Portability  Rank2Types 

Stability  provisional 
Maintainer  Edward Kmett <ekmett@gmail.com> 
Safe Haskell  SafeInferred 
A
is a generalization of something Fold
s aFoldable
. It allows
you to extract multiple results from a container. A Foldable
container
can be characterized by the behavior of
foldMap :: (
.
Since we want to be able to work with monomorphic containers, we could
generalize this signature to Foldable
t, Monoid
m) => (a > m) > t a > mforall m.
,
and then decorate it with Monoid
m => (a > m) > s > mAccessor
to obtain
typeFold
s a = forall m.Monoid
m =>Getting
m s s a 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.
 type Fold s a = forall f. (Gettable f, Applicative f) => (a > f a) > s > f s
 (^?) :: s > Getting (First a) s t a b > Maybe a
 (^..) :: s > Getting [a] s t a b > [a]
 folding :: (Foldable f, Applicative g, Gettable g) => (s > f a) > LensLike g s t a b
 folded :: Foldable f => Fold (f a) a
 unfolded :: (b > Maybe (a, b)) > Fold b a
 iterated :: (a > a) > Fold a a
 filtered :: Applicative f => (a > Bool) > SimpleLensLike f a a
 backwards :: LensLike (Backwards f) s t a b > LensLike f s t a b
 repeated :: Fold a a
 replicated :: Int > Fold a a
 cycled :: (Applicative f, Gettable f) => LensLike f s t a b > LensLike f s t a b
 takingWhile :: (Gettable f, Applicative f) => (a > Bool) > Getting (Endo (f s)) s s a a > LensLike f s s a a
 droppingWhile :: (Gettable f, Applicative f) => (a > Bool) > Getting (Endo (f s, f s)) s s a a > LensLike f s s a a
 foldMapOf :: Getting r s t a b > (a > r) > s > r
 foldOf :: Getting a s t a b > s > a
 foldrOf :: Getting (Endo r) s t a b > (a > r > r) > r > s > r
 foldlOf :: Getting (Dual (Endo r)) s t a b > (r > a > r) > r > s > r
 toListOf :: Getting [a] s t a b > s > [a]
 anyOf :: Getting Any s t a b > (a > Bool) > s > Bool
 allOf :: Getting All s t a b > (a > Bool) > s > Bool
 andOf :: Getting All s t Bool b > s > Bool
 orOf :: Getting Any s t Bool b > s > Bool
 productOf :: Getting (Product a) s t a b > s > a
 sumOf :: Getting (Sum a) s t a b > s > a
 traverseOf_ :: Functor f => Getting (Traversed f) s t a b > (a > f r) > s > f ()
 forOf_ :: Functor f => Getting (Traversed f) s t a b > s > (a > f r) > f ()
 sequenceAOf_ :: Functor f => Getting (Traversed f) s t (f ()) b > s > f ()
 mapMOf_ :: Monad m => Getting (Sequenced m) s t a b > (a > m r) > s > m ()
 forMOf_ :: Monad m => Getting (Sequenced m) s t a b > s > (a > m r) > m ()
 sequenceOf_ :: Monad m => Getting (Sequenced m) s t (m a) b > s > m ()
 asumOf :: Alternative f => Getting (Endo (f a)) s t (f a) b > s > f a
 msumOf :: MonadPlus m => Getting (Endo (m a)) s t (m a) b > s > m a
 concatMapOf :: Getting [r] s t a b > (a > [r]) > s > [r]
 concatOf :: Getting [r] s t [r] b > s > [r]
 elemOf :: Eq a => Getting Any s t a b > a > s > Bool
 notElemOf :: Eq a => Getting All s t a b > a > s > Bool
 lengthOf :: Getting (Sum Int) s t a b > s > Int
 nullOf :: Getting All s t a b > s > Bool
 headOf :: Getting (First a) s t a b > s > Maybe a
 lastOf :: Getting (Last a) s t a b > s > Maybe a
 maximumOf :: Getting (Max a) s t a b > s > Maybe a
 minimumOf :: Getting (Min a) s t a b > s > Maybe a
 maximumByOf :: Getting (Endo (Maybe a)) s t a b > (a > a > Ordering) > s > Maybe a
 minimumByOf :: Getting (Endo (Maybe a)) s t a b > (a > a > Ordering) > s > Maybe a
 findOf :: Getting (First a) s t a b > (a > Bool) > s > Maybe a
 foldrOf' :: Getting (Dual (Endo (r > r))) s t a b > (a > r > r) > r > s > r
 foldlOf' :: Getting (Endo (r > r)) s t a b > (r > a > r) > r > s > r
 foldr1Of :: Getting (Endo (Maybe a)) s t a b > (a > a > a) > s > a
 foldl1Of :: Getting (Dual (Endo (Maybe a))) s t a b > (a > a > a) > s > a
 foldrMOf :: Monad m => Getting (Dual (Endo (r > m r))) s t a b > (a > r > m r) > r > s > m r
 foldlMOf :: Monad m => Getting (Endo (r > m r)) s t a b > (r > a > m r) > r > s > m r
 newtype ReifiedFold s a = ReifyFold {
 reflectFold :: Fold s a
Folds
type Fold s a = forall f. (Gettable f, Applicative f) => (a > f a) > s > f sSource
A Fold
describes how to retrieve multiple values in a way that can be composed
with other lenslike constructions.
