An infix version of `itoListOf`

.

(^@?) :: s -> IndexedGetting i (Endo (Maybe (i, a))) s a -> Maybe (i, a) infixl 8 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 ->`IndexedTraversal'`

i s a ->`Maybe`

(i, a)

(^@?!) :: s -> IndexedGetting i (Endo (i, a)) s a -> (i, a) infixl 8 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 ->`IndexedLens'`

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

) :: s ->`IndexedTraversal'`

i s a -> (i, a)

# Control.Lens.Getter

(^.) :: s -> Getting a s a -> a infixl 8 Source

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 a -> (i, a) infixl 8 Source

View the index and value of an `IndexedGetter`

or `IndexedLens`

.

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 (`.`

).

(`^@.`

) :: 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`

.

# Control.Lens.Indexed

(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r infixr 9 Source

Compose an `Indexed`

function with a non-indexed function.

Mnemonically, the `<`

points to the indexing we want to preserve.

`>>>`

`let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]`

`>>>`

[(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]`nestedMap^..(itraversed<.itraversed).withIndex`

(.>) :: (st -> r) -> (kab -> st) -> kab -> r infixr 9 Source

Compose a non-indexed function with an `Indexed`

function.

Mnemonically, the `>`

points to the indexing we want to preserve.

This is the same as `(`

.`.`

)

`f `

(and `.`

g`f `

) gives you the index of `.>`

g`g`

unless `g`

is index-preserving, like a
`Prism`

, `Iso`

or `Equality`

, in which case it'll pass through the index of `f`

.

`>>>`

`let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]`

`>>>`

[(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]`nestedMap^..(itraversed.>itraversed).withIndex`

(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r infixr 9 Source

Composition of `Indexed`

functions.

Mnemonically, the `<`

and `>`

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

`>>>`

`let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]`

`>>>`

[((1,10),"one,ten"),((1,20),"one,twenty"),((2,30),"two,thirty"),((2,40),"two,forty")]`nestedMap^..(itraversed<.>itraversed).withIndex`

# Control.Lens.Lens

(%%~) :: Optical p q f s t a b -> p a (f b) -> q s (f t) infixr 4 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.

`>>>`

("nananananana","Batman")`[66,97,116,109,97,110] & each %%~ \a -> ("na", chr a)`

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 => Over p ((,) r) s s a b -> p a (r, b) -> m r infix 4 Source

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

(&) :: a -> (a -> b) -> b infixl 1

(&~) :: s -> State s a -> s infixl 1 Source

This can be used to chain lens operations using `op=`

syntax
rather than `op~`

syntax for simple non-type-changing cases.

`>>>`

(30,40)`(10,20) & _1 .~ 30 & _2 .~ 40`

`>>>`

(30,40)`(10,20) &~ do _1 .= 30; _2 .= 40`

This does not support type-changing assignment, *e.g.*

`>>>`

("hello",20)`(10,20) & _1 .~ "hello"`

(??) :: Functor f => f (a -> b) -> a -> f b infixl 1 Source

This is convenient to `flip`

argument order of composite functions defined as:

fab ?? a = fmap ($ a) fab

For the `Functor`

instance `f = ((->) r)`

you can reason about this function as if the definition was `(`

:`??`

) ≡ `flip`

`>>>`

h a x`(h ?? x) a`

`>>>`

[1]`execState ?? [] $ modify (1:)`

`>>>`

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

`>>>`

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

(<%~) :: Profunctor p => Optical p q ((,) b) s t a b -> p a b -> q s (b, t) infixr 4 Source

(<//~) :: Fractional a => Optical (->) q ((,) a) s t a a -> a -> q s (a, t) infixr 4 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`

a =>`Lens'`

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

) ::`Fractional`

a =>`Iso'`

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

(<^^~) :: (Fractional a, Integral e) => Optical (->) q ((,) a) s t a a -> e -> q s (a, t) infixr 4 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 operation, (`^^~`

) is more flexible.

(`<^^~`

) :: (`Fractional`

a,`Integral`

e) =>`Lens'`

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

) :: (`Fractional`

a,`Integral`

e) =>`Iso'`

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

(<<+~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) infixr 4 Source

Increment the target of a numerically valued `Lens`

and return the old value.

When you do not need the old value, (`+~`

) is more flexible.

`>>>`

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

`>>>`

(b,(a,b + c))`(a,b) & _2 <<+~ c`

(`<<+~`

) ::`Num`

a =>`Lens'`

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

) ::`Num`

a =>`Iso'`

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

(<<-~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) infixr 4 Source

Decrement the target of a numerically valued `Lens`

and return the old value.

When you do not need the old value, (`-~`

) is more flexible.

`>>>`

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

`>>>`

(b,(a,b - c))`(a,b) & _2 <<-~ c`

(`<<-~`

) ::`Num`

a =>`Lens'`

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

) ::`Num`

a =>`Iso'`

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

(<<*~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) infixr 4 Source

Multiply the target of a numerically valued `Lens`

and return the old value.

When you do not need the old value, (`-~`

) is more flexible.

