Control.Lens.Fold

A Fold s a is a generalization of something Foldable. It allows you to extract multiple results from a container. A Foldable container can be characterized by the behavior of foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m. Since we want to be able to work with monomorphic containers, we could generalize this signature to forall m. Monoid m => (a -> m) -> s -> m, and then decorate it with Const to obtain

type Fold s a = forall m. Monoid m => Getting m s a

Every Getter is a valid Fold that simply doesn't use the Monoid it is passed.

In practice the type we use is slightly more complicated to allow for better error messages and for it to be transformed by certain Applicative transformers.

Everything you can do with a Foldable container, you can with with a Fold and there are combinators that generalize the usual Foldable operations here.

Folds

type Fold s a = forall f. (Functor f, Applicative f) => (a -> f a) -> s -> f s

A Fold describes how to retrieve multiple values in a way that can be composed with other LensLike constructions.

A Fold s a provides a structure with operations very similar to those of the Foldable typeclass, see foldMapOf and the other Fold combinators.

By convention, if there exists a foo method that expects a Foldable (f a), then there should be a fooOf method that takes a Fold s a and a value of type s.

A Getter is a legal Fold that just ignores the supplied Monoid.

Unlike a Traversal a Fold is read-only. Since a Fold cannot be used to write back there are no Lens laws that apply.

Getting Started

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

A convenient infix (flipped) version of toListOf.

>>> [[1,2],[3]]^..id
[[[1,2],[3]]]
>>> [[1,2],[3]]^..traverse
[[1,2],[3]]
>>> [[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

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. This is because ^? works by using the First monoid, which can occasionally cause space leaks.

>>> Left 4 ^?_Left
Just 4

>>> Right 4 ^?_Left
Nothing

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

>>> "world" ^? ix 20
Nothing

This operator works as an infix version of preview.

(^?) ≡ flip preview

It may be helpful to think of ^? as having one of the following more specialized types:

(^?) :: 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 (Endo1 a) s a -> a infixl 8

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

pre :: Getting (First a) s a -> Getter s (Maybe a)

This converts a Fold to a IndexPreservingGetter that returns the first element, if it exists, as a Maybe.

pre :: Getter s a     -> IndexPreservingGetter s (Maybe a)
pre :: Fold s a       -> IndexPreservingGetter s (Maybe a)
pre :: Traversal' s a -> IndexPreservingGetter s (Maybe a)
pre :: Lens' s a      -> IndexPreservingGetter s (Maybe a)
pre :: Iso' s a       -> IndexPreservingGetter s (Maybe a)
pre :: Prism' s a     -> IndexPreservingGetter s (Maybe a)

preview :: MonadReader s m => Getting (First a) s a -> m (Maybe a)

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens). See also firstOf and ^?, which are similar with some subtle differences (explained below).

listToMaybe . toList ≡ preview folded

preview = view . pre

Unlike ^?, this function uses a MonadReader to read the value to be focused in on. This allows one to pass the value as the last argument by using the MonadReader instance for (->) s However, it may also be used as part of some deeply nested transformer stack.

preview uses a monoidal value to obtain the result. This means that it generally has good performance, but can occasionally cause space leaks or even stack overflows on some data types. There is another function, firstOf, which avoids these issues at the cost of a slight constant performance cost and a little less flexibility.

It may be helpful to think of preview as having one of the following more specialized types:

preview :: Getter s a     -> s -> Maybe a
preview :: Fold s a       -> s -> Maybe a
preview :: Lens' s a      -> s -> Maybe a
preview :: Iso' s a       -> s -> Maybe a
preview :: Traversal' s a -> s -> Maybe a

preview :: MonadReader s m => Getter s a     -> m (Maybe a)
preview :: MonadReader s m => Fold s a       -> m (Maybe a)
preview :: MonadReader s m => Lens' s a      -> m (Maybe a)
preview :: MonadReader s m => Iso' s a       -> m (Maybe a)
preview :: MonadReader s m => Traversal' s a -> m (Maybe a)

previews :: MonadReader s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens).

This is usually applied in the Reader Monad (->) s.

preuse :: MonadState s m => Getting (First a) s a -> m (Maybe a)

Retrieve the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuse = use . pre

preuse :: MonadState s m => Getter s a     -> m (Maybe a)
preuse :: MonadState s m => Fold s a       -> m (Maybe a)
preuse :: MonadState s m => Lens' s a      -> m (Maybe a)
preuse :: MonadState s m => Iso' s a       -> m (Maybe a)
preuse :: MonadState s m => Traversal' s a -> m (Maybe a)

preuses :: MonadState s m => Getting (First r) s a -> (a -> r) -> m (Maybe r)

Retrieve a function of the first value targeted by a Fold or Traversal (or Just the result from a Getter or Lens) into the current state.

preuses = uses . pre

preuses :: MonadState s m => Getter s a     -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Fold s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Lens' s a      -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Iso' s a       -> (a -> r) -> m (Maybe r)
preuses :: MonadState s m => Traversal' s a -> (a -> r) -> m (Maybe r)

has :: Getting Any s a -> s -> Bool

Check to see if this Fold or Traversal matches 1 or more entries.

>>> has (element 0) []
False

>>> has _Left (Left 12)
True

>>> has _Right (Left 12)
False

This will always return True for a Lens or Getter.

