/
Foldable.scala
622 lines (571 loc) · 20.3 KB
/
Foldable.scala
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package cats
import scala.collection.mutable
import cats.instances.either._
import cats.kernel.CommutativeMonoid
import simulacrum.typeclass
import Foldable.sentinel
/**
* 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 folds `fa` from left-to-right.
* - `foldRight(fa, b)(f)` lazily folds `fa` from right-to-left.
*
* Beyond these it provides many other useful methods related to
* folding over F[A] values.
*
* See: [[http://www.cs.nott.ac.uk/~pszgmh/fold.pdf A tutorial on the universality and expressiveness of fold]]
*/
@typeclass trait Foldable[F[_]] extends UnorderedFoldable[F] { self =>
/**
* 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)
* }}}
*/
def foldLeft[A, B](fa: F[A], b: B)(f: (B, A) => B): B
/**
* 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
* }}}
*/
def foldRight[A, B](fa: F[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B]
def reduceLeftToOption[A, B](fa: F[A])(f: A => B)(g: (B, A) => B): Option[B] =
foldLeft(fa, Option.empty[B]) {
case (Some(b), a) => Some(g(b, a))
case (None, a) => Some(f(a))
}
def reduceRightToOption[A, B](fa: F[A])(f: A => B)(g: (A, Eval[B]) => Eval[B]): Eval[Option[B]] =
foldRight(fa, Now(Option.empty[B])) { (a, lb) =>
lb.flatMap {
case Some(b) => g(a, Now(b)).map(Some(_))
case None => Later(Some(f(a)))
}
}
/**
* Reduce the elements of this structure down to a single value by applying
* the provided aggregation function in a left-associative manner.
*
* @return `None` if the structure is empty, otherwise the result of combining
* the cumulative left-associative result of the `f` operation over all of the
* elements.
*
* @see [[reduceRightOption]] for a right-associative alternative.
*
* @see [[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 reduceLeftOption[A](fa: F[A])(f: (A, A) => A): Option[A] =
reduceLeftToOption(fa)(identity)(f)
/**
* Reduce the elements of this structure down to a single value by applying
* the provided aggregation function in a right-associative manner.
*
* @return `None` if the structure is empty, otherwise the result of combining
* the cumulative right-associative result of the `f` operation over the
* `A` elements.
*
* @see [[reduceLeftOption]] for a left-associative alternative
*
* @see [[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 reduceRightOption[A](fa: F[A])(f: (A, Eval[A]) => Eval[A]): Eval[Option[A]] =
reduceRightToOption(fa)(identity)(f)
/**
* Find the minimum `A` item in this structure according to the `Order[A]`.
*
* @return `None` if the structure is empty, otherwise the minimum element
* wrapped in a `Some`.
*
* @see [[Reducible#minimum]] for a version that doesn't need to return an
* `Option` for structures that are guaranteed to be non-empty.
*
* @see [[maximumOption]] for maximum instead of minimum.
*/
def minimumOption[A](fa: F[A])(implicit A: Order[A]): Option[A] =
reduceLeftOption(fa)(A.min)
/**
* Find the maximum `A` item in this structure according to the `Order[A]`.
*
* @return `None` if the structure is empty, otherwise the maximum element
* wrapped in a `Some`.
*
* @see [[Reducible#maximum]] for a version that doesn't need to return an
* `Option` for structures that are guaranteed to be non-empty.
*
* @see [[minimumOption]] for minimum instead of maximum.
*/
def maximumOption[A](fa: F[A])(implicit A: Order[A]): Option[A] =
reduceLeftOption(fa)(A.max)
/**
* Get the element at the index of the `Foldable`.
*/
def get[A](fa: F[A])(idx: Long): Option[A] =
if (idx < 0L) None
else
foldM[Either[A, ?], A, Long](fa, 0L) { (i, a) =>
if (i == idx) Left(a) else Right(i + 1L)
} match {
case Left(a) => Some(a)
case Right(_) => None
}
def collectFirst[A, B](fa: F[A])(pf: PartialFunction[A, B]): Option[B] =
foldRight(fa, Eval.now(Option.empty[B])) { (a, lb) =>
// trick from TravsersableOnce
val x = pf.applyOrElse(a, sentinel)
if (x.asInstanceOf[AnyRef] ne sentinel) Eval.now(Some(x.asInstanceOf[B]))
else lb
}.value
/**
* Like `collectFirst` from `scala.collection.Traversable` but takes `A => Option[B]`
* instead of `PartialFunction`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 collectFirstSome[A, B](fa: F[A])(f: A => Option[B]): Option[B] =
foldRight(fa, Eval.now(Option.empty[B])) { (a, lb) =>
val ob = f(a)
if (ob.isDefined) Eval.now(ob) else lb
}.value
/**
* Fold implemented using the given Monoid[A] instance.