A
provides a structure with operations very similar to those of the Fold
s aFoldable
typeclass, see foldMapOf
and the other Fold
combinators.
By convention, if there exists a foo
method that expects a
, then there should be a
Foldable
(f a)fooOf
method that takes a
and a value of type Fold
s as
.
A Getter
is a legal Fold
that just ignores the supplied Monoid
Unlike a Traversal
a Fold
is readonly. Since a Fold
cannot be used to write back
there are no lens laws that apply.
(^?) :: s > Getting (First a) s t a b > Maybe aSource
Perform a safe head
of a Fold
or Traversal
or retrieve Just
the result
from a Getter
or Lens
.
When using a Traversal
as a partial Lens
, or a Fold
as a partial Getter
this can be a convenient
way to extract the optional value.
(^?
) ≡flip
headOf
(^?
) :: s >Getter
s a >Maybe
a (^?
) :: s >Fold
s a >Maybe
a (^?
) :: s >Simple
Lens
s a >Maybe
a (^?
) :: s >Simple
Iso
s a >Maybe
a (^?
) :: s >Simple
Traversal
s a >Maybe
a
(^..) :: s > Getting [a] s t a b > [a]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 >Simple
Lens
s a > [a] (^..
) :: s >Simple
Iso
s a > [a] (^..
) :: s >Simple
Traversal
s a > [a]
Building Folds
filtered :: Applicative f => (a > Bool) > SimpleLensLike f a aSource
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.
As a counter example, consider that given evens =
the second filtered
even
Traversal
law is violated:
over
evenssucc
.
over
evenssucc
/=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!
filtered
:: (a >Bool
) >Fold
a a
backwards :: LensLike (Backwards f) s t a b > LensLike f s t a bSource
This allows you to traverse the elements of a Traversal
or Fold
in the opposite order.
This will demote an IndexedTraversal
or IndexedFold
to a regular Traversal
or Fold
;
to preserve the indices, use ibackwards
instead.
Note: backwards
should have no impact on a Getter
, Setter
, Lens
or Iso
.
replicated :: Int > Fold a aSource
A fold that replicates its input n
times.
replicate
n ≡toListOf
(replicated
n)
cycled :: (Applicative f, Gettable f) => LensLike f s t a b > LensLike f s t a bSource
Transform a fold into a fold that loops over its elements over and over.