>>> has _1 ("hello","world")
True

has :: Getter s a     -> s -> Bool
has :: Fold s a       -> s -> Bool
has :: Iso' s a       -> s -> Bool
has :: Lens' s a      -> s -> Bool
has :: Traversal' s a -> s -> Bool

hasn't :: Getting All s a -> s -> Bool

Check to see if this Fold or Traversal has no matches.

>>> hasn't _Left (Right 12)
True

>>> hasn't _Left (Left 12)
False

Building Folds

folding :: Foldable f => (s -> f a) -> Fold s a

Obtain a Fold by lifting an operation that returns a Foldable result.

This can be useful to lift operations from Data.List and elsewhere into a Fold.

>>> [1,2,3,4]^..folding tail
[2,3,4]

foldring :: (Functor f, Applicative f) => ((a -> f a -> f a) -> f a -> s -> f a) -> LensLike f s t a b

Obtain a Fold by lifting foldr like function.

>>> [1,2,3,4]^..foldring foldr
[1,2,3,4]

unfolded :: (b -> Maybe (a, b)) -> Fold b a

Build a Fold that unfolds its values from a seed.

unfoldr ≡ toListOf . unfolded

>>> 10^..unfolded (\b -> if b == 0 then Nothing else Just (b, b-1))
[10,9,8,7,6,5,4,3,2,1]

iterated :: Applicative f => (a -> a) -> LensLike' f a a

x ^. iterated f returns an infinite Fold1 of repeated applications of f to x.

toListOf (iterated f) a ≡ iterate f a

iterated :: (a -> a) -> Fold1 a a

filtered :: (forall a. Lift (Either a) p, Applicative f) => (a -> Bool) -> Optic' p f a a

Obtain a Fold that can be composed with to filter another Lens, Iso, Getter, Fold (or Traversal).

Note: This is not a legal Traversal, unless you are very careful not to invalidate the predicate on the target.

Note: This is also not a legal Prism, unless you are very careful not to inject a value that fails the predicate.

As a counter example, consider that given evens = filtered even the second Traversal law is violated:

over evens succ . over evens succ /= over evens (succ . succ)

So, in order for this to qualify as a legal Traversal you can only use it for actions that preserve the result of the predicate!

>>> [1..10]^..folded.filtered even
[2,4,6,8,10]

This will preserve an index if it is present.

backwards :: (Profunctor p, Profunctor q) => Optical p q (Backwards f) s t a b -> Optical p q f s t a b

This allows you to traverse the elements of a pretty much any LensLike construction in the opposite order.

This will preserve indexes on Indexed types and will give you the elements of a (finite) Fold or Traversal in the opposite order.

This has no practical impact on a Getter, Setter, Lens or Iso.

NB: To write back through an Iso, you want to use from. Similarly, to write back through an Prism, you want to use re.

repeated :: Applicative f => LensLike' f a a

Form a Fold1 by repeating the input forever.

repeat ≡ toListOf repeated

>>> timingOut $ 5^..taking 20 repeated
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

repeated :: Fold1 a a

replicated :: Int -> Fold a a

A Fold that replicates its input n times.

replicate n ≡ toListOf (replicated n)

>>> 5^..replicated 20
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5]

cycled :: Applicative f => LensLike f s t a b -> LensLike f s t a b

Transform a non-empty Fold into a Fold1 that loops over its elements over and over.

>>> timingOut $ [1,2,3]^..taking 7 (cycled traverse)
[1,2,3,1,2,3,1]

cycled :: Fold1 s a -> Fold1 s a

Folding

foldMapOf :: Getting r s a -> (a -> r) -> s -> r

Map each part of a structure viewed through a Lens, Getter, Fold or Traversal to a monoid and combine the results.

>>> foldMapOf (folded . both . _Just) Sum [(Just 21, Just 21)]
Sum {getSum = 42}

foldMap = foldMapOf folded

foldMapOf ≡ views
ifoldMapOf l = foldMapOf l . Indexed

foldMapOf ::                Getter s a      -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Fold s a        -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Fold1 s a       -> (a -> r) -> s -> r
foldMapOf ::                Lens' s a       -> (a -> r) -> s -> r
foldMapOf ::                Iso' s a        -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Traversal' s a  -> (a -> r) -> s -> r
foldMapOf :: Semigroup r => Traversal1' s a -> (a -> r) -> s -> r
foldMapOf :: Monoid r    => Prism' s a      -> (a -> r) -> s -> r

foldMapOf :: Getting r s a -> (a -> r) -> s -> r

foldOf :: Getting a s a -> s -> a

Combine the elements of a structure viewed through a Lens, Getter, Fold or Traversal using a monoid.

>>> foldOf (folded.folded) [[Sum 1,Sum 4],[Sum 8, Sum 8],[Sum 21]]
Sum {getSum = 42}

fold = foldOf folded

foldOf ≡ view

foldOf ::             Getter s m     -> s -> m
foldOf :: Monoid m => Fold s m       -> s -> m
foldOf ::             Lens' s m      -> s -> m
foldOf ::             Iso' s m       -> s -> m
foldOf :: Monoid m => Traversal' s m -> s -> m
foldOf :: Monoid m => Prism' s m     -> s -> m

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r

Right-associative fold of parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldr ≡ foldrOf folded

foldrOf :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf :: Traversal' s a -> (a -> r -> r) -> r -> s -> r
foldrOf :: Prism' s a     -> (a -> r -> r) -> r -> s -> r

ifoldrOf l ≡ foldrOf l . Indexed

foldrOf :: Getting (Endo r) s a -> (a -> r -> r) -> r -> s -> r

foldlOf :: Getting (Dual (Endo r)) s a -> (r -> a -> r) -> r -> s -> r

Left-associative fold of the parts of a structure that are viewed through a Lens, Getter, Fold or Traversal.

foldl ≡ foldlOf folded

foldlOf :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf :: Traversal' s a -> (r -> a -> r) -> r -> s -> r
foldlOf :: Prism' s a     -> (r -> a -> r) -> r -> s -> r

toListOf :: Getting (Endo [a]) s a -> s -> [a]

Extract a list of the targets of a Fold. See also (^..).

toList ≡ toListOf folded
(^..) ≡ flip toListOf

toNonEmptyOf :: Getting (NonEmptyDList a) s a -> s -> NonEmpty a

Extract a NonEmpty of the targets of Fold1.

