lens-4.2: Lenses, Folds and Traversals

Copyright(C) 2012-14 Edward Kmett
LicenseBSD-style (see the file LICENSE)
MaintainerEdward Kmett <ekmett@gmail.com>
Stabilityexperimental
Portabilitynon-portable
Safe HaskellSafe-Inferred
LanguageHaskell98

Control.Lens.Operators

Contents

Description

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

Synopsis

Control.Lens.Action

(^!) :: Monad m => s -> Acting m a s a -> m a infixr 8 Source

Perform an Action.

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

(^!!) :: Monad m => s -> Acting m [a] s a -> m [a] infixr 8 Source

Perform a MonadicFold and collect all of the results in a list.

>>> ["ab","cd","ef"]^!!folded.acts
["ace","acf","ade","adf","bce","bcf","bde","bdf"]
1,2
^!!folded.act (i -> putStr (show i ++ ": ") >> getLine).each.to succ 1: aa 2: bb "bbcc"

(^!?) :: Monad m => s -> Acting m (Leftmost a) s a -> m (Maybe a) infixr 8 Source

Perform a MonadicFold and collect the leftmost result.

Note: this still causes all effects for all elements.

>>> [Just 1, Just 2, Just 3]^!?folded.acts
Just (Just 1)
>>> [Just 1, Nothing]^!?folded.acts
Nothing

(^@!) :: Monad m => s -> IndexedActing i m (i, a) s a -> m (i, a) infixr 8 Source

Perform an IndexedAction.

(^@!!) :: Monad m => s -> IndexedActing i m [(i, a)] s a -> m [(i, a)] infixr 8 Source

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

(^@!?) :: Monad m => s -> IndexedActing i m (Leftmost (i, a)) s a -> m (Maybe (i, a)) infixr 8 Source

Perform an IndexedMonadicFold and collect the Leftmost result.

Note: this still causes all effects for all elements.

Control.Lens.Cons

(<|) :: Cons s s a a => a -> s -> s infixr 5 Source

cons an element onto a container.

This is an infix alias for cons.

>>> a <| []
[a]
>>> a <| [b, c]
[a,b,c]
>>> a <| Seq.fromList []
fromList [a]
>>> a <| Seq.fromList [b, c]
fromList [a,b,c]

(|>) :: Snoc s s a a => s -> a -> s infixl 5 Source

snoc an element onto the end of a container.

This is an infix alias for snoc.

>>> Seq.fromList [] |> a
fromList [a]
>>> Seq.fromList [b, c] |> a
fromList [b,c,a]
>>> LazyT.pack "hello" |> '!'
"hello!"

Control.Lens.Fold

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

A convenient infix (flipped) version of toListOf.

>>> [[1,2],[3]]^..traverse.traverse
[1,2,3]
>>> (1,2)^..both
[1,2]
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.

>>> Left 4 ^?_Left
Just 4
>>> Right 4 ^?_Left
Nothing
>>> "world" ^? ix 3
Just 'l'
>>> "world" ^? ix 20
Nothing
('^?') ≡ 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 -> Getting (Endo a) s a -> a infixl 8 Source

Perform an *UNSAFE* head of a Fold or Traversal assuming that it is there.

>>> Left 4 ^?! _Left
4
>>> "world" ^?! ix 3
'l'
('^?!') :: 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 -> 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 (.).

>>> (a,b)^._2
b
>>> ("hello","world")^._2
"world"
>>> import Data.Complex
>>> ((0, 1 :+ 2), 3)^._1._2.to magnitude
2.23606797749979
('^.') ::             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")])]
>>> nestedMap^..(itraversed<.itraversed).withIndex
[(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]

(.>) :: (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 . g (and f .> g) gives you the index of 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")])]
>>> nestedMap^..(itraversed.>itraversed).withIndex
[(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]

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

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.

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.

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

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

This is the flipped version of ($), which is more common in languages like F# as (|>) where it is needed for inference. Here it is supplied for notational convenience and given a precedence that allows it to be nested inside uses of ($).

>>> a & f
f a
>>> "hello" & length & succ
6

This combinator is commonly used when applying multiple Lens operations in sequence.

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

This reads somewhat similar to:

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

(&~) :: 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.

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

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

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

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

Infix flipped fmap.

