Difference between fold and foldLeft or foldRight?

问题:

NOTE: I am on Scala 2.8—can that be a problem?

Why can't I use the fold function the same way as foldLeft or foldRight?

In the Set scaladoc it says that:

The result of folding may only be a supertype of this parallel collection's type parameter T.

But I see no type parameter T in the function signature:

def fold [A1 >: A] (z: A1)(op: (A1, A1) ⇒ A1): A1

What is the difference between the foldLeft-Right and fold, and how do I use the latter?

EDIT: For example how would I write a fold to add all elements in a list? With foldLeft it would be:

val foo = List(1, 2, 3)
foo.foldLeft(0)(_ + _)

// now try fold:
foo.fold(0)(_ + _)
>:7: error: value fold is not a member of List[Int]
  foo.fold(0)(_ + _)
    ^

回答1:

You're right about the old version of Scala being a problem. If you look at the scaladoc page for Scala 2.8.1, you'll see no fold defined there (which is consistent with your error message). Apparently, fold was introduced in Scala 2.9.

回答2:

Short answer:

foldRight associates to the right. I.e. elements will be accumulated in right-to-left order:

List(a,b,c).foldRight(z)(f) = f(a, f(b, f(c, z)))

foldLeft associates to the left. I.e. an accumulator will be initialized and elements will be added to the accumulator in left-to-right order:

List(a,b,c).foldLeft(z)(f) = f(f(f(z, a), b), c)

fold is associative in that the order in which the elements are added together is not defined. I.e. the arguments to fold form a monoid.

回答3:

fold, contrary to foldRight and foldLeft, does not offer any guarantee about the order in which the elements of the collection will be processed. You'll probably want to use fold, with its more constrained signature, with parallel collections, where the lack of guaranteed processing order helps the parallel collection implements folding in a parallel way. The reason for changing the signature is similar: with the additional constraints, it's easier to make a parallel fold.

回答4:

For your particular example you would code it the same way you would with foldLeft.

val ns = List(1, 2, 3, 4)
val s0 = ns.foldLeft (0) (_+_) //10
val s1 = ns.fold (0) (_+_) //10
assert(s0 == s1)

回答5:

Agree with other answers. thought of giving a simple illustrative example:

 object MyClass {
 def main(args: Array[String]) {
val numbers = List(5, 4, 8, 6, 2)
 val a =  numbers.fold(0) { (z, i) =>
 {
     println("fold val1 " + z +" val2 " + i)
  z + i

 }
}
println(a)
 val b =  numbers.foldLeft(0) { (z, i) =>
 println("foldleft val1 " + z +" val2 " + i)
  z + i

}
println(b)
   val c =  numbers.foldRight(0) { (z, i) =>
   println("fold right val1 " + z +" val2 " + i)
  z + i

}
println(c)
 }
}

Result is self explanatory :

fold val1 0 val2 5
fold val1 5 val2 4
fold val1 9 val2 8
fold val1 17 val2 6
fold val1 23 val2 2
25
foldleft val1 0 val2 5
foldleft val1 5 val2 4
foldleft val1 9 val2 8
foldleft val1 17 val2 6
foldleft val1 23 val2 2
25
fold right val1 2 val2 0
fold right val1 6 val2 2
fold right val1 8 val2 8
fold right val1 4 val2 16
fold right val1 5 val2 20
25

回答6:

fold() does parallel processing so does not guarantee the processing order. where as foldLeft and foldRight process the items in sequentially for left to right (in case of foldLeft) or right to left (in case of foldRight)

Examples of sum the list -

val numList = List(1, 2, 3, 4, 5)

val r1 = numList.par.fold(0)((acc, value) => {
  println("adding accumulator=" + acc + ", value=" + value + " => " + (acc + value))
  acc + value
})
println("fold(): " + r1)
println("#######################")
/*
 * You can see from the output that,
 * fold process the elements of parallel collection in parallel
 * So it is parallel not linear operation.
 * 
 * adding accumulator=0, value=4 => 4
 * adding accumulator=0, value=3 => 3
 * adding accumulator=0, value=1 => 1
 * adding accumulator=0, value=5 => 5
 * adding accumulator=4, value=5 => 9
 * adding accumulator=0, value=2 => 2
 * adding accumulator=3, value=9 => 12
 * adding accumulator=1, value=2 => 3
 * adding accumulator=3, value=12 => 15
 * fold(): 15
 */

val r2 = numList.par.foldLeft(0)((acc, value) => {
  println("adding accumulator=" + acc + ", value=" + value + " => " + (acc + value))
  acc + value
})
println("foldLeft(): " + r2)
println("#######################")
/*
 * You can see that foldLeft
 * picks elements from left to right.
 * It means foldLeft does sequence operation
 * 
 * adding accumulator=0, value=1 => 1
 * adding accumulator=1, value=2 => 3
 * adding accumulator=3, value=3 => 6
 * adding accumulator=6, value=4 => 10
 * adding accumulator=10, value=5 => 15
 * foldLeft(): 15
 * #######################
 */

// --> Note in foldRight second arguments is accumulated one.
val r3 = numList.par.foldRight(0)((value, acc) => {
 println("adding value=" + value + ", acc=" + acc + " => " + (value + acc))
  acc + value
})
println("foldRight(): " + r3)
println("#######################")

/*
 * You can see that foldRight
 * picks elements from right to left.
 * It means foldRight does sequence operation.
 * 
 * adding value=5, acc=0 => 5
 * adding value=4, acc=5 => 9
 * adding value=3, acc=9 => 12
 * adding value=2, acc=12 => 14
 * adding value=1, acc=14 => 15
 * foldRight(): 15
 * #######################
 */