>>> toNonEmptyOf both1 ("hello", "world")
"hello" :| ["world"]

toNonEmptyOf :: Getter s a      -> s -> NonEmpty a
toNonEmptyOf :: Fold1 s a       -> s -> NonEmpty a
toNonEmptyOf :: Lens' s a       -> s -> NonEmpty a
toNonEmptyOf :: Iso' s a        -> s -> NonEmpty a
toNonEmptyOf :: Traversal1' s a -> s -> NonEmpty a
toNonEmptyOf :: Prism' s a      -> s -> NonEmpty a

anyOf :: Getting Any s a -> (a -> Bool) -> s -> Bool

Returns True if any target of a Fold satisfies a predicate.

>>> anyOf both (=='x') ('x','y')
True
>>> import Data.Data.Lens
>>> anyOf biplate (== "world") (((),2::Int),"hello",("world",11::Int))
True

any ≡ anyOf folded

ianyOf l ≡ anyOf l . Indexed

anyOf :: Getter s a     -> (a -> Bool) -> s -> Bool
anyOf :: Fold s a       -> (a -> Bool) -> s -> Bool
anyOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
anyOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
anyOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
anyOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

allOf :: Getting All s a -> (a -> Bool) -> s -> Bool

Returns True if every target of a Fold satisfies a predicate.

>>> allOf both (>=3) (4,5)
True
>>> allOf folded (>=2) [1..10]
False

all ≡ allOf folded

iallOf l = allOf l . Indexed

allOf :: Getter s a     -> (a -> Bool) -> s -> Bool
allOf :: Fold s a       -> (a -> Bool) -> s -> Bool
allOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
allOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
allOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
allOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

noneOf :: Getting Any s a -> (a -> Bool) -> s -> Bool

Returns True only if no targets of a Fold satisfy a predicate.

>>> noneOf each (is _Nothing) (Just 3, Just 4, Just 5)
True
>>> noneOf (folded.folded) (<10) [[13,99,20],[3,71,42]]
False

inoneOf l = noneOf l . Indexed

noneOf :: Getter s a     -> (a -> Bool) -> s -> Bool
noneOf :: Fold s a       -> (a -> Bool) -> s -> Bool
noneOf :: Lens' s a      -> (a -> Bool) -> s -> Bool
noneOf :: Iso' s a       -> (a -> Bool) -> s -> Bool
noneOf :: Traversal' s a -> (a -> Bool) -> s -> Bool
noneOf :: Prism' s a     -> (a -> Bool) -> s -> Bool

andOf :: Getting All s Bool -> s -> Bool

Returns True if every target of a Fold is True.

>>> andOf both (True,False)
False
>>> andOf both (True,True)
True

and ≡ andOf folded

andOf :: Getter s Bool     -> s -> Bool
andOf :: Fold s Bool       -> s -> Bool
andOf :: Lens' s Bool      -> s -> Bool
andOf :: Iso' s Bool       -> s -> Bool
andOf :: Traversal' s Bool -> s -> Bool
andOf :: Prism' s Bool     -> s -> Bool

orOf :: Getting Any s Bool -> s -> Bool

Returns True if any target of a Fold is True.

>>> orOf both (True,False)
True
>>> orOf both (False,False)
False

or ≡ orOf folded

orOf :: Getter s Bool     -> s -> Bool
orOf :: Fold s Bool       -> s -> Bool
orOf :: Lens' s Bool      -> s -> Bool
orOf :: Iso' s Bool       -> s -> Bool
orOf :: Traversal' s Bool -> s -> Bool
orOf :: Prism' s Bool     -> s -> Bool

productOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a

Calculate the Product of every number targeted by a Fold.

>>> productOf both (4,5)
20
>>> productOf folded [1,2,3,4,5]
120

product ≡ productOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Product . foldMapOf

productOf :: Num a => Getter s a     -> s -> a
productOf :: Num a => Fold s a       -> s -> a
productOf :: Num a => Lens' s a      -> s -> a
productOf :: Num a => Iso' s a       -> s -> a
productOf :: Num a => Traversal' s a -> s -> a
productOf :: Num a => Prism' s a     -> s -> a

sumOf :: Num a => Getting (Endo (Endo a)) s a -> s -> a

Calculate the Sum of every number targeted by a Fold.

