trait Foldable[F[_]] extends UnorderedFoldable[F] with Serializable
Data structures that can be folded to a summary value.
In the case of a collection (such as List
or Vector
), these
methods will fold together (combine) the values contained in the
collection to produce a single result. Most collection types have
foldLeft
methods, which will usually be used by the associated
Foldable[_]
instance.
Instances of Foldable should be ordered collections to allow for consistent folding.
Use the UnorderedFoldable
type class if you want to fold over unordered collections.
Foldable[F] is implemented in terms of two basic methods:
foldLeft(fa, b)(f)
eagerly foldsfa
from left-to-right.foldRight(fa, b)(f)
lazily foldsfa
from right-to-left.
Beyond these it provides many other useful methods related to folding over F[A] values.
See: A tutorial on the universality and expressiveness of fold
- Self Type
- Foldable[F]
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- Foldable
- UnorderedFoldable
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- Serializable
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Abstract Value Members
-
abstract
def
foldLeft[A, B](fa: F[A], b: B)(f: (B, A) ⇒ B): B
Left associative fold on 'F' using the function 'f'.
Left associative fold on 'F' using the function 'f'.
Example:
scala> import cats.Foldable, cats.implicits._ scala> val fa = Option(1) Folding by addition to zero: scala> Foldable[Option].foldLeft(fa, Option(0))((a, n) => a.map(_ + n)) res0: Option[Int] = Some(1)
With syntax extensions,
foldLeft
can be used like:Folding `Option` with addition from zero: scala> fa.foldLeft(Option(0))((a, n) => a.map(_ + n)) res1: Option[Int] = Some(1) There's also an alias `foldl` which is equivalent: scala> fa.foldl(Option(0))((a, n) => a.map(_ + n)) res2: Option[Int] = Some(1)
-
abstract
def
foldRight[A, B](fa: F[A], lb: Eval[B])(f: (A, Eval[B]) ⇒ Eval[B]): Eval[B]
Right associative lazy fold on
F
using the folding function 'f'.Right associative lazy fold on
F
using the folding function 'f'.This method evaluates
lb
lazily (in some cases it will not be needed), and returns a lazy value. We are using(A, Eval[B]) => Eval[B]
to support laziness in a stack-safe way. Chained computation should be performed via .map and .flatMap.For more detailed information about how this method works see the documentation for
Eval[_]
.Example:
scala> import cats.Foldable, cats.Eval, cats.implicits._ scala> val fa = Option(1) Folding by addition to zero: scala> val folded1 = Foldable[Option].foldRight(fa, Eval.now(0))((n, a) => a.map(_ + n)) Since `foldRight` yields a lazy computation, we need to force it to inspect the result: scala> folded1.value res0: Int = 1 With syntax extensions, we can write the same thing like this: scala> val folded2 = fa.foldRight(Eval.now(0))((n, a) => a.map(_ + n)) scala> folded2.value res1: Int = 1 Unfortunately, since `foldRight` is defined on many collections - this extension clashes with the operation defined in `Foldable`. To get past this and make sure you're getting the lazy `foldRight` defined in `Foldable`, there's an alias `foldr`: scala> val folded3 = fa.foldr(Eval.now(0))((n, a) => a.map(_ + n)) scala> folded3.value res1: Int = 1
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
##(): Int
- Definition Classes
- AnyRef → Any
-
final
def
==(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
clone(): AnyRef
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- protected[java.lang]
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- @native() @throws( ... )
- def collectFirst[A, B](fa: F[A])(pf: PartialFunction[A, B]): Option[B]
-
def
collectFirstSome[A, B](fa: F[A])(f: (A) ⇒ Option[B]): Option[B]
Like
collectFirst
fromscala.collection.Traversable
but takesA => Option[B]
instead ofPartialFunction
s.Like
collectFirst
fromscala.collection.Traversable
but takesA => Option[B]
instead ofPartialFunction
s.scala> import cats.implicits._ scala> val keys = List(1, 2, 4, 5) scala> val map = Map(4 -> "Four", 5 -> "Five") scala> keys.collectFirstSome(map.get) res0: Option[String] = Some(Four) scala> val map2 = Map(6 -> "Six", 7 -> "Seven") scala> keys.collectFirstSome(map2.get) res1: Option[String] = None
-
def
combineAll[A](fa: F[A])(implicit arg0: Monoid[A]): A
Alias for fold.
- def compose[G[_]](implicit arg0: Foldable[G]): Foldable[[α]F[G[α]]]
-
def
dropWhile_[A](fa: F[A])(p: (A) ⇒ Boolean): List[A]
Convert F[A] to a List[A], dropping all initial elements which match
p
. -
final
def
eq(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
equals(arg0: Any): Boolean
- Definition Classes
- AnyRef → Any
-
def
exists[A](fa: F[A])(p: (A) ⇒ Boolean): Boolean
Check whether at least one element satisfies the predicate.