>>>
take 6 $ toListOf (cycled traverse) [1,2,3]
[1,2,3,1,2,3]
takingWhile :: (Gettable f, Applicative f) => (a > Bool) > Getting (Endo (f s)) s s a a > LensLike f s s a aSource
droppingWhile :: (Gettable f, Applicative f) => (a > Bool) > Getting (Endo (f s, f s)) s s a a > LensLike f s s a aSource
Folding
foldMapOf :: Getting r s t a b > (a > r) > s > rSource
foldMap
=foldMapOf
folded
foldMapOf
≡views
foldMapOf
::Getter
s a > (a > r) > s > rfoldMapOf
::Monoid
r =>Fold
s a > (a > r) > s > rfoldMapOf
::Simple
Lens
s a > (a > r) > s > rfoldMapOf
::Simple
Iso
s a > (a > r) > s > rfoldMapOf
::Monoid
r =>Simple
Traversal
s a > (a > r) > s > r
foldrOf :: Getting (Endo r) s t a b > (a > r > r) > r > s > rSource
Rightassociative 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 > rfoldrOf
::Fold
s a > (a > r > r) > r > s > rfoldrOf
::Simple
Lens
s a > (a > r > r) > r > s > rfoldrOf
::Simple
Iso
s a > (a > r > r) > r > s > rfoldrOf
::Simple
Traversal
s a > (a > r > r) > r > s > r
foldlOf :: Getting (Dual (Endo r)) s t a b > (r > a > r) > r > s > rSource
Leftassociative 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 > rfoldlOf
::Fold
s a > (r > a > r) > r > s > rfoldlOf
::Simple
Lens
s a > (r > a > r) > r > s > rfoldlOf
::Simple
Iso
s a > (r > a > r) > r > s > rfoldlOf
::Simple
Traversal
s a > (r > a > r) > r > s > r
anyOf :: Getting Any s t a b > (a > Bool) > s > BoolSource
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))
True
any
≡anyOf
folded
anyOf
::Getter
s a > (a >Bool
) > s >Bool
anyOf
::Fold
s a > (a >Bool
) > s >Bool
anyOf
::Simple
Lens
s a > (a >Bool
) > s >Bool
anyOf
::Simple
Iso
s a > (a >Bool
) > s >Bool
anyOf
::Simple
Traversal
s a > (a >Bool
) > s >Bool
allOf :: Getting All s t a b > (a > Bool) > s > BoolSource
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
allOf
::Getter
s a > (a >Bool
) > s >Bool
allOf
::Fold
s a > (a >Bool
) > s >Bool
allOf
::Simple
Lens
s a > (a >Bool
) > s >Bool
allOf
::Simple
Iso
s a > (a >Bool
) > s >Bool
allOf
::Simple
Traversal
s a > (a >Bool
) > s >Bool
andOf :: Getting All s t Bool b > s > BoolSource
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
sBool
> s >Bool
andOf
::Fold
sBool
> s >Bool
andOf
::Simple
Lens
sBool
> s >Bool
andOf
::Simple
Iso
sBool
> s >Bool
andOf
::Simple
Traversal
sBool
> s >Bool
orOf :: Getting Any s t Bool b > s > BoolSource
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
sBool
> s >Bool
orOf
::Fold
sBool
> s >Bool
orOf
::Simple
Lens
sBool
> s >Bool
orOf
::Simple
Iso
sBool
> s >Bool
orOf
::Simple
Traversal
sBool
> s >Bool
productOf :: Getting (Product a) s t a b > s > aSource
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
productOf
::Getter
s a > s > aproductOf
::Num
a =>Fold
s a > s > aproductOf
::Simple
Lens
s a > s > aproductOf
::Simple
Iso
s a > s > aproductOf
::Num
a =>Simple
Traversal
s a > s > a
sumOf :: Getting (Sum a) s t a b > s > aSource
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
sumOf
_1
:: (a, b) > asumOf
(folded
._1
) :: (Foldable
f,Num
a) => f (a, b) > a
sumOf
::Getter
s a > s > asumOf
::Num
a =>Fold
s a > s > asumOf
::Simple
Lens
s a > s > asumOf
::Simple
Iso
s a > s > asumOf
::Num
a =>Simple
Traversal
s a > s > a
traverseOf_ :: Functor f => Getting (Traversed f) s t a b > (a > f r) > s > f ()Source
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_
traverseLeft
::Applicative
f => (a > f b) >Either
a c > f ()
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 =>Simple
Lens
s a > (a > f r) > s > f ()traverseOf_
::Functor
f =>Simple
Iso
s a > (a > f r) > s > f ()traverseOf_
::Applicative
f =>Simple
Traversal
s a > (a > f r) > s > f ()
forOf_ :: Functor f => Getting (Traversed f) s t a b > s > (a > f r) > f ()Source
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
The rather specific signature of forOf_
allows it to be used as if the signature was any of:
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 =>Simple
Lens
s a > s > (a > f r) > f ()forOf_
::Functor
f =>Simple
Iso
s a > s > (a > f r) > f ()forOf_
::Applicative
f =>Simple
Traversal
s a > s > (a > f r) > f ()
sequenceAOf_ :: Functor f => Getting (Traversed f) s t (f ()) b > s > f ()Source
Evaluate each action in observed by a Fold
on a structure from left to right, ignoring the results.
sequenceA_
≡sequenceAOf_
folded
sequenceAOf_
::Functor
f =>Getter
s (f ()) > s > f ()sequenceAOf_
::Applicative
f =>Fold
s (f ()) > s > f ()sequenceAOf_
::Functor
f =>Simple
Lens
s (f ()) > s > f ()sequenceAOf_
::Functor
f =>Simple
Iso
s (f ()) > s > f ()sequenceAOf_
::Applicative
f =>Simple
Traversal
s (f ()) > s > f ()
mapMOf_ :: Monad m => Getting (Sequenced m) s t a b > (a > m r) > s > m ()Source
Map each target of a Fold
on a structure to a monadic action, evaluate these actions from left to right, and ignore the results.