>>> sumOf both (5,6)
11
>>> sumOf folded [1,2,3,4]
10
>>> sumOf (folded.both) [(1,2),(3,4)]
10
>>> import Data.Data.Lens
>>> sumOf biplate [(1::Int,[]),(2,[(3::Int,4::Int)])] :: Int
10

sum ≡ sumOf folded

This operation may be more strict than you would expect. If you want a lazier version use ala Sum . foldMapOf

sumOf _1 :: Num a => (a, b) -> a
sumOf (folded . _1) :: (Foldable f, Num a) => f (a, b) -> a

sumOf :: Num a => Getter s a     -> s -> a
sumOf :: Num a => Fold s a       -> s -> a
sumOf :: Num a => Lens' s a      -> s -> a
sumOf :: Num a => Iso' s a       -> s -> a
sumOf :: Num a => Traversal' s a -> s -> a
sumOf :: Num a => Prism' s a     -> s -> a

traverseOf_ :: Functor f => Getting (Traversed r f) s a -> (a -> f r) -> s -> f ()

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike traverseOf do not construct a new structure. traverseOf_ generalizes traverse_ to work over any Fold.

When passed a Getter, traverseOf_ can work over any Functor, but when passed a Fold, traverseOf_ requires an Applicative.

>>> traverseOf_ both putStrLn ("hello","world")
hello
world

traverse_ ≡ traverseOf_ folded

traverseOf_ _2 :: Functor f => (c -> f r) -> (d, c) -> f ()
traverseOf_ _Left :: Applicative f => (a -> f b) -> Either a c -> f ()

itraverseOf_ l ≡ traverseOf_ l . Indexed

The rather specific signature of traverseOf_ allows it to be used as if the signature was any of:

traverseOf_ :: Functor f     => Getter s a     -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Fold s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Lens' s a      -> (a -> f r) -> s -> f ()
traverseOf_ :: Functor f     => Iso' s a       -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Traversal' s a -> (a -> f r) -> s -> f ()
traverseOf_ :: Applicative f => Prism' s a     -> (a -> f r) -> s -> f ()

forOf_ :: Functor f => Getting (Traversed r f) s a -> s -> (a -> f r) -> f ()

Traverse over all of the targets of a Fold (or Getter), computing an Applicative (or Functor)-based answer, but unlike forOf do not construct a new structure. forOf_ generalizes for_ to work over any Fold.

When passed a Getter, forOf_ can work over any Functor, but when passed a Fold, forOf_ requires an Applicative.

for_ ≡ forOf_ folded

>>> forOf_ both ("hello","world") putStrLn
hello
world

The rather specific signature of forOf_ allows it to be used as if the signature was any of:

iforOf_ l s ≡ forOf_ l s . Indexed

forOf_ :: Functor f     => Getter s a     -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Fold s a       -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Lens' s a      -> s -> (a -> f r) -> f ()
forOf_ :: Functor f     => Iso' s a       -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Traversal' s a -> s -> (a -> f r) -> f ()
forOf_ :: Applicative f => Prism' s a     -> s -> (a -> f r) -> f ()

sequenceAOf_ :: Functor f => Getting (Traversed a f) s (f a) -> s -> f ()

Evaluate each action in observed by a Fold on a structure from left to right, ignoring the results.

sequenceA_ ≡ sequenceAOf_ folded

>>> sequenceAOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequenceAOf_ :: Functor f     => Getter s (f a)     -> s -> f ()
sequenceAOf_ :: Applicative f => Fold s (f a)       -> s -> f ()
sequenceAOf_ :: Functor f     => Lens' s (f a)      -> s -> f ()
sequenceAOf_ :: Functor f     => Iso' s (f a)       -> s -> f ()
sequenceAOf_ :: Applicative f => Traversal' s (f a) -> s -> f ()
sequenceAOf_ :: Applicative f => Prism' s (f a)     -> s -> f ()

traverse1Of_ :: Functor f => Getting (TraversedF r f) s a -> (a -> f r) -> s -> f ()

Traverse over all of the targets of a Fold1, computing an Apply based answer.

As long as you have Applicative or Functor effect you are better using traverseOf_. The traverse1Of_ is useful only when you have genuine Apply effect.

>>> traverse1Of_ both1 (\ks -> Map.fromList [ (k, ()) | k <- ks ]) ("abc", "bcd")
fromList [('b',()),('c',())]

traverse1Of_ :: Apply f => Fold1 s a -> (a -> f r) -> s -> f ()

Since: 4.16

for1Of_ :: Functor f => Getting (TraversedF r f) s a -> s -> (a -> f r) -> f ()

See forOf_ and traverse1Of_.

>>> for1Of_ both1 ("abc", "bcd") (\ks -> Map.fromList [ (k, ()) | k <- ks ])
fromList [('b',()),('c',())]

for1Of_ :: Apply f => Fold1 s a -> s -> (a -> f r) -> f ()

Since: 4.16

sequence1Of_ :: Functor f => Getting (TraversedF a f) s (f a) -> s -> f ()

See sequenceAOf_ and traverse1Of_.

sequence1Of_ :: Apply f => Fold1 s (f a) -> s -> f ()

Since: 4.16

mapMOf_ :: Monad m => Getting (Sequenced r m) s a -> (a -> m r) -> s -> m ()

Map each target of a Fold on a structure to a monadic action, evaluate these actions from left to right, and ignore the results.

>>> mapMOf_ both putStrLn ("hello","world")
hello
world

mapM_ ≡ mapMOf_ folded

mapMOf_ :: Monad m => Getter s a     -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Fold s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Lens' s a      -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Iso' s a       -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Traversal' s a -> (a -> m r) -> s -> m ()
mapMOf_ :: Monad m => Prism' s a     -> (a -> m r) -> s -> m ()

forMOf_ :: Monad m => Getting (Sequenced r m) s a -> s -> (a -> m r) -> m ()

forMOf_ is mapMOf_ with two of its arguments flipped.

