On Sat, Oct 24, 2015 at 08:12:11PM +0200, Janis Voigtländer wrote:
It has already been established in this thread what Charles meant by 3.
He meant that a fold-function that has the property he is after would guarantee that it:
a) takes all the content elements from a data structure, say x1,...,xn,
b) builds an application tree with the to-be-folded, binary operation f in the internal nodes of a binary tree, whose leafs, read from left to right, form exactly the sequence x1,...,xn,
c) evaluates that application tree.
Do you agree that what I describe above is a property of a given fold-like function, not of the f handed to that fold-like function?
And do you agree that what I describe above is a property that is weaker than (and so, in particular different from) for example the property "this fold-like function is foldl or foldr".
I do agree. I would be interested whether you think such a property could differ from my earlier proposed property: "the function factors through `foldl f`", i.e. is `g . foldl f` for some `g`. (Actually when I wrote that I suppose I meant `g . foldl f z` for some `g` and `z`) Tom