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 =>Simple
Lens
s a > (a > m r) > s > m ()mapMOf_
::Monad
m =>Simple
Iso
s a > (a > m r) > s > m ()mapMOf_
::Monad
m =>Simple
Traversal
s a > (a > m r) > s > m ()
forMOf_ :: Monad m => Getting (Sequenced m) s t a b > s > (a > m r) > m ()Source
forMOf_
is mapMOf_
with two of its arguments flipped.
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 =>Simple
Lens
s a > s > (a > m r) > m ()forMOf_
::Monad
m =>Simple
Iso
s a > s > (a > m r) > m ()forMOf_
::Monad
m =>Simple
Traversal
s a > s > (a > m r) > m ()
sequenceOf_ :: Monad m => Getting (Sequenced m) s t (m a) b > s > m ()Source
Evaluate each monadic action referenced by a Fold
on the structure from left to right, and ignore the results.
sequence_
≡sequenceOf_
folded
sequenceOf_
::Monad
m =>Getter
s (m a) > s > m ()sequenceOf_
::Monad
m =>Fold
s (m a) > s > m ()sequenceOf_
::Monad
m =>Simple
Lens
s (m a) > s > m ()sequenceOf_
::Monad
m =>Simple
Iso
s (m a) > s > m ()sequenceOf_
::Monad
m =>Simple
Traversal
s (m a) > s > m ()
asumOf :: Alternative f => Getting (Endo (f a)) s t (f a) b > s > f aSource
The sum of a collection of actions, generalizing concatOf
.
asum
≡asumOf
folded
asumOf
::Alternative
f =>Getter
s a > s > f aasumOf
::Alternative
f =>Fold
s a > s > f aasumOf
::Alternative
f =>Simple
Lens
s a > s > f aasumOf
::Alternative
f =>Simple
Iso
s a > s > f aasumOf
::Alternative
f =>Simple
Traversal
s a > s > f a
msumOf :: MonadPlus m => Getting (Endo (m a)) s t (m a) b > s > m aSource
The sum of a collection of actions, generalizing concatOf
.
msum
≡msumOf
folded
msumOf
::MonadPlus
m =>Getter
s a > s > m amsumOf
::MonadPlus
m =>Fold
s a > s > m amsumOf
::MonadPlus
m =>Simple
Lens
s a > s > m amsumOf
::MonadPlus
m =>Simple
Iso
s a > s > m amsumOf
::MonadPlus
m =>Simple
Traversal
s a > s > m a
concatMapOf :: Getting [r] s t a b > (a > [r]) > s > [r]Source
Map a function over all the targets of a Fold
of a container and concatenate the resulting lists.
concatMap
≡concatMapOf
folded
concatMapOf
::Getter
s a > (a > [r]) > s > [r]concatMapOf
::Fold
s a > (a > [r]) > s > [r]concatMapOf
::Simple
Lens
s a > (a > [r]) > s > [r]concatMapOf
::Simple
Iso
s a > (a > [r]) > s > [r]concatMapOf
::Simple
Traversal
s a > (a > [r]) > s > [r]
concatOf :: Getting [r] s t [r] b > s > [r]Source
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
::Simple
Iso
s [r] > s > [r]concatOf
::Simple
Lens
s [r] > s > [r]concatOf
::Simple
Traversal
s [r] > s > [r]
elemOf :: Eq a => Getting Any s t a b > a > s > BoolSource
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 =>Simple
Lens
s a > a > s >Bool
elemOf
::Eq
a =>Simple
Iso
s a > a > s >Bool
elemOf
::Eq
a =>Simple
Traversal
s a > a > s >Bool
notElemOf :: Eq a => Getting All s t a b > a > s > BoolSource
Does the element not occur anywhere within a given Fold
of the structure?