(<&>) = flip fmap

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

This is convenient to flip argument order of composite functions.

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

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

Modify the target of a Lens and return the result.

When you do not need the result of the addition, (%~) is more flexible.

(<%~) ::             Lens s t a b      -> (a -> b) -> s -> (b, t)
(<%~) ::             Iso s t a b       -> (a -> b) -> s -> (b, t)
(<%~) :: Monoid b => Traversal s t a b -> (a -> b) -> s -> (b, t)

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

Increment the target of a numerically valued Lens and return the result.

When you do not need the result of the addition, (+~) is more flexible.

(<+~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<+~) :: Num a => Iso' s a  -> a -> s -> (a, s)

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

Decrement the target of a numerically valued Lens and return the result.

When you do not need the result of the subtraction, (-~) is more flexible.

(<-~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<-~) :: Num a => Iso' s a  -> a -> s -> (a, s)

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

Multiply the target of a numerically valued Lens and return the result.

When you do not need the result of the multiplication, (*~) is more flexible.

(<*~) :: Num a => Lens' s a -> a -> s -> (a, s)
(<*~) :: Num a => Iso'  s a -> a -> s -> (a, s)

(<//~) :: 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)

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

Raise the target of a numerically valued Lens to a non-negative Integral power and return the result.

When you do not need the result of the operation, ('Control.Lens.Setter.^~') is more flexible.

(':: ('Num' a, 'Integral' e) = Lens' s a -> e -> s -> (a, s)
(':: ('Num' a, 'Integral' e) = Iso' s a -> e -> 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, ('Control.Lens.Setter.^^~') 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 t a a -> a -> q s (a, t) infixr 4 Source

Raise the target of a floating-point valued Lens to an arbitrary power and return the result.

When you do not need the result of the operation, (**~) is more flexible.

(<**~) :: Floating a => Lens' s a -> a -> s -> (a, s)
(<**~) :: Floating a => Iso' s a  -> a -> s -> (a, s)

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

Logically || a Boolean valued Lens and return the result.

When you do not need the result of the operation, (||~) is more flexible.

(<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<||~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

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

Logically && a Boolean valued Lens and return the result.

When you do not need the result of the operation, (&&~) is more flexible.

(<&&~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<&&~) :: Iso' s Bool  -> Bool -> s -> (Bool, s)

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

Modify the target of a Lens, but return the old value.

When you do not need the old value, (%~) is more flexible.

(<<%~) ::             Lens s t a b      -> (a -> b) -> s -> (a, t)
(<<%~) ::             Iso s t a b       -> (a -> b) -> s -> (a, t)
(<<%~) :: Monoid a => Traversal s t a b -> (a -> b) -> s -> (a, t)

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

Replace the target of a Lens, but return the old value.

When you do not need the old value, (.~) is more flexible.

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

(<<+~) :: Num a => Optical' (->) q ((,) a) s a -> a -> q s (a, s) 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,b) & _1 <<+~ c
(a,(a + c,b))
>>> (a,b) & _2 <<+~ c
(b,(a,b + 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) 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,b) & _1 <<-~ c
(a,(a - c,b))
>>> (a,b) & _2 <<-~ c
(b,(a,b - 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) 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,b) & _1 <<*~ c
(a,(a * c,b))
>>> (a,b) & _2 <<*~ c
(b,(a,b * 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) 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,b) & _1 <<//~ c
(a,(a / c,b))
>>> ("Hawaii",10) & _2 <<//~ 2
(10.0,("Hawaii",5.0))
(<<//~) :: Fractional a => Lens' s a -> a -> s -> (a, s)
(<<//~) :: Fractional a => Iso' s a -> a -> s -> (a, s)

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

Raise the target of a numerically valued Lens to a non-negative power and return the old value.

When you do not need the old value, ('Control.Lens.Setter.^~') is more flexible.