Check whether at least one element satisfies the predicate.
If there are no elements, the result is
false
.- Definition Classes
- Foldable → UnorderedFoldable
-
def
existsM[G[_], A](fa: F[A])(p: (A) ⇒ G[Boolean])(implicit G: Monad[G]): G[Boolean]
Check whether at least one element satisfies the effectful predicate.
Check whether at least one element satisfies the effectful predicate.
If there are no elements, the result is
false
.existsM
short-circuits, i.e. once atrue
result is encountered, no further effects are produced.For example:
scala> import cats.implicits._ scala> val F = Foldable[List] scala> F.existsM(List(1,2,3,4))(n => Option(n <= 4)) res0: Option[Boolean] = Some(true) scala> F.existsM(List(1,2,3,4))(n => Option(n > 4)) res1: Option[Boolean] = Some(false) scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) Option(true) else Option(false)) res2: Option[Boolean] = Some(true) scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) Option(true) else None) res3: Option[Boolean] = Some(true) scala> F.existsM(List(1,2,3,4))(n => if (n <= 2) None else Option(true)) res4: Option[Boolean] = None
-
def
filter_[A](fa: F[A])(p: (A) ⇒ Boolean): List[A]
Convert F[A] to a List[A], only including elements which match
p
. -
def
finalize(): Unit
- Attributes
- protected[java.lang]
- Definition Classes
- AnyRef
- Annotations
- @throws( classOf[java.lang.Throwable] )
-
def
find[A](fa: F[A])(f: (A) ⇒ Boolean): Option[A]
Find the first element matching the predicate, if one exists.
-
def
fold[A](fa: F[A])(implicit A: Monoid[A]): A
Fold implemented using the given Monoid[A] instance.
-
def
foldK[G[_], A](fga: F[G[A]])(implicit G: MonoidK[G]): G[A]
Fold implemented using the given
MonoidK[G]
instance.Fold implemented using the given
MonoidK[G]
instance.This method is identical to fold, except that we use the universal monoid (
MonoidK[G]
) to get aMonoid[G[A]]
instance.For example:
scala> import cats.implicits._ scala> val F = Foldable[List] scala> F.foldK(List(1 :: 2 :: Nil, 3 :: 4 :: 5 :: Nil)) res0: List[Int] = List(1, 2, 3, 4, 5)
-
final
def
foldLeftM[G[_], A, B](fa: F[A], z: B)(f: (B, A) ⇒ G[B])(implicit G: Monad[G]): G[B]
Alias for foldM.
-
def
foldM[G[_], A, B](fa: F[A], z: B)(f: (B, A) ⇒ G[B])(implicit G: Monad[G]): G[B]
Perform a stack-safe monadic left fold from the source context
F
into the target monadG
.Perform a stack-safe monadic left fold from the source context
F
into the target monadG
.This method can express short-circuiting semantics. Even when
fa
is an infinite structure, this method can potentially terminate if thefoldRight
implementation forF
and thetailRecM
implementation forG
are sufficiently lazy.Instances for concrete structures (e.g.
List
) will often have a more efficient implementation than the default one in terms offoldRight
. -
def
foldMap[A, B](fa: F[A])(f: (A) ⇒ B)(implicit B: Monoid[B]): B
Fold implemented by mapping
A
values intoB
and then combining them using the givenMonoid[B]
instance. -
def
foldMapM[G[_], A, B](fa: F[A])(f: (A) ⇒ G[B])(implicit G: Monad[G], B: Monoid[B]): G[B]
Monadic folding on
F
by mappingA
values toG[B]
, combining theB
values using the givenMonoid[B]
instance.Monadic folding on
F
by mappingA
values toG[B]
, combining theB
values using the givenMonoid[B]
instance.Similar to foldM, but using a
Monoid[B]
.scala> import cats.Foldable scala> import cats.implicits._ scala> val evenNumbers = List(2,4,6,8,10) scala> val evenOpt: Int => Option[Int] = | i => if (i % 2 == 0) Some(i) else None scala> Foldable[List].foldMapM(evenNumbers)(evenOpt) res0: Option[Int] = Some(30) scala> Foldable[List].foldMapM(evenNumbers :+ 11)(evenOpt) res1: Option[Int] = None
-
def
forall[A](fa: F[A])(p: (A) ⇒ Boolean): Boolean
Check whether all elements satisfy the predicate.
Check whether all elements satisfy the predicate.