notElem
≡notElemOf
folded
notElemOf
::Eq
a =>Getter
s a > a > s >Bool
notElemOf
::Eq
a =>Fold
s a > a > s >Bool
notElemOf
::Eq
a =>Simple
Iso
s a > a > s >Bool
notElemOf
::Eq
a =>Simple
Lens
s a > a > s >Bool
notElemOf
::Eq
a =>Simple
Traversal
s a > a > s >Bool
lengthOf :: Getting (Sum Int) s t a b > s > IntSource
Note: this can be rather inefficient for large containers.
length
≡lengthOf
folded
>>>
lengthOf _1 ("hello",())
1
lengthOf
(folded
.folded
) ::Foldable
f => f (g a) >Int
lengthOf
::Getter
s a > s >Int
lengthOf
::Fold
s a > s >Int
lengthOf
::Simple
Lens
s a > s >Int
lengthOf
::Simple
Iso
s a > s >Int
lengthOf
::Simple
Traversal
s a > s >Int
nullOf :: Getting All s t a b > s > BoolSource
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
(folded
.
_1
.
folded
) ::Foldable
f => f (g a, b) >Bool
nullOf
::Getter
s a > s >Bool
nullOf
::Fold
s a > s >Bool
nullOf
::Simple
Iso
s a > s >Bool
nullOf
::Simple
Lens
s a > s >Bool
nullOf
::Simple
Traversal
s a > s >Bool
headOf :: Getting (First a) s t a b > s > Maybe aSource
Perform a safe head
of a Fold
or Traversal
or retrieve Just
the result
from a Getter
or Lens
. See also (^?
).
listToMaybe
.
toList
≡headOf
folded
headOf
::Getter
s a > s >Maybe
aheadOf
::Fold
s a > s >Maybe
aheadOf
::Simple
Lens
s a > s >Maybe
aheadOf
::Simple
Iso
s a > s >Maybe
aheadOf
::Simple
Traversal
s a > s >Maybe
a
maximumOf :: Getting (Max a) s t a b > s > Maybe aSource
Obtain the maximum element (if any) targeted by a Fold
or Traversal
Note: maximumOf on a valid Iso
, Lens
or Getter
will always return Just
a value.
maximum
≡fromMaybe
(error
empty).
maximumOf
folded
maximumOf
::Getter
s a > s >Maybe
amaximumOf
::Ord
a =>Fold
s a > s >Maybe
amaximumOf
::Simple
Iso
s a > s >Maybe
amaximumOf
::Simple
Lens
s a > s >Maybe
amaximumOf
::Ord
a =>Simple
Traversal
s a > s >Maybe
a
minimumOf :: Getting (Min a) s t a b > s > Maybe aSource
Obtain the minimum element (if any) targeted by a Fold
or Traversal
Note: minimumOf on a valid Iso
, Lens
or Getter
will always return Just
a value.
minimum
≡fromMaybe
(error
empty).
minimumOf
folded
minimumOf
::Getter
s a > s >Maybe
aminimumOf
::Ord
a =>Fold
s a > s >Maybe
aminimumOf
::Simple
Iso
s a > s >Maybe
aminimumOf
::Simple
Lens
s a > s >Maybe
aminimumOf
::Ord
a =>Simple
Traversal
s a > s >Maybe
a
maximumByOf :: Getting (Endo (Maybe a)) s t a b > (a > a > Ordering) > s > Maybe aSource
Obtain the maximum element (if any) targeted by a Fold
, Traversal
, Lens
, Iso
,
or Getter
according to a user supplied ordering.
maximumBy
cmp ≡fromMaybe
(error
empty).
maximumByOf
folded
cmp
maximumByOf
::Getter
s a > (a > a >Ordering
) > s >Maybe
amaximumByOf
::Fold
s a > (a > a >Ordering
) > s >Maybe
amaximumByOf
::Simple
Iso
s a > (a > a >Ordering
) > s >Maybe
amaximumByOf
::Simple
Lens
s a > (a > a >Ordering
) > s >Maybe
amaximumByOf
::Simple
Traversal
s a > (a > a >Ordering
) > s >Maybe
a
minimumByOf :: Getting (Endo (Maybe a)) s t a b > (a > a > Ordering) > s > Maybe aSource
Obtain the minimum element (if any) targeted by a Fold
, Traversal
, Lens
, Iso
or Getter
according to a user supplied ordering.
minimumBy
cmp ≡fromMaybe
(error
empty).
