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)

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

Given a function which returns a G effect, thread this effect through the running of this function on all the values in F, returning an F[B] in a G context.

Example:

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> def countWords(words: List[String]): Map[String, Int] = words.groupBy(identity).map { case (k, v) => (k, v.length) }
scala> NonEmptyList.of(List("How", "do", "you", "fly"), List("What", "do", "you", "do")).nonEmptyTraverse(countWords)
res0: Map[String,cats.data.NonEmptyList[Int]] = Map(do -> NonEmptyList(1, 2), you -> NonEmptyList(1, 1))

Apply f to the "initial element" of fa and combine it with every other value using the given function g.

Apply f to the "initial element" of fa and lazily combine it with every other value using the given function g.

Replaces the A value in F[A] with the supplied value.

Example:

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForList

scala> Functor[List].as(List(1,2,3), "hello")
res0: List[String] = List(hello, hello, hello)

Like collectFirst from scala.collection.Traversable but takes A => Option[B] instead of PartialFunctions.

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

Alias for fold.

Convert F[A] to a List[A], dropping all initial elements which match p.

Check whether at least one element satisfies the predicate.

If there are no elements, the result is false.

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 a true 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

Convert F[A] to a List[A], only including elements which match p.

Find the first element matching the predicate, if one exists.

Thread all the G effects through the F structure and flatten to invert the structure from F[G[F[A]]] to G[F[A]].

Example:

scala> import cats.implicits._
scala> val x: List[Option[List[Int]]] = List(Some(List(1, 2)), Some(List(3)))
scala> val y: List[Option[List[Int]]] = List(None, Some(List(3)))
scala> x.flatSequence
res0: Option[List[Int]] = Some(List(1, 2, 3))
scala> y.flatSequence
res1: Option[List[Int]] = None

A traverse followed by flattening the inner result.

Example:

scala> import cats.implicits._
scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
scala> val x = Option(List("1", "two", "3"))
scala> x.flatTraverse(_.map(parseInt))
res0: List[Option[Int]] = List(Some(1), None, Some(3))

Alias for map, since map can't be injected as syntax if the implementing type already had a built-in .map method.

Example:

scala> import cats.implicits._

scala> val m: Map[Int, String] = Map(1 -> "hi", 2 -> "there", 3 -> "you")

scala> m.fmap(_ ++ "!")
res0: Map[Int,String] = Map(1 -> hi!, 2 -> there!, 3 -> you!)

Fold implemented using the given Monoid[A] 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 a Monoid[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)

Alias for foldM.

Perform a stack-safe monadic left fold from the source context F into the target monad G.

This method can express short-circuiting semantics. Even when fa is an infinite structure, this method can potentially terminate if the foldRight implementation for F and the tailRecM implementation for G are sufficiently lazy.

Instances for concrete structures (e.g. List) will often have a more efficient implementation than the default one in terms of foldRight.

Fold implemented by mapping A values into B and then combining them using the given Monoid[B] instance.

Monadic folding on F by mapping A values to G[B], combining the B values using the given Monoid[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

Check whether all elements satisfy the predicate.

If there are no elements, the result is true.

Check whether all elements satisfy the effectful predicate.

If there are no elements, the result is true. forallM short-circuits, i.e. once a false 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

Tuple the values in fa with the result of applying a function with the value

Example:

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForOption

scala> Functor[Option].fproduct(Option(42))(_.toString)
res0: Option[(Int, String)] = Some((42,42))

Get the element at the index of the Foldable.

Transform an F[A] into an F[B] by providing a transformation from A to B and one from B to A.

Example:

scala> import cats.implicits._
scala> import scala.concurrent.duration._
scala> val durSemigroup: Semigroup[FiniteDuration] =
     | Invariant[Semigroup].imap(Semigroup[Long])(Duration.fromNanos)(_.toNanos)
scala> durSemigroup.combine(2.seconds, 3.seconds)
res1: FiniteDuration = 5 seconds

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

Returns true if there are no elements. Otherwise false.

Lift a function f to operate on Functors

Example:

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForOption

scala> val o = Option(42)
scala> Functor[Option].lift((x: Int) => x + 10)(o)
res0: Option[Int] = Some(52)

Akin to map, but also provides the value's index in structure F when calling the function.