>>> forMOf_ both ("hello","world") putStrLn
hello
world

forM_ ≡ forMOf_ folded

forMOf_ :: Monad m => Getter s a     -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Fold s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Lens' s a      -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Iso' s a       -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Traversal' s a -> s -> (a -> m r) -> m ()
forMOf_ :: Monad m => Prism' s a     -> s -> (a -> m r) -> m ()

sequenceOf_ :: Monad m => Getting (Sequenced a m) s (m a) -> s -> m ()

Evaluate each monadic action referenced by a Fold on the structure from left to right, and ignore the results.

>>> sequenceOf_ both (putStrLn "hello",putStrLn "world")
hello
world

sequence_ ≡ sequenceOf_ folded

sequenceOf_ :: Monad m => Getter s (m a)     -> s -> m ()
sequenceOf_ :: Monad m => Fold s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Lens' s (m a)      -> s -> m ()
sequenceOf_ :: Monad m => Iso' s (m a)       -> s -> m ()
sequenceOf_ :: Monad m => Traversal' s (m a) -> s -> m ()
sequenceOf_ :: Monad m => Prism' s (m a)     -> s -> m ()

asumOf :: Alternative f => Getting (Endo (f a)) s (f a) -> s -> f a

The sum of a collection of actions, generalizing concatOf.

>>> asumOf both ("hello","world")
"helloworld"

>>> asumOf each (Nothing, Just "hello", Nothing)
Just "hello"

asum ≡ asumOf folded

asumOf :: Alternative f => Getter s (f a)     -> s -> f a
asumOf :: Alternative f => Fold s (f a)       -> s -> f a
asumOf :: Alternative f => Lens' s (f a)      -> s -> f a
asumOf :: Alternative f => Iso' s (f a)       -> s -> f a
asumOf :: Alternative f => Traversal' s (f a) -> s -> f a
asumOf :: Alternative f => Prism' s (f a)     -> s -> f a

msumOf :: MonadPlus m => Getting (Endo (m a)) s (m a) -> s -> m a

The sum of a collection of actions, generalizing concatOf.

>>> msumOf both ("hello","world")
"helloworld"

>>> msumOf each (Nothing, Just "hello", Nothing)
Just "hello"

msum ≡ msumOf folded

msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a

concatMapOf :: Getting [r] s a -> (a -> [r]) -> s -> [r]

Map a function over all the targets of a Fold of a container and concatenate the resulting lists.

>>> concatMapOf both (\x -> [x, x + 1]) (1,3)
[1,2,3,4]

concatMap ≡ concatMapOf folded

concatMapOf :: Getter s a     -> (a -> [r]) -> s -> [r]
concatMapOf :: Fold s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Lens' s a      -> (a -> [r]) -> s -> [r]
concatMapOf :: Iso' s a       -> (a -> [r]) -> s -> [r]
concatMapOf :: Traversal' s a -> (a -> [r]) -> s -> [r]

concatOf :: Getting [r] s [r] -> s -> [r]

Concatenate all of the lists targeted by a Fold into a longer list.

>>> concatOf both ("pan","ama")
"panama"

concat ≡ concatOf folded
concatOf ≡ view

concatOf :: Getter s [r]     -> s -> [r]
concatOf :: Fold s [r]       -> s -> [r]
concatOf :: Iso' s [r]       -> s -> [r]
concatOf :: Lens' s [r]      -> s -> [r]
concatOf :: Traversal' s [r] -> s -> [r]

elemOf :: Eq a => Getting Any s a -> a -> s -> Bool

Does the element occur anywhere within a given Fold of the structure?

>>> elemOf both "hello" ("hello","world")
True

elem ≡ elemOf folded

elemOf :: Eq a => Getter s a     -> a -> s -> Bool
elemOf :: Eq a => Fold s a       -> a -> s -> Bool
elemOf :: Eq a => Lens' s a      -> a -> s -> Bool
elemOf :: Eq a => Iso' s a       -> a -> s -> Bool
elemOf :: Eq a => Traversal' s a -> a -> s -> Bool
elemOf :: Eq a => Prism' s a     -> a -> s -> Bool

notElemOf :: Eq a => Getting All s a -> a -> s -> Bool

Does the element not occur anywhere within a given Fold of the structure?

>>> notElemOf each 'd' ('a','b','c')
True

>>> notElemOf each 'a' ('a','b','c')
False

notElem ≡ notElemOf folded

notElemOf :: Eq a => Getter s a     -> a -> s -> Bool
notElemOf :: Eq a => Fold s a       -> a -> s -> Bool
notElemOf :: Eq a => Iso' s a       -> a -> s -> Bool
notElemOf :: Eq a => Lens' s a      -> a -> s -> Bool
notElemOf :: Eq a => Traversal' s a -> a -> s -> Bool
notElemOf :: Eq a => Prism' s a     -> a -> s -> Bool

lengthOf :: Getting (Endo (Endo Int)) s a -> s -> Int

Calculate the number of targets there are for a Fold in a given container.

Note: This can be rather inefficient for large containers and just like length, this will not terminate for infinite folds.

length ≡ lengthOf folded

>>> lengthOf _1 ("hello",())
1

>>> lengthOf traverse [1..10]
10

>>> lengthOf (traverse.traverse) [[1,2],[3,4],[5,6]]
6

lengthOf (folded . folded) :: (Foldable f, Foldable g) => f (g a) -> Int

lengthOf :: Getter s a     -> s -> Int
lengthOf :: Fold s a       -> s -> Int
lengthOf :: Lens' s a      -> s -> Int
lengthOf :: Iso' s a       -> s -> Int
lengthOf :: Traversal' s a -> s -> Int

nullOf :: Getting All s a -> s -> Bool

Returns True if this Fold or Traversal has no targets in the given container.