minimumByOf
folded
cmp
minimumByOf
::Getter
s a > (a > a >Ordering
) > s >Maybe
aminimumByOf
::Fold
s a > (a > a >Ordering
) > s >Maybe
aminimumByOf
::Simple
Iso
s a > (a > a >Ordering
) > s >Maybe
aminimumByOf
::Simple
Lens
s a > (a > a >Ordering
) > s >Maybe
aminimumByOf
::Simple
Traversal
s a > (a > a >Ordering
) > s >Maybe
a
findOf :: Getting (First a) s t a b > (a > Bool) > s > Maybe aSource
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
::Getter
s a > (a >Bool
) > s >Maybe
afindOf
::Fold
s a > (a >Bool
) > s >Maybe
afindOf
::Simple
Iso
s a > (a >Bool
) > s >Maybe
afindOf
::Simple
Lens
s a > (a >Bool
) > s >Maybe
afindOf
::Simple
Traversal
s a > (a >Bool
) > s >Maybe
a
foldrOf' :: Getting (Dual (Endo (r > r))) s t a b > (a > r > r) > r > s > rSource
Strictly fold right over the elements of a structure.
foldr'
≡foldrOf'
folded
foldrOf'
::Getter
s a > (a > r > r) > r > s > rfoldrOf'
::Fold
s a > (a > r > r) > r > s > rfoldrOf'
::Simple
Iso
s a > (a > r > r) > r > s > rfoldrOf'
::Simple
Lens
s a > (a > r > r) > r > s > rfoldrOf'
::Simple
Traversal
s a > (a > r > r) > r > s > r
foldlOf' :: Getting (Endo (r > r)) s t a b > (r > a > r) > r > s > rSource
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 > rfoldlOf'
::Fold
s a > (r > a > r) > r > s > rfoldlOf'
::Simple
Iso
s a > (r > a > r) > r > s > rfoldlOf'
::Simple
Lens
s a > (r > a > r) > r > s > rfoldlOf'
::Simple
Traversal
s a > (r > a > r) > r > s > r
foldr1Of :: Getting (Endo (Maybe a)) s t a b > (a > a > a) > s > aSource
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
l f ≡foldr1
f.
toListOf
lfoldr1
≡foldr1Of
folded
foldr1Of
::Getter
s a > (a > a > a) > s > afoldr1Of
::Fold
s a > (a > a > a) > s > afoldr1Of
::Simple
Iso
s a > (a > a > a) > s > afoldr1Of
::Simple
Lens
s a > (a > a > a) > s > afoldr1Of
::Simple
Traversal
s a > (a > a > a) > s > a
foldl1Of :: Getting (Dual (Endo (Maybe a))) s t a b > (a > a > a) > s > aSource
A variant of foldlOf
that has no base case and thus may only be applied to lenses and strutures such
that the lens views at least one element of the structure.
foldl1Of
l f ≡foldl1Of
l f .toList
foldl1
≡foldl1Of
folded
foldl1Of
::Getter
s a > (a > a > a) > s > afoldl1Of
::Fold
s a > (a > a > a) > s > afoldl1Of
::Simple
Iso
s a > (a > a > a) > s > afoldl1Of
::Simple
Lens
s a > (a > a > a) > s > afoldl1Of
::Simple
Traversal
s a > (a > a > a) > s > a
foldrMOf :: Monad m => Getting (Dual (Endo (r > m r))) s t a b > (a > r > m r) > r > s > m rSource
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 rfoldrMOf
::Monad
m =>Fold
s a > (a > r > m r) > r > s > m rfoldrMOf
::Monad
m =>Simple
Iso
s a > (a > r > m r) > r > s > m rfoldrMOf
::Monad
m =>Simple
Lens
s a > (a > r > m r) > r > s > m rfoldrMOf
::Monad
m =>Simple
Traversal
s a > (a > r > m r) > r > s > m r
foldlMOf :: Monad m => Getting (Endo (r > m r)) s t a b > (r > a > m r) > r > s > m rSource
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 rfoldlMOf
::Monad
m =>Fold
s a > (r > a > m r) > r > s > m rfoldlMOf
::Monad
m =>Simple
Iso
s a > (r > a > m r) > r > s > m rfoldlMOf
::Monad
m =>Simple
Lens
s a > (r > a > m r) > r > s > m rfoldlMOf
::Monad
m =>Simple
Traversal
s a > (r > a > m r) > r > s > m r
Storing Folds
newtype ReifiedFold s a Source
Useful for storing folds in containers.
ReifyFold  