`>>>`

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

`>>>`

(b,(a,b * c))`(a,b) & _2 <<*~ c`

(`<<*~`

) ::`Num`

a =>`Lens'`

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

) ::`Num`

a =>`Iso'`

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

(<<//~) :: Fractional a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) infixr 4 Source

Divide the target of a numerically valued `Lens`

and return the old value.

When you do not need the old value, (`//~`

) is more flexible.

`>>>`

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

`>>>`

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

(`<<//~`

) :: Fractional a =>`Lens'`

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

) :: Fractional a =>`Iso'`

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

(<<^^~) :: (Fractional a, Integral e) => Optical' (->) q ((,) a) s a -> e -> q s (a, s) infixr 4 Source

Raise the target of a fractionally valued `Lens`

to an integral power and return the old value.

When you do not need the old value, (`^^~`

) is more flexible.

(`<<^^~`

) :: (`Fractional`

a,`Integral`

e) =>`Lens'`

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

) :: (`Fractional`

a,`Integral`

e) =>`Iso'`

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

(<<**~) :: Floating a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) infixr 4 Source

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

to an arbitrary power and return the old value.

When you do not need the old value, (`**~`

) is more flexible.

`>>>`

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

`>>>`

(b,(a,b**c))`(a,b) & _2 <<**~ c`

(`<<**~`

) ::`Floating`

a =>`Lens'`

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

) ::`Floating`

a =>`Iso'`

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

(<<||~) :: Optical' (->) q ((,) Bool) s Bool -> Bool -> q s (Bool, s) infixr 4 Source

Logically `||`

the target of a `Bool`

-valued `Lens`

and return the old value.

When you do not need the old value, (`||~`

) is more flexible.

`>>>`

(False,(True,6))`(False,6) & _1 <<||~ True`

`>>>`

(True,("hello",True))`("hello",True) & _2 <<||~ False`

(`<<||~`

) ::`Lens'`

s`Bool`

->`Bool`

-> s -> (`Bool`

, s) (`<<||~`

) ::`Iso'`

s`Bool`

->`Bool`

-> s -> (`Bool`

, s)

(<<&&~) :: Optical' (->) q ((,) Bool) s Bool -> Bool -> q s (Bool, s) infixr 4 Source

Logically `&&`

the target of a `Bool`

-valued `Lens`

and return the old value.

When you do not need the old value, (`&&~`

) is more flexible.

`>>>`

(False,(False,6))`(False,6) & _1 <<&&~ True`

`>>>`

(True,("hello",False))`("hello",True) & _2 <<&&~ False`

(`<<&&~`

) ::`Lens'`

s Bool -> Bool -> s -> (Bool, s) (`<<&&~`

) ::`Iso'`

s Bool -> Bool -> s -> (Bool, s)

(<<<>~) :: Monoid r => Optical' (->) q ((,) r) s r -> r -> q s (r, s) infixr 4 Source

Modify the target of a monoidally valued `Lens`

by `mappend`

ing a new value and return the old value.

When you do not need the old value, (`<>~`

) is more flexible.

`>>>`

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

`>>>`

("Bond",("James","Bond, 007"))`_2 <<<>~ ", 007" $ ("James", "Bond")`

(`<<<>~`

) ::`Monoid`

r =>`Lens'`

s r -> r -> s -> (r, s) (`<<<>~`

) ::`Monoid`

r =>`Iso'`

s r -> r -> s -> (r, s)

(<%=) :: (Profunctor p, MonadState s m) => Over p ((,) b) s s a b -> p a b -> m b infix 4 Source

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

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

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

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

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

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

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

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

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

(<<%=) :: (Strong p, MonadState s m) => Over p ((,) a) s s a b -> p a b -> m a infix 4 Source

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

(<<.=) :: MonadState s m => LensLike ((,) a) s s a b -> b -> m a infix 4 Source

Replace the target of a `Lens`

into your `Monad'`

s state with a user supplied
value 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 -> m a (`<<.=`

) ::`MonadState`

s m =>`Iso'`

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

) :: (`MonadState`

s m,`Monoid`

t) =>`Traversal'`

s a -> a -> m a

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

Modify the target of a `Lens`

into your `Monad'`

s state by adding a value
and return the *old* value that was replaced.

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

) 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

(<<-=) :: (MonadState s m, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source

Modify the target of a `Lens`

into your `Monad'`

s state by subtracting a value
and return the *old* value that was replaced.

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

) 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

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

Modify the target of a `Lens`

into your `Monad'`

s state by multipling a value
and return the *old* value that was replaced.

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

) 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

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

Modify the target of a `Lens`

into your `Monad`

s state by dividing by a value
and return the *old* value that was replaced.

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

) 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

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

Modify the target of a `Lens`

into your `Monad'`

s state by raising it by a non-negative power
and return the *old* value that was replaced.

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 -> a -> m a

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

Modify the target of a `Lens`

into your `Monad'`

s state by raising it by an integral power
and return the *old* value that was replaced.

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

) is more flexible.