Note: nullOf on a valid Iso, Lens or Getter should always return False.

null ≡ nullOf folded

This may be rather inefficient compared to the null check of many containers.

>>> nullOf _1 (1,2)
False

>>> nullOf ignored ()
True

>>> nullOf traverse []
True

>>> nullOf (element 20) [1..10]
True

nullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

nullOf :: Getter s a     -> s -> Bool
nullOf :: Fold s a       -> s -> Bool
nullOf :: Iso' s a       -> s -> Bool
nullOf :: Lens' s a      -> s -> Bool
nullOf :: Traversal' s a -> s -> Bool

notNullOf :: Getting Any s a -> s -> Bool

Returns True if this Fold or Traversal has any targets in the given container.

A more "conversational" alias for this combinator is has.

Note: notNullOf on a valid Iso, Lens or Getter should always return True.

not . null ≡ notNullOf folded

This may be rather inefficient compared to the not . null check of many containers.

>>> notNullOf _1 (1,2)
True

>>> notNullOf traverse [1..10]
True

>>> notNullOf folded []
False

>>> notNullOf (element 20) [1..10]
False

notNullOf (folded . _1 . folded) :: (Foldable f, Foldable g) => f (g a, b) -> Bool

notNullOf :: Getter s a     -> s -> Bool
notNullOf :: Fold s a       -> s -> Bool
notNullOf :: Iso' s a       -> s -> Bool
notNullOf :: Lens' s a      -> s -> Bool
notNullOf :: Traversal' s a -> s -> Bool

firstOf :: Getting (Leftmost a) s a -> s -> Maybe a

Retrieve the First entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than preview or ^?' and gives you back access to the outermost Just constructor more quickly, but does so in a way that builds an intermediate structure, and thus may have worse constant factors. This also means that it can not be used in any MonadReader, but must instead have s passed as its last argument, unlike preview.

Note: this could been named headOf.

>>> firstOf traverse [1..10]
Just 1

>>> firstOf both (1,2)
Just 1

>>> firstOf ignored ()
Nothing

firstOf :: Getter s a     -> s -> Maybe a
firstOf :: Fold s a       -> s -> Maybe a
firstOf :: Lens' s a      -> s -> Maybe a
firstOf :: Iso' s a       -> s -> Maybe a
firstOf :: Traversal' s a -> s -> Maybe a

first1Of :: Getting (First a) s a -> s -> a

Retrieve the First entry of a Fold1 or Traversal1 or the result from a Getter or Lens.

>>> first1Of traverse1 (1 :| [2..10])
1

>>> first1Of both1 (1,2)
1

Note: this is different from ^..

>>> first1Of traverse1 ([1,2] :| [[3,4],[5,6]])
[1,2]

>>> ([1,2] :| [[3,4],[5,6]]) ^. traverse1
[1,2,3,4,5,6]

first1Of :: Getter s a      -> s -> a
first1Of :: Fold1 s a       -> s -> a
first1Of :: Lens' s a       -> s -> a
first1Of :: Iso' s a        -> s -> a
first1Of :: Traversal1' s a -> s -> a

lastOf :: Getting (Rightmost a) s a -> s -> Maybe a

Retrieve the Last entry of a Fold or Traversal or retrieve Just the result from a Getter or Lens.

The answer is computed in a manner that leaks space less than ala Last . foldMapOf and gives you back access to the outermost Just constructor more quickly, but may have worse constant factors.

>>> lastOf traverse [1..10]
Just 10

>>> lastOf both (1,2)
Just 2

>>> lastOf ignored ()
Nothing

lastOf :: Getter s a     -> s -> Maybe a
lastOf :: Fold s a       -> s -> Maybe a
lastOf :: Lens' s a      -> s -> Maybe a
lastOf :: Iso' s a       -> s -> Maybe a
lastOf :: Traversal' s a -> s -> Maybe a

last1Of :: Getting (Last a) s a -> s -> a

Retrieve the Last entry of a Fold1 or Traversal1 or retrieve the result from a Getter or Lens.o

>>> last1Of traverse1 (1 :| [2..10])
10

>>> last1Of both1 (1,2)
2

last1Of :: Getter s a      -> s -> Maybe a
last1Of :: Fold1 s a       -> s -> Maybe a
last1Of :: Lens' s a       -> s -> Maybe a
last1Of :: Iso' s a        -> s -> Maybe a
last1Of :: Traversal1' s a -> s -> Maybe a

maximumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a

Obtain the maximum element (if any) targeted by a Fold or Traversal safely.

Note: maximumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> maximumOf traverse [1..10]
Just 10

>>> maximumOf traverse []
Nothing

>>> maximumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 6

maximum ≡ fromMaybe (error "empty") . maximumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMax (foldMapOf l Max) has lazier semantics but could leak memory.

maximumOf :: Ord a => Getter s a     -> s -> Maybe a
maximumOf :: Ord a => Fold s a       -> s -> Maybe a
maximumOf :: Ord a => Iso' s a       -> s -> Maybe a
maximumOf :: Ord a => Lens' s a      -> s -> Maybe a
maximumOf :: Ord a => Traversal' s a -> s -> Maybe a

maximum1Of :: Ord a => Getting (Max a) s a -> s -> a

Obtain the maximum element targeted by a Fold1 or Traversal1.