*/
def fold[A](fa: F[A])(implicit A: Monoid[A]): A =
foldLeft(fa, A.empty) { (acc, a) =>
A.combine(acc, a)
}
/**
* Alias for [[fold]].
*/
def combineAll[A: Monoid](fa: F[A]): A = fold(fa)
/**
* Fold implemented by mapping `A` values into `B` and then
* combining them using the given `Monoid[B]` instance.
*/
def foldMap[A, B](fa: F[A])(f: A => B)(implicit B: Monoid[B]): B =
foldLeft(fa, B.empty)((b, a) => B.combine(b, f(a)))
/**
* 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`.
*/
def foldM[G[_], A, B](fa: F[A], z: B)(f: (B, A) => G[B])(implicit G: Monad[G]): G[B] = {
val src = Foldable.Source.fromFoldable(fa)(self)
G.tailRecM((z, src)) { case (b, src) => src.uncons match {
case Some((a, src)) => G.map(f(b, a))(b => Left((b, src.value)))
case None => G.pure(Right(b))
}}
}
/**
* Alias for [[foldM]].
*/
final def foldLeftM[G[_], A, B](fa: F[A], z: B)(f: (B, A) => G[B])(implicit G: Monad[G]): G[B] =
foldM(fa, z)(f)
/**
* 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
* }}}
*/
def foldMapM[G[_], A, B](fa: F[A])(f: A => G[B])(implicit G: Monad[G], B: Monoid[B]): G[B] =
foldM(fa, B.empty)((b, a) => G.map(f(a))(B.combine(b, _)))
/**
* 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.
*/
def traverse_[G[_], A, B](fa: F[A])(f: A => G[B])(implicit G: Applicative[G]): G[Unit] =
foldRight(fa, Always(G.pure(()))) { (a, acc) =>
G.map2Eval(f(a), acc) { (_, _) => () }
}.value
/**
* 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
* }}}
*/
def sequence_[G[_]: Applicative, A](fga: F[G[A]]): G[Unit] =
traverse_(fga)(identity)
/**
* 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)
* }}}
*/
def foldK[G[_], A](fga: F[G[A]])(implicit G: MonoidK[G]): G[A] =
fold(fga)(G.algebra)
/**
* Find the first element matching the predicate, if one exists.
*/
def find[A](fa: F[A])(f: A => Boolean): Option[A] =
foldRight(fa, Now(Option.empty[A])) { (a, lb) =>
if (f(a)) Now(Some(a)) else lb
}.value
/**
* Check whether at least one element satisfies the predicate.
*
* If there are no elements, the result is `false`.
*/
override def exists[A](fa: F[A])(p: A => Boolean): Boolean =
foldRight(fa, Eval.False) { (a, lb) =>
if (p(a)) Eval.True else lb
}.value
/**
* Check whether all elements satisfy the predicate.
*
* If there are no elements, the result is `true`.
*/
override def forall[A](fa: F[A])(p: A => Boolean): Boolean =
foldRight(fa, Eval.True) { (a, lb) =>
if (p(a)) lb else Eval.False
}.value
/**
* 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
* }}}
*/
def existsM[G[_], A](fa: F[A])(p: A => G[Boolean])(implicit G: Monad[G]): G[Boolean] = {
G.tailRecM(Foldable.Source.fromFoldable(fa)(self)) {
src => src.uncons match {
case Some((a, src)) => G.map(p(a))(bb => if (bb) Right(true) else Left(src.value))
case None => G.pure(Right(false))
}
}
}
/**
* 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
* }}}
*/
def forallM[G[_], A](fa: F[A])(p: A => G[Boolean])(implicit G: Monad[G]): G[Boolean] = {
G.tailRecM(Foldable.Source.fromFoldable(fa)(self)) {
src => src.uncons match {
case Some((a, src)) => G.map(p(a))(bb => if (!bb) Right(false) else Left(src.value))
case None => G.pure(Right(true))
}
}
}
/**
* Convert F[A] to a List[A].