If there are no elements, the result is
true
.- Definition Classes
- Foldable → UnorderedFoldable
-
def
forallM[G[_], A](fa: F[A])(p: (A) ⇒ G[Boolean])(implicit G: Monad[G]): G[Boolean]
Check whether all elements satisfy the effectful predicate.
Check whether all elements satisfy the effectful predicate.
If there are no elements, the result is
true
.forallM
short-circuits, i.e. once afalse
result is encountered, no further effects are produced.For example:
scala> import cats.implicits._ scala> val F = Foldable[List] scala> F.forallM(List(1,2,3,4))(n => Option(n <= 4)) res0: Option[Boolean] = Some(true) scala> F.forallM(List(1,2,3,4))(n => Option(n <= 1)) res1: Option[Boolean] = Some(false) scala> F.forallM(List(1,2,3,4))(n => if (n <= 2) Option(true) else Option(false)) res2: Option[Boolean] = Some(false) scala> F.forallM(List(1,2,3,4))(n => if (n <= 2) Option(false) else None) res3: Option[Boolean] = Some(false) scala> F.forallM(List(1,2,3,4))(n => if (n <= 2) None else Option(false)) res4: Option[Boolean] = None
-
def
get[A](fa: F[A])(idx: Long): Option[A]
Get the element at the index of the
Foldable
. -
final
def
getClass(): Class[_]
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
hashCode(): Int
- Definition Classes
- AnyRef → Any
- Annotations
- @native()
-
def
intercalate[A](fa: F[A], a: A)(implicit A: Monoid[A]): A
Intercalate/insert an element between the existing elements while folding.
Intercalate/insert an element between the existing elements while folding.
scala> import cats.implicits._ scala> Foldable[List].intercalate(List("a","b","c"), "-") res0: String = a-b-c scala> Foldable[List].intercalate(List("a"), "-") res1: String = a scala> Foldable[List].intercalate(List.empty[String], "-") res2: String = "" scala> Foldable[Vector].intercalate(Vector(1,2,3), 1) res3: Int = 8
-
def
intersperseList[A](xs: List[A], x: A): List[A]
- Attributes
- protected
-
def
isEmpty[A](fa: F[A]): Boolean
Returns true if there are no elements.
Returns true if there are no elements. Otherwise false.
- Definition Classes
- Foldable → UnorderedFoldable
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
maximumOption[A](fa: F[A])(implicit A: Order[A]): Option[A]
Find the maximum
A
item in this structure according to theOrder[A]
.Find the maximum
A
item in this structure according to theOrder[A]
.- returns
None
if the structure is empty, otherwise the maximum element wrapped in aSome
.
- See also
Reducible#maximum for a version that doesn't need to return an
Option
for structures that are guaranteed to be non-empty.minimumOption for minimum instead of maximum.
-
def
minimumOption[A](fa: F[A])(implicit A: Order[A]): Option[A]
Find the minimum
A
item in this structure according to theOrder[A]
.Find the minimum
A
item in this structure according to theOrder[A]
.- returns
None
if the structure is empty, otherwise the minimum element wrapped in aSome
.
- See also
Reducible#minimum for a version that doesn't need to return an
Option
for structures that are guaranteed to be non-empty.maximumOption for maximum instead of minimum.
-
final
def
ne(arg0: AnyRef): Boolean
- Definition Classes
- AnyRef
-
def
nonEmpty[A](fa: F[A]): Boolean
- Definition Classes
- Foldable → UnorderedFoldable
-
final
def
notify(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
final
def
notifyAll(): Unit
- Definition Classes
- AnyRef
- Annotations
- @native()
-
def
partitionEither[A, B, C](fa: F[A])(f: (A) ⇒ Either[B, C])(implicit A: Alternative[F]): (F[B], F[C])
Separate this Foldable into a Tuple by a separating function
A => Either[B, C]
Equivalent toFunctor#map
and thenAlternative#separate
.Separate this Foldable into a Tuple by a separating function
A => Either[B, C]
Equivalent toFunctor#map
and thenAlternative#separate
.scala> import cats.implicits._ scala> val list = List(1,2,3,4) scala> Foldable[List].partitionEither(list)(a => if (a % 2 == 0) Left(a.toString) else Right(a)) res0: (List[String], List[Int]) = (List(2, 4),List(1, 3)) scala> Foldable[List].partitionEither(list)(a => Right(a * 4)) res1: (List[Nothing], List[Int]) = (List(),List(4, 8, 12, 16))
-
def
reduceLeftOption[A](fa: F[A])(f: (A, A) ⇒ A): Option[A]
Reduce the elements of this structure down to a single value by applying the provided aggregation function in a left-associative manner.
Reduce the elements of this structure down to a single value by applying the provided aggregation function in a left-associative manner.
