A functional iterator is a function that traverses a data structure and calls in turn a given function over the elements of that structure to compute some value. Another approach is sometimes possible: loops.
There are three kinds of functional iterations over sets: the fold, the map (not to be confused with the map data structure) and the iteration.
Let us consider first here the fold, which is the most general form of functional iteration. The folded function takes two arguments: an accumulator and the structure element at hand, with which it then produces a new accumulator. This enables having a partial result that becomes complete when the traversal of the data structure is over.
Set.fold performs a fold over a set, in increasing
order of its elements. The function
Set.fold_desc folds in
decreasing order. The different in their types is the type of the
folded operation: with
Set.fold, that function takes the accumulator
first, whereas with
Set.fold_desc, the accumulator comes second.
Note: See the predefined namespace Set