(':: ('Num' a, 'Integral' e) = Lens' s a -> e -> s -> (a, s)
(':: ('Num' a, 'Integral' e) = Iso' s a -> e -> s -> (a, s)

(<<^^~) :: (Fractional a, Integral e) => Optical' (->) q ((,) a) s a -> e -> q s (a, s) 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, ('Control.Lens.Setter.^^~') 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) 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,b) & _1 <<**~ c
(a,(a**c,b))
>>> (a,b) & _2 <<**~ c
(b,(a,b**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) 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,6) & _1 <<||~ True
(False,(True,6))
>>> ("hello",True) & _2 <<||~ False
(True,("hello",True))
(<<||~) :: Lens' s Bool -> Bool -> s -> (Bool, s)
(<<||~) :: Iso' s Bool -> Bool -> s -> (Bool, s)

(<<&&~) :: Optical' (->) q ((,) Bool) s Bool -> Bool -> q s (Bool, s) 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,6) & _1 <<&&~ True
(False,(False,6))
>>> ("hello",True) & _2 <<&&~ False
(True,("hello",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) Source

Modify the target of a monoidally valued Lens by mappending a new value and return the old value.

When you do not need the old value, (<>~) is more flexible.

>>> (Sum a,b) & _1 <<<>~ Sum c
(Sum {getSum = a},(Sum {getSum = a + c},b))
>>> _2 <<<>~ ", 007" $ ("James", "Bond")
("Bond",("James","Bond, 007"))
(<<<>~) :: 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, Num a) => LensLike' ((,) a) s a -> a -> m a infix 4 Source

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

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

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

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

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

(<//=) :: (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, ('Control.Lens.Setter.^=') 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, ('Control.Lens.Setter.^^=') 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

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

Logically || a Boolean valued Lens into your 'Monad'\'s state and return the result.

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

Logically && a Boolean valued Lens into your 'Monad'\'s state and return the result.

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

(<<%=) :: (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 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 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 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 Source

Modify the target of a Lens into your Monads 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 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, ('Control.Lens.Setter.^=') 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 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, ('Control.Lens.Setter.^^=') 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 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 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 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 Source

Modify the target of a Lens into your 'Monad'\'s state by mappending 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.

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

mappend a monoidal value onto the end of the target of a Lens and return the result.

When you do not need the result of the operation, (<>~) is more flexible.

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

mappend a monoidal value onto the end of the target of a Lens into your 'Monad'\'s state and return the result.

When you do not need the result of the operation, (<>=) is more flexible.

(<%@~) :: 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

(^#) :: s -> ALens s t a b -> a infixl 8 Source

A version of ('Control.Lens.Getter.^.') that works on ALens.

>>> ("hello","world")^#_2
"world"

(#~) :: ALens s t a b -> b -> s -> t infixr 4 Source

A version of (.~) that works on ALens.

>>> ("hello","there") & _2 #~ "world"
("hello","world")

(#%~) :: ALens s t a b -> (a -> b) -> s -> t infixr 4 Source

A version of (%~) that works on ALens.

>>> ("hello","world") & _2 #%~ length
("hello",5)

(#%%~) :: Functor f => ALens s t a b -> (a -> f b) -> s -> f t infixr 4 Source

A version of (%%~) that works on ALens.

>>> ("hello","world") & _2 #%%~ \x -> (length x, x ++ "!")
(5,("hello","world!"))

(#=) :: MonadState s m => ALens s s a b -> b -> m () infix 4 Source

A version of (.=) that works on ALens.

(#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m () infix 4 Source

A version of (%=) that works on ALens.

(<#%~) :: ALens s t a b -> (a -> b) -> s -> (b, t) infixr 4 Source

A version of (<%~) that works on ALens.

>>> ("hello","world") & _2 <#%~ length
(5,("hello",5))

(<#%=) :: MonadState s m => ALens s s a b -> (a -> b) -> m b infix 4 Source

A version of (<%=) that works on ALens.

(#%%=) :: MonadState s m => ALens s s a b -> (a -> (r, b)) -> m r infix 4 Source

A version of (%%=) that works on ALens.

(<#~) :: ALens s t a b -> b -> s -> (b, t) infixr 4 Source

A version of (<.~) that works on ALens.

>>> ("hello","there") & _2 <#~ "world"
("world",("hello","world"))

(<#=) :: MonadState s m => ALens s s a b -> b -> m b infix 4 Source

A version of (<.=) that works on ALens.