- returns
None
if the structure is empty, otherwise the result of combining the cumulative left-associative result of thef
operation over all of the elements.
- See also
reduceRightOption for a right-associative alternative.
Reducible#reduceLeft for a version that doesn't need to return an
Option
for structures that are guaranteed to be non-empty. Example:scala> import cats.implicits._ scala> val l = List(6, 3, 2) This is equivalent to (6 - 3) - 2 scala> Foldable[List].reduceLeftOption(l)(_ - _) res0: Option[Int] = Some(1) scala> Foldable[List].reduceLeftOption(List.empty[Int])(_ - _) res1: Option[Int] = None
- def reduceLeftToOption[A, B](fa: F[A])(f: (A) ⇒ B)(g: (B, A) ⇒ B): Option[B]
-
def
reduceRightOption[A](fa: F[A])(f: (A, Eval[A]) ⇒ Eval[A]): Eval[Option[A]]
Reduce the elements of this structure down to a single value by applying the provided aggregation function in a right-associative manner.
Reduce the elements of this structure down to a single value by applying the provided aggregation function in a right-associative manner.
- returns
None
if the structure is empty, otherwise the result of combining the cumulative right-associative result of thef
operation over theA
elements.
- See also
reduceLeftOption for a left-associative alternative
Reducible#reduceRight for a version that doesn't need to return an
Option
for structures that are guaranteed to be non-empty. Example:scala> import cats.implicits._ scala> val l = List(6, 3, 2) This is eqivalent to 6 - (3 - 2) scala> Foldable[List].reduceRightOption(l)((current, rest) => rest.map(current - _)).value res0: Option[Int] = Some(5) scala> Foldable[List].reduceRightOption(List.empty[Int])((current, rest) => rest.map(current - _)).value res1: Option[Int] = None
- def reduceRightToOption[A, B](fa: F[A])(f: (A) ⇒ B)(g: (A, Eval[B]) ⇒ Eval[B]): Eval[Option[B]]
-
def
sequence_[G[_], A](fga: F[G[A]])(implicit arg0: Applicative[G]): G[Unit]
Sequence
F[G[A]]
usingApplicative[G]
.Sequence
F[G[A]]
usingApplicative[G]
.This is similar to
traverse_
except it operates onF[G[A]]
values, so no additional functions are needed.For example:
scala> import cats.implicits._ scala> val F = Foldable[List] scala> F.sequence_(List(Option(1), Option(2), Option(3))) res0: Option[Unit] = Some(()) scala> F.sequence_(List(Option(1), None, Option(3))) res1: Option[Unit] = None
-
def
size[A](fa: F[A]): Long
The size of this UnorderedFoldable.
The size of this UnorderedFoldable.
This is overridden in structures that have more efficient size implementations (e.g. Vector, Set, Map).
Note: will not terminate for infinite-sized collections.
- Definition Classes
- UnorderedFoldable
-
final
def
synchronized[T0](arg0: ⇒ T0): T0
- Definition Classes
- AnyRef
-
def
takeWhile_[A](fa: F[A])(p: (A) ⇒ Boolean): List[A]
Convert F[A] to a List[A], retaining only initial elements which match
p
. -
def
toList[A](fa: F[A]): List[A]
Convert F[A] to a List[A].
-
def
toString(): String
- Definition Classes
- AnyRef → Any
-
def
traverse_[G[_], A, B](fa: F[A])(f: (A) ⇒ G[B])(implicit G: Applicative[G]): G[Unit]
Traverse
F[A]
usingApplicative[G]
.Traverse
F[A]
usingApplicative[G]
.A
values will be mapped intoG[B]
and combined usingApplicative#map2
.For example:
scala> import cats.implicits._ scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption scala> val F = Foldable[List] scala> F.traverse_(List("333", "444"))(parseInt) res0: Option[Unit] = Some(()) scala> F.traverse_(List("333", "zzz"))(parseInt) res1: Option[Unit] = None
This method is primarily useful when
G[_]
represents an action or effect, and the specificA
aspect ofG[A]
is not otherwise needed. -
def
unorderedFold[A](fa: F[A])(implicit arg0: CommutativeMonoid[A]): A
- Definition Classes
- Foldable → UnorderedFoldable
-
def
unorderedFoldMap[A, B](fa: F[A])(f: (A) ⇒ B)(implicit arg0: CommutativeMonoid[B]): B
- Definition Classes
- Foldable → UnorderedFoldable
-
final
def
wait(): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long, arg1: Int): Unit
- Definition Classes
- AnyRef
- Annotations
- @throws( ... )
-
final
def
wait(arg0: Long): Unit
- Definition Classes
- AnyRef
- Annotations
- @native() @throws( ... )