(`<<^^=`

) :: (`MonadState`

s m,`Fractional`

a,`Integral`

e) =>`Lens'`

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

) :: (`MonadState`

s m,`Fractional`

a,`Integral`

e) =>`Iso'`

s a -> e -> m a

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

Modify the target of a `Lens`

into your `Monad'`

s state by raising it by an arbitrary power
and return the *old* value that was replaced.

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

(<<||=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source

Modify the target of a `Lens`

into your `Monad'`

s state by taking its logical `||`

with a value
and return the *old* value that was replaced.

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

) is more flexible.

(`<<||=`

) ::`MonadState`

s m =>`Lens'`

s`Bool`

->`Bool`

-> m`Bool`

(`<<||=`

) ::`MonadState`

s m =>`Iso'`

s`Bool`

->`Bool`

-> m`Bool`

(<<&&=) :: MonadState s m => LensLike' ((,) Bool) s Bool -> Bool -> m Bool infix 4 Source

Modify the target of a `Lens`

into your `Monad'`

s state by taking its logical `&&`

with a value
and return the *old* value that was replaced.

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

) is more flexible.

(`<<&&=`

) ::`MonadState`

s m =>`Lens'`

s`Bool`

->`Bool`

-> m`Bool`

(`<<&&=`

) ::`MonadState`

s m =>`Iso'`

s`Bool`

->`Bool`

-> m`Bool`

(<<<>=) :: (MonadState s m, Monoid r) => LensLike' ((,) r) s r -> r -> m r infix 4 Source

Modify the target of a `Lens`

into your `Monad'`

s state by `mappend`

ing a value
and return the *old* value that was replaced.

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

) is more flexible.

(`<<<>=`

) :: (`MonadState`

s m,`Monoid`

r) =>`Lens'`

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

) :: (`MonadState`

s m,`Monoid`

r) =>`Iso'`

s r -> r -> m r

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

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.

(<%@~) :: Optical (Indexed i) q ((,) b) s t a b -> (i -> a -> b) -> q s (b, t) infixr 4 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)

(<<%@~) :: Optical (Indexed i) q ((,) a) s t a b -> (i -> a -> b) -> q s (a, t) infixr 4 Source

Adjust the target of an `IndexedLens`

returning the old value, or
adjust all of the targets of an `IndexedTraversal`

and return a monoidal summary
of the old values along with the answer.

(`<<%@~`

) ::`IndexedLens`

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

) ::`Monoid`

a =>`IndexedTraversal`

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

(%%@~) :: IndexedLensLike i f s t a b -> (i -> a -> f b) -> s -> f t infixr 4 Source

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 (`%%@~`

) ::`Applicative`

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 r infix 4 Source

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

(<%@=) :: MonadState s m => IndexedLensLike i ((,) b) s s a b -> (i -> a -> b) -> m b infix 4 Source

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

(<<%@=) :: MonadState s m => IndexedLensLike i ((,) a) s s a b -> (i -> a -> b) -> m a infix 4 Source

Adjust the target of an `IndexedLens`

returning the old value, or
adjust all of the targets of an `IndexedTraversal`

within the current state, and
return a monoidal summary of the old values.

(`<<%@=`

) ::`MonadState`

s m =>`IndexedLens`

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

) :: (`MonadState`

s m,`Monoid`

b) =>`IndexedTraversal`

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

# Control.Lens.Plated

(...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b infixr 9 Source

Compose through a plate

# Control.Lens.Review

(#) :: AReview t b -> b -> t infixr 8 Source

An infix alias for `review`

.

`unto`

f # x ≡ f x l # x ≡ x`^.`

`re`

l

This is commonly used when using a `Prism`

as a smart constructor.

`>>>`

Left 4`_Left # 4`

But it can be used for any `Prism`

`>>>`

"7b"`base 16 # 123`

(#) ::`Iso'`

s a -> a -> s (#) ::`Prism'`

s a -> a -> s (#) ::`Review`

s a -> a -> s (#) ::`Equality'`

s a -> a -> s

# Control.Lens.Setter

(%~) :: Profunctor p => Setting p s t a b -> p a b -> s -> t infixr 4 Source

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

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

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

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

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

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

Set with pass-through.

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

If you do not need a copy of the intermediate result, then using `l `

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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`

`>>>`

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

(`**~`

) ::`Floating`

a =>`Setter'`

s a -> a -> s -> s (`**~`

) ::`Floating`

a =>`Iso'`

s a -> a -> s -> s (`**~`

) ::`Floating`

a =>`Lens'`

s a -> a -> s -> s (`**~`

) ::`Floating`

a =>`Traversal'`

s a -> a -> s -> s

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

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

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

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 s a b -> b -> m () infix 4 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 ()

*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 () infix 4 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 ()

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

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

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

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

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

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

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

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

(<~) :: MonadState s m => ASetter s s a b -> m b -> m () infixr 2 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 => ASetter s s a b -> b -> m b infix 4 Source

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

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

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

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

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 () infix 4 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 ()

(%@~) :: AnIndexedSetter i s t a b -> (i -> a -> b) -> s -> t infixr 4 Source

Adjust every target of an `IndexedSetter`

, `IndexedLens`

or `IndexedTraversal`

with access to the index.

(`%@~`

) ≡`iover`

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 () infix 4 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 ()