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 s t a 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

>>> base 16 # 123
"7b"
(#) :: 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,c) & _3 %~ f
(a,b,f c)
>>> (a,b) & both %~ f
(f a,f b)
>>> _2 %~ length $ (1,"hello")
(1,5)
>>> traverse %~ f $ [a,b,c]
[f a,f b,f c]
>>> traverse %~ even $ [1,2,3]
[False,True,False]
>>> traverse.traverse %~ length $ [["hello","world"],["!!!"]]
[[5,5],[3]]
(%~) :: Setter s t a b    -> (a -> b) -> s -> t
(%~) :: Iso s t a b       -> (a -> b) -> s -> t
(%~) :: Lens s t a b      -> (a -> b) -> s -> t
(%~) :: Traversal s t a b -> (a -> b) -> s -> t

(.~) :: 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,d) & _4 .~ e
(a,b,c,e)
>>> (42,"world") & _1 .~ "hello"
("hello","world")
>>> (a,b) & both .~ c
(c,c)
(.~) :: Setter s t a b    -> b -> s -> t
(.~) :: Iso s t a b       -> b -> s -> t
(.~) :: Lens s t a b      -> b -> s -> t
(.~) :: Traversal s t a b -> b -> s -> t

(?~) :: ASetter s t a (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)
>>> Nothing & id ?~ a
Just a
>>> Map.empty & at 3 ?~ x
fromList [(3,x)]
(?~) :: Setter s t a (Maybe b)    -> b -> s -> t
(?~) :: Iso s t a (Maybe b)       -> b -> s -> t
(?~) :: Lens s t a (Maybe b)      -> b -> s -> t
(?~) :: Traversal s t a (Maybe b) -> b -> s -> t

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

Set with pass-through.

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

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

>>> (a,b) & _1 <.~ c
(c,(c,b))
>>> ("good","morning","vietnam") & _3 <.~ "world"
("world",("good","morning","world"))
>>> (42,Map.fromList [("goodnight","gracie")]) & _2.at "hello" <.~ Just "world"
(Just "world",(42,fromList [("goodnight","gracie"),("hello","world")]))
(<.~) :: Setter s t a b    -> b -> s -> (b, t)
(<.~) :: Iso s t a b       -> b -> s -> (b, t)
(<.~) :: Lens s t a b      -> b -> s -> (b, t)
(<.~) :: Traversal s t a b -> b -> s -> (b, t)

(<?~) :: ASetter s t a (Maybe b) -> b -> s -> (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 ?~ d directly is a good idea.

>>> import Data.Map as Map
>>> _2.at "hello" <?~ "world" $ (42,Map.fromList [("goodnight","gracie")])
("world",(42,fromList [("goodnight","gracie"),("hello","world")]))
(<?~) :: Setter s t a (Maybe b)    -> b -> s -> (b, t)
(<?~) :: Iso s t a (Maybe b)       -> b -> s -> (b, t)
(<?~) :: Lens s t a (Maybe b)      -> b -> s -> (b, t)
(<?~) :: Traversal s t a (Maybe b) -> b -> s -> (b, t)

(+~) :: 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,b) & _1 +~ c
(a + c,b)
>>> (a,b) & both +~ c
(a + c,b + c)
>>> (1,2) & _2 +~ 1
(1,3)
>>> [(a,b),(c,d)] & traverse.both +~ e
[(a + e,b + e),(c + e,d + e)]
(+~) :: Num a => Setter' s a    -> a -> s -> s
(+~) :: Num a => Iso' s a       -> a -> s -> s
(+~) :: Num a => Lens' s a      -> a -> s -> s
(+~) :: Num a => Traversal' s a -> a -> s -> s

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

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

>>> (a,b) & _1 *~ c
(a * c,b)
>>> (a,b) & both *~ c
(a * c,b * c)
>>> (1,2) & _2 *~ 4
(1,8)
>>> Just 24 & mapped *~ 2
Just 48
(*~) :: Num a => Setter' s a    -> a -> s -> s
(*~) :: Num a => Iso' s a       -> a -> s -> s
(*~) :: Num a => Lens' s a      -> a -> s -> s
(*~) :: Num a => Traversal' s a -> a -> s -> s

