Fold and foldLeft method difference

As defined by Scala, foldLeft is a linear operation while fold is allowed to be a tree operation. For example:

List(1,2,3,4,5).foldLeft(0)(_ + _)
// This is the only valid order of operations
0+1 = 1
      1+2 = 3
            3+3 = 6
                  6+4 = 10
                        10 + 5 = 15
                                 15  // done

List(1,2,3,4,5).fold(0)(_ + _)
// This is valid
0+1 = 1             0+3 = 3           0+5 = 5
      1+2 = 3             3+4 = 7           5
            3         +         7=10        5
                                  10    +   5 = 15
                                                15  // done

In order to allow arbitrary tree decompositions of a sequential list, you must have a zero that doesn’t do anything (so you can add it wherever you need it in the tree) and you must create the same sort of thing that you take as your binary arguments so the types don’t change on you depending on how you decompose the tree.

(Being able to evaluate as a tree is nice for parallelization. If you want to be able to transform your output time as you go, you need both a combination operator and a standard start-value-transforms-sequence-element-to-desired-type function just like foldLeft has. Scala has this and calls it aggregate, but in some ways this is more like foldLeft than fold is.)