>>> maximum1Of traverse1 (1 :| [2..10])
10

maximum1Of :: Ord a => Getter s a      -> s -> a
maximum1Of :: Ord a => Fold1 s a       -> s -> a
maximum1Of :: Ord a => Iso' s a        -> s -> a
maximum1Of :: Ord a => Lens' s a       -> s -> a
maximum1Of :: Ord a => Traversal1' s a -> s -> a

minimumOf :: Ord a => Getting (Endo (Endo (Maybe a))) s a -> s -> Maybe a

Obtain the minimum element (if any) targeted by a Fold or Traversal safely.

Note: minimumOf on a valid Iso, Lens or Getter will always return Just a value.

>>> minimumOf traverse [1..10]
Just 1

>>> minimumOf traverse []
Nothing

>>> minimumOf (folded.filtered even) [1,4,3,6,7,9,2]
Just 2

minimum ≡ fromMaybe (error "empty") . minimumOf folded

In the interest of efficiency, This operation has semantics more strict than strictly necessary. rmap getMin (foldMapOf l Min) has lazier semantics but could leak memory.

minimumOf :: Ord a => Getter s a     -> s -> Maybe a
minimumOf :: Ord a => Fold s a       -> s -> Maybe a
minimumOf :: Ord a => Iso' s a       -> s -> Maybe a
minimumOf :: Ord a => Lens' s a      -> s -> Maybe a
minimumOf :: Ord a => Traversal' s a -> s -> Maybe a

minimum1Of :: Ord a => Getting (Min a) s a -> s -> a

Obtain the minimum element targeted by a Fold1 or Traversal1.

>>> minimum1Of traverse1 (1 :| [2..10])
1

minimum1Of :: Ord a => Getter s a      -> s -> a
minimum1Of :: Ord a => Fold1 s a       -> s -> a
minimum1Of :: Ord a => Iso' s a        -> s -> a
minimum1Of :: Ord a => Lens' s a       -> s -> a
minimum1Of :: Ord a => Traversal1' s a -> s -> a

maximumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a

Obtain the maximum element (if any) targeted by a Fold, Traversal, Lens, Iso, or Getter according to a user supplied Ordering.

>>> maximumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "mustard"

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

maximumBy cmp ≡ fromMaybe (error "empty") . maximumByOf folded cmp

maximumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
maximumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

minimumByOf :: Getting (Endo (Endo (Maybe a))) s a -> (a -> a -> Ordering) -> s -> Maybe a

Obtain the minimum element (if any) targeted by a Fold, Traversal, Lens, Iso or Getter according to a user supplied Ordering.

In the interest of efficiency, This operation has semantics more strict than strictly necessary.

>>> minimumByOf traverse (compare `on` length) ["mustard","relish","ham"]
Just "ham"

minimumBy cmp ≡ fromMaybe (error "empty") . minimumByOf folded cmp

minimumByOf :: Getter s a     -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Fold s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Iso' s a       -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Lens' s a      -> (a -> a -> Ordering) -> s -> Maybe a
minimumByOf :: Traversal' s a -> (a -> a -> Ordering) -> s -> Maybe a

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a

The findOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findOf each even (1,3,4,6)
Just 4

>>> findOf folded even [1,3,5,7]
Nothing

findOf :: Getter s a     -> (a -> Bool) -> s -> Maybe a
findOf :: Fold s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Iso' s a       -> (a -> Bool) -> s -> Maybe a
findOf :: Lens' s a      -> (a -> Bool) -> s -> Maybe a
findOf :: Traversal' s a -> (a -> Bool) -> s -> Maybe a

find ≡ findOf folded
ifindOf l ≡ findOf l . Indexed

A simpler version that didn't permit indexing, would be:

findOf :: Getting (Endo (Maybe a)) s a -> (a -> Bool) -> s -> Maybe a
findOf l p = foldrOf l (a y -> if p a then Just a else y) Nothing

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)

The findMOf function takes a Lens (or Getter, Iso, Fold, or Traversal), a monadic predicate and a structure and returns in the monad the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,4,6)
"Checking 1"
"Checking 3"
"Checking 4"
Just 4

>>> findMOf each ( \x -> print ("Checking " ++ show x) >> return (even x)) (1,3,5,7)
"Checking 1"
"Checking 3"
"Checking 5"
"Checking 7"
Nothing

findMOf :: (Monad m, Getter s a)     -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Fold s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Iso' s a)       -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Lens' s a)      -> (a -> m Bool) -> s -> m (Maybe a)
findMOf :: (Monad m, Traversal' s a) -> (a -> m Bool) -> s -> m (Maybe a)

findMOf folded :: (Monad m, Foldable f) => (a -> m Bool) -> f a -> m (Maybe a)
ifindMOf l ≡ findMOf l . Indexed

A simpler version that didn't permit indexing, would be:

findMOf :: Monad m => Getting (Endo (m (Maybe a))) s a -> (a -> m Bool) -> s -> m (Maybe a)
findMOf l p = foldrOf l (a y -> p a >>= x -> if x then return (Just a) else y) $ return Nothing

foldrOf' :: Getting (Dual (Endo (Endo r))) s a -> (a -> r -> r) -> r -> s -> r

Strictly fold right over the elements of a structure.