Find the maximum A item in this structure according to the Order[A].

Find the minimum A item in this structure according to the Order[A].

Thread all the G effects through the F structure and flatten to invert the structure from F[G[F[A]]] to G[F[A]].

Example:

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> val x = NonEmptyList.of(Map(0 ->NonEmptyList.of(1, 2)), Map(0 -> NonEmptyList.of(3)))
scala> val y: NonEmptyList[Map[Int, NonEmptyList[Int]]] = NonEmptyList.of(Map(), Map(1 -> NonEmptyList.of(3)))
scala> x.nonEmptyFlatSequence
res0: Map[Int,cats.data.NonEmptyList[Int]] = Map(0 -> NonEmptyList(1, 2, 3))
scala> y.nonEmptyFlatSequence
res1: Map[Int,cats.data.NonEmptyList[Int]] = Map()

A nonEmptyTraverse followed by flattening the inner result.

Example:

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> val x = NonEmptyList.of(List("How", "do", "you", "fly"), List("What", "do", "you", "do"))
scala> x.nonEmptyFlatTraverse(_.groupByNel(identity) : Map[String, NonEmptyList[String]])
res0: Map[String,cats.data.NonEmptyList[String]] = Map(do -> NonEmptyList(do, do, do), you -> NonEmptyList(you, you))

Intercalate/insert an element between the existing elements while reducing.

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> val nel = NonEmptyList.of("a", "b", "c")
scala> Reducible[NonEmptyList].nonEmptyIntercalate(nel, "-")
res0: String = a-b-c
scala> Reducible[NonEmptyList].nonEmptyIntercalate(NonEmptyList.of("a"), "-")
res1: String = a

Partition this Reducible by a separating function A => Either[B, C]

scala> import cats.data.NonEmptyList
scala> val nel = NonEmptyList.of(1,2,3,4)
scala> Reducible[NonEmptyList].nonEmptyPartition(nel)(a => if (a % 2 == 0) Left(a.toString) else Right(a))
res0: cats.data.Ior[cats.data.NonEmptyList[String],cats.data.NonEmptyList[Int]] = Both(NonEmptyList(2, 4),NonEmptyList(1, 3))
scala> Reducible[NonEmptyList].nonEmptyPartition(nel)(a => Right(a * 4))
res1: cats.data.Ior[cats.data.NonEmptyList[Nothing],cats.data.NonEmptyList[Int]] = Right(NonEmptyList(4, 8, 12, 16))

Thread all the G effects through the F structure to invert the structure from F[G[A]] to G[F[A]].

Example:

scala> import cats.implicits._
scala> import cats.data.NonEmptyList
scala> val x = NonEmptyList.of(Map("do" -> 1, "you" -> 1), Map("do" -> 2, "you" -> 1))
scala> val y = NonEmptyList.of(Map("How" -> 3, "do" -> 1, "you" -> 1), Map[String,Int]())
scala> x.nonEmptySequence
res0: Map[String,NonEmptyList[Int]] = Map(do -> NonEmptyList(1, 2), you -> NonEmptyList(1, 1))
scala> y.nonEmptySequence
res1: Map[String,NonEmptyList[Int]] = Map()

Sequence F[G[A]] using Apply[G].

This method is similar to Foldable.sequence_ but requires only an Apply instance for G instead of Applicative. See the nonEmptyTraverse_ documentation for a description of the differences.

Traverse F[A] using Apply[G].

A values will be mapped into G[B] and combined using Apply#map2.

This method is similar to Foldable.traverse_. There are two main differences:

1. We only need an Apply instance for G here, since we don't need to call Applicative.pure for a starting value. 2. This performs a strict left-associative traversal and thus must always traverse the entire data structure. Prefer Foldable.traverse_ if you have an Applicative instance available for G and want to take advantage of short-circuiting the traversal.

Separate this Foldable into a Tuple by a separating function A => Either[B, C] Equivalent to Functor#map and then Alternative#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))

Reduce a F[A] value using the given Semigroup[A].

Reduce a F[G[A]] value using SemigroupK[G], a universal semigroup for G[_].

This method is a generalization of reduce.

Left-associative reduction on F using the function f.

Implementations should override this method when possible.

Monadic variant of reduceLeftTo

Reduce the elements of this structure down to a single value by applying the provided aggregation function in a left-associative manner.