(-~) :: 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,b) & _1 -~ c
(a - c,b)
>>> (a,b) & both -~ c
(a - c,b - c)
>>> _1 -~ 2 $ (1,2)
(-1,2)
>>> mapped.mapped -~ 1 $ [[4,5],[6,7]]
[[3,4],[5,6]]
(-~) :: Num a => Setter' s a    -> a -> s -> s
(-~) :: Num a => Iso' s a       -> a -> s -> s
(-~) :: Num a => Lens' s a      -> a -> s -> s
(-~) :: Num a => Traversal' s a -> a -> s -> s

(//~) :: 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,b) & _1 //~ c
(a / c,b)
>>> (a,b) & both //~ c
(a / c,b / c)
>>> ("Hawaii",10) & _2 //~ 2
("Hawaii",5.0)
(//~) :: Fractional a => Setter' s a    -> a -> s -> s
(//~) :: Fractional a => Iso' s a       -> a -> s -> s
(//~) :: Fractional a => Lens' s a      -> a -> s -> s
(//~) :: Fractional a => Traversal' s a -> a -> s -> s

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

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

>>> (1,3) & _2 ^~ 2
(1,9)
('^~') :: (Num a, Integral e) => Setter' s a    -> e -> s -> s
('^~') :: (Num a, Integral e) => Iso' s a       -> e -> s -> s
('^~') :: (Num a, Integral e) => Lens' s a      -> e -> s -> s
('^~') :: (Num a, Integral e) => Traversal' s a -> e -> s -> s

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

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

>>> (1,2) & _2 ^^~ (-1)
(1,0.5)
('^^~') :: (Fractional a, Integral e) => Setter' s a    -> e -> s -> s
('^^~') :: (Fractional a, Integral e) => Iso' s a       -> e -> s -> s
('^^~') :: (Fractional a, Integral e) => Lens' s a      -> e -> s -> s
('^^~') :: (Fractional a, Integral e) => Traversal' s a -> e -> s -> s

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

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

>>> (a,b) & _1 **~ c
(a**c,b)
>>> (a,b) & both **~ c
(a**c,b**c)
>>> _2 **~ 10 $ (3,2)
(3,1024.0)
(**~) :: Floating a => Setter' s a    -> a -> s -> s
(**~) :: Floating a => Iso' s a       -> a -> s -> s
(**~) :: Floating a => Lens' s a      -> a -> s -> s
(**~) :: Floating a => Traversal' s a -> a -> s -> s

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

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

>>> both ||~ True $ (False,True)
(True,True)
>>> both ||~ False $ (False,True)
(False,True)
(||~) :: Setter' s Bool    -> Bool -> s -> s
(||~) :: Iso' s Bool       -> Bool -> s -> s
(||~) :: Lens' s Bool      -> Bool -> s -> s
(||~) :: Traversal' s Bool -> Bool -> s -> s

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

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

>>> both &&~ True $ (False, True)
(False,True)
>>> both &&~ False $ (False, True)
(False,False)
(&&~) :: Setter' s Bool    -> Bool -> s -> s
(&&~) :: Iso' s Bool       -> Bool -> s -> s
(&&~) :: Lens' s Bool      -> Bool -> s -> s
(&&~) :: Traversal' s Bool -> Bool -> s -> s

(.=) :: 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.

>>> execState (do _1 .= c; _2 .= d) (a,b)
(c,d)
>>> execState (both .= c) (a,b)
(c,c)
(.=) :: MonadState s m => Iso' s a       -> a -> m ()
(.=) :: MonadState s m => Lens' s a      -> a -> m ()
(.=) :: MonadState s m => Traversal' s a -> a -> m ()
(.=) :: MonadState s m => Setter' s a    -> a -> m ()

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

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

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

>>> execState (do _1 %= f;_2 %= g) (a,b)
(f a,g b)
>>> execState (do both %= f) (a,b)
(f a,f b)
(%=) :: MonadState s m => Iso' s a       -> (a -> a) -> m ()
(%=) :: MonadState s m => Lens' s a      -> (a -> a) -> m ()
(%=) :: MonadState s m => Traversal' s a -> (a -> a) -> m ()
(%=) :: MonadState s m => Setter' s a    -> (a -> a) -> m ()
(%=) :: MonadState s m => ASetter s s a b -> (a -> b) -> m ()

(?=) :: MonadState s m => 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.