foldr' ≡ foldrOf' folded

foldrOf' :: Getter s a     -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Fold s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Iso' s a       -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Lens' s a      -> (a -> r -> r) -> r -> s -> r
foldrOf' :: Traversal' s a -> (a -> r -> r) -> r -> s -> r

foldlOf' :: Getting (Endo (Endo r)) s a -> (r -> a -> r) -> r -> s -> r

Fold over the elements of a structure, associating to the left, but strictly.

foldl' ≡ foldlOf' folded

foldlOf' :: Getter s a     -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Fold s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Iso' s a       -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Lens' s a      -> (r -> a -> r) -> r -> s -> r
foldlOf' :: Traversal' s a -> (r -> a -> r) -> r -> s -> r

foldr1Of :: Getting (Endo1 a) s a -> (a -> a -> a) -> s -> a

A variant of foldrOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldr1Of each (+) (1,2,3,4)
10

foldr1Of l f ≡ foldr1 f . toListOf l
foldr1 ≡ foldr1Of folded

foldr1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldr1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldr1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldr1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldl1Of :: Getting (Dual (Endo1 a)) s a -> (a -> a -> a) -> s -> a

A variant of foldlOf that has no base case and thus may only be applied to lenses and structures such that the Lens views at least one element of the structure.

>>> foldl1Of each (+) (1,2,3,4)
10

foldl1Of l f ≡ foldl1 f . toListOf l
foldl1 ≡ foldl1Of folded

foldl1Of :: Getter s a     -> (a -> a -> a) -> s -> a
foldl1Of :: Fold s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Iso' s a       -> (a -> a -> a) -> s -> a
foldl1Of :: Lens' s a      -> (a -> a -> a) -> s -> a
foldl1Of :: Traversal' s a -> (a -> a -> a) -> s -> a

foldrMOf :: Monad m => Getting (Dual (Endo (r -> m r))) s a -> (a -> r -> m r) -> r -> s -> m r

Monadic fold over the elements of a structure, associating to the right, i.e. from right to left.

foldrM ≡ foldrMOf folded

foldrMOf :: Monad m => Getter s a     -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Fold s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Iso' s a       -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Lens' s a      -> (a -> r -> m r) -> r -> s -> m r
foldrMOf :: Monad m => Traversal' s a -> (a -> r -> m r) -> r -> s -> m r

foldlMOf :: Monad m => Getting (Endo (r -> m r)) s a -> (r -> a -> m r) -> r -> s -> m r

Monadic fold over the elements of a structure, associating to the left, i.e. from left to right.

foldlM ≡ foldlMOf folded

foldlMOf :: Monad m => Getter s a     -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Fold s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Iso' s a       -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Lens' s a      -> (r -> a -> m r) -> r -> s -> m r
foldlMOf :: Monad m => Traversal' s a -> (r -> a -> m r) -> r -> s -> m r

lookupOf :: Eq k => Getting (Endo (Maybe v)) s (k, v) -> k -> s -> Maybe v

The lookupOf function takes a Fold (or Getter, Traversal, Lens, Iso, etc.), a key, and a structure containing key/value pairs. It returns the first value corresponding to the given key. This function generalizes lookup to work on an arbitrary Fold instead of lists.

>>> lookupOf folded 4 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'b'

>>> lookupOf each 2 [(2, 'a'), (4, 'b'), (4, 'c')]
Just 'a'

lookupOf :: Eq k => Fold s (k,v) -> k -> s -> Maybe v

Internal types

data Leftmost a

Used for firstOf.

Instances

Semigroup (Leftmost a)

Defined in Control.Lens.Internal.Fold

Methods

(<>) :: Leftmost a -> Leftmost a -> Leftmost a

sconcat :: NonEmpty (Leftmost a) -> Leftmost a

stimes :: Integral b => b -> Leftmost a -> Leftmost a

Monoid (Leftmost a)

Defined in Control.Lens.Internal.Fold

Methods

mempty :: Leftmost a

mappend :: Leftmost a -> Leftmost a -> Leftmost a

mconcat :: [Leftmost a] -> Leftmost a

data Rightmost a

Used for lastOf.

Instances

Semigroup (Rightmost a)

Defined in Control.Lens.Internal.Fold

Methods

(<>) :: Rightmost a -> Rightmost a -> Rightmost a

sconcat :: NonEmpty (Rightmost a) -> Rightmost a

stimes :: Integral b => b -> Rightmost a -> Rightmost a

Monoid (Rightmost a)

Defined in Control.Lens.Internal.Fold

Methods

mempty :: Rightmost a

mappend :: Rightmost a -> Rightmost a -> Rightmost a

mconcat :: [Rightmost a] -> Rightmost a

data Traversed a f

Used internally by traverseOf_ and the like.

The argument a of the result should not be used!

Instances

Applicative f => Semigroup (Traversed a f)

Defined in Control.Lens.Internal.Fold

Methods

(<>) :: Traversed a f -> Traversed a f -> Traversed a f

sconcat :: NonEmpty (Traversed a f) -> Traversed a f

stimes :: Integral b => b -> Traversed a f -> Traversed a f

data Sequenced a m

Used internally by mapM_ and the like.

The argument a of the result should not be used!

See 4.16 Changelog entry for the explanation of "why not Apply f =>"?

Instances

Monad m => Semigroup (Sequenced a m)

Defined in Control.Lens.Internal.Fold

Methods

(<>) :: Sequenced a m -> Sequenced a m -> Sequenced a m

sconcat :: NonEmpty (Sequenced a m) -> Sequenced a m

stimes :: Integral b => b -> Sequenced a m -> Sequenced a m