Overridden from Foldable for efficiency.

Apply f to each element of fa and combine them using the given Semigroup[B].

Monadic reducing by mapping the A values to G[B]. combining the B values using the given Semigroup[B] instance.

Similar to reduceLeftM, but using a Semigroup[B].

scala> import cats.Reducible
scala> import cats.data.NonEmptyList
scala> import cats.implicits._
scala> val evenOpt: Int => Option[Int] =
     |   i => if (i % 2 == 0) Some(i) else None
scala> val allEven = NonEmptyList.of(2,4,6,8,10)
allEven: cats.data.NonEmptyList[Int] = NonEmptyList(2, 4, 6, 8, 10)
scala> val notAllEven = allEven ++ List(11)
notAllEven: cats.data.NonEmptyList[Int] = NonEmptyList(2, 4, 6, 8, 10, 11)
scala> Reducible[NonEmptyList].reduceMapM(allEven)(evenOpt)
res0: Option[Int] = Some(30)
scala> Reducible[NonEmptyList].reduceMapM(notAllEven)(evenOpt)
res1: Option[Int] = None

Right-associative reduction on F using the function f.

Reduce the elements of this structure down to a single value by applying the provided aggregation function in a right-associative manner.

Overridden from Foldable for efficiency.

Thread all the G effects through the F structure to invert the structure from F[G[A]] to G[F[A]].

Example:

scala> import cats.implicits._
scala> val x: List[Option[Int]] = List(Some(1), Some(2))
scala> val y: List[Option[Int]] = List(None, Some(2))
scala> x.sequence
res0: Option[List[Int]] = Some(List(1, 2))
scala> y.sequence
res1: Option[List[Int]] = None

Sequence F[G[A]] using Applicative[G].

This is similar to traverse_ except it operates on F[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

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.

Convert F[A] to a List[A], retaining only initial elements which match p.

Convert F[A] to a List[A].

Given a function which returns a G effect, thread this effect through the running of this function on all the values in F, returning an F[B] in a G context.

Example:

scala> import cats.implicits._
scala> def parseInt(s: String): Option[Int] = Either.catchOnly[NumberFormatException](s.toInt).toOption
scala> List("1", "2", "3").traverse(parseInt)
res0: Option[List[Int]] = Some(List(1, 2, 3))
scala> List("1", "two", "3").traverse(parseInt)
res1: Option[List[Int]] = None

Akin to traverse, but also provides the value's index in structure F when calling the function.

This performs the traversal in a single pass but requires that effect G is monadic. An applicative traversal can be performed in two passes using zipWithIndex followed by traverse.

Traverse F[A] using Applicative[G].

A values will be mapped into G[B] and combined using Applicative#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 specific A aspect of G[A] is not otherwise needed.

Tuples the A value in F[A] with the supplied B value, with the B value on the left.

Example:

scala> import scala.collection.immutable.Queue
scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForQueue

scala> Functor[Queue].tupleLeft(Queue("hello", "world"), 42)
res0: scala.collection.immutable.Queue[(Int, String)] = Queue((42,hello), (42,world))

Tuples the A value in F[A] with the supplied B value, with the B value on the right.

Example:

scala> import scala.collection.immutable.Queue
scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForQueue

scala> Functor[Queue].tupleRight(Queue("hello", "world"), 42)
res0: scala.collection.immutable.Queue[(String, Int)] = Queue((hello,42), (world,42))

Empty the fa of the values, preserving the structure

Example:

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForList

scala> Functor[List].void(List(1,2,3))
res0: List[Unit] = List((), (), ())

Lifts natural subtyping covariance of covariant Functors.

NOTE: In certain (perhaps contrived) situations that rely on universal equality this can result in a ClassCastException, because it is implemented as a type cast. It could be implemented as map(identity), but according to the functor laws, that should be equal to fa, and a type cast is often much more performant. See this example of widen creating a ClassCastException.

Example:

scala> import cats.Functor
scala> import cats.implicits.catsStdInstancesForOption

scala> val s = Some(42)
scala> Functor[Option].widen(s)
res0: Option[Int] = Some(42)

Traverses through the structure F, pairing the values with assigned indices.

The behavior is consistent with the Scala collection library's zipWithIndex for collections such as List.