*/
def toList[A](fa: F[A]): List[A] =
foldLeft(fa, mutable.ListBuffer.empty[A]) { (buf, a) =>
buf += a
}.toList
/**
* 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))
* }}}
*/
def partitionEither[A, B, C](fa: F[A])(f: A => Either[B, C])(implicit A: Alternative[F]): (F[B], F[C]) = {
import cats.instances.tuple._
implicit val mb: Monoid[F[B]] = A.algebra[B]
implicit val mc: Monoid[F[C]] = A.algebra[C]
foldMap(fa)(a => f(a) match {
case Right(c) => (A.empty[B], A.pure(c))
case Left(b) => (A.pure(b), A.empty[C])
})
}
/**
* Convert F[A] to a List[A], only including elements which match `p`.
*/
def filter_[A](fa: F[A])(p: A => Boolean): List[A] =
foldLeft(fa, mutable.ListBuffer.empty[A]) { (buf, a) =>
if (p(a)) buf += a else buf
}.toList
/**
* Convert F[A] to a List[A], retaining only initial elements which
* match `p`.
*/
def takeWhile_[A](fa: F[A])(p: A => Boolean): List[A] =
foldRight(fa, Now(List.empty[A])) { (a, llst) =>
if (p(a)) llst.map(a :: _) else Now(Nil)
}.value
/**
* Convert F[A] to a List[A], dropping all initial elements which
* match `p`.
*/
def dropWhile_[A](fa: F[A])(p: A => Boolean): List[A] =
foldLeft(fa, mutable.ListBuffer.empty[A]) { (buf, a) =>
if (buf.nonEmpty || !p(a)) buf += a else buf
}.toList
/**
* Returns true if there are no elements. Otherwise false.
*/
override def isEmpty[A](fa: F[A]): Boolean =
foldRight(fa, Eval.True)((_, _) => Eval.False).value
override def nonEmpty[A](fa: F[A]): Boolean =
!isEmpty(fa)
/**
* 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 intercalate[A](fa: F[A], a: A)(implicit A: Monoid[A]): A =
A.combineAll(intersperseList(toList(fa), a))
protected def intersperseList[A](xs: List[A], x: A): List[A] = {
val bld = List.newBuilder[A]
val it = xs.iterator
if (it.hasNext) {
bld += it.next
while(it.hasNext) {
bld += x
bld += it.next
}
}
bld.result
}
def compose[G[_]: Foldable]: Foldable[λ[α => F[G[α]]]] =
new ComposedFoldable[F, G] {
val F = self
val G = Foldable[G]
}
override def unorderedFold[A: CommutativeMonoid](fa: F[A]): A = fold(fa)
override def unorderedFoldMap[A, B: CommutativeMonoid](fa: F[A])(f: (A) => B): B =
foldMap(fa)(f)
}
object Foldable {
private val sentinel: Function1[Any, Any] = new scala.runtime.AbstractFunction1[Any, Any]{ def apply(a: Any) = this }
def iterateRight[A, B](iterable: Iterable[A], lb: Eval[B])(f: (A, Eval[B]) => Eval[B]): Eval[B] = {
def loop(it: Iterator[A]): Eval[B] =
Eval.defer(if (it.hasNext) f(it.next, loop(it)) else lb)
Eval.always(iterable.iterator).flatMap(loop)
}
/**
* Isomorphic to
*
* type Source[+A] = () => Option[(A, Source[A])]
*
* (except that recursive type aliases are not allowed).
*
* It could be made a value class after
* https://github.com/scala/bug/issues/9600 is resolved.
*/
private sealed abstract class Source[+A] {
def uncons: Option[(A, Eval[Source[A]])]
}
private object Source {
val Empty: Source[Nothing] = new Source[Nothing] {
def uncons = None
}
def cons[A](a: A, src: Eval[Source[A]]): Source[A] = new Source[A] {
def uncons = Some((a, src))
}
def fromFoldable[F[_], A](fa: F[A])(implicit F: Foldable[F]): Source[A] =
F.foldRight[A, Source[A]](fa, Now(Empty))((a, evalSrc) =>
Later(cons(a, evalSrc))
).value
}
}