>>> execState (do at 1 ?= a; at 2 ?= b) Map.empty
fromList [(1,a),(2,b)]
>>> execState (do _1 ?= b; _2 ?= c) (Just a, Nothing)
(Just b,Just c)
(?=) :: MonadState s m => Iso' s (Maybe a)       -> a -> m ()
(?=) :: MonadState s m => Lens' s (Maybe a)      -> a -> m ()
(?=) :: MonadState s m => Traversal' s (Maybe a) -> a -> m ()
(?=) :: MonadState s m => Setter' s (Maybe a)    -> a -> m ()

(+=) :: (MonadState s m, 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
>>> execState (do _1 += c; _2 += d) (a,b)
(a + c,b + d)
>>> execState (do _1.at 1.non 0 += 10) (Map.fromList [(2,100)],"hello")
(fromList [(1,10),(2,100)],"hello")
(+=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(+=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(+=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(+=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

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

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

>>> execState (do _1 -= c; _2 -= d) (a,b)
(a - c,b - d)
(-=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(-=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(-=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(-=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

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

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

>>> execState (do _1 *= c; _2 *= d) (a,b)
(a * c,b * d)
(*=) :: (MonadState s m, Num a) => Setter' s a    -> a -> m ()
(*=) :: (MonadState s m, Num a) => Iso' s a       -> a -> m ()
(*=) :: (MonadState s m, Num a) => Lens' s a      -> a -> m ()
(*=) :: (MonadState s m, Num a) => Traversal' s a -> a -> m ()

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

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

>>> execState (do _1 //= c; _2 //= d) (a,b)
(a / c,b / d)
(//=) :: (MonadState s m, Fractional a) => Setter' s a    -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Iso' s a       -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Lens' s a      -> a -> m ()
(//=) :: (MonadState s m, Fractional a) => Traversal' s a -> a -> m ()

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

>>> execState (do _1 **= c; _2 **= d) (a,b)
(a**c,b**d)
(**=) ::  (MonadState s m, Floating a) => Setter' s a    -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Iso' s a       -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Lens' s a      -> a -> m ()
(**=) ::  (MonadState s m, Floating a) => Traversal' s a -> a -> m ()

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

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

>>> execState (do _1 &&= True; _2 &&= False; _3 &&= True; _4 &&= False) (True,True,False,False)
(True,False,False,False)
(&&=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(&&=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(&&=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(&&=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

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

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

>>> execState (do _1 ||= True; _2 ||= False; _3 ||= True; _4 ||= False) (True,True,False,False)
(True,True,True,False)
(||=) :: MonadState s m => Setter' s Bool    -> Bool -> m ()
(||=) :: MonadState s m => Iso' s Bool       -> Bool -> m ()
(||=) :: MonadState s m => Lens' s Bool      -> Bool -> m ()
(||=) :: MonadState s m => Traversal' s Bool -> Bool -> m ()

(<~) :: MonadState s m => 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
   ...

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

(<.=) :: 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 .= d will avoid unused binding warnings.

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

(<?=) :: MonadState s m => ASetter s s a (Maybe b) -> b -> m 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 ?= d will avoid unused binding warnings.

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

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

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

>>> (Sum a,b) & _1 <>~ Sum c
(Sum {getSum = a + c},b)
>>> (Sum a,Sum b) & both <>~ Sum c
(Sum {getSum = a + c},Sum {getSum = b + c})
>>> both <>~ "!!!" $ ("hello","world")
("hello!!!","world!!!")
(<>~) :: Monoid a => Setter s t a a    -> a -> s -> t
(<>~) :: Monoid a => Iso s t a a       -> a -> s -> t
(<>~) :: Monoid a => Lens s t a a      -> a -> s -> t
(<>~) :: Monoid a => Traversal s t a a -> a -> s -> t

(<>=) :: (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 mappending a value.

>>> execState (do _1 <>= Sum c; _2 <>= Product d) (Sum a,Product b)
(Sum {getSum = a + c},Product {getProduct = b * d})
>>> execState (both <>= "!!!") ("hello","world")
("hello!!!","world!!!")
(<>=) :: (MonadState s m, Monoid a) => Setter' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Iso' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Lens' s a -> a -> m ()
(<>=) :: (MonadState s m, Monoid a) => Traversal' s a -> a -> m ()

(%@~) :: 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.

(%@~) ≡ 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 () 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 ()