On Fri, Oct 23, 2015 at 6:07 PM, Charles Durham <ratzes@gmail.com> wrote:

I can think of a few properties that folds can honor:

1. Promises to call f on all data (does not have any guarantees on order)
2. Promises to call f on all data in order (like a left fold)
3. Promises to call f "associatively" (perhaps can be formalized as an in order break down of the data into tree structures)

For what concerns traversable functors, traversals enjoy properties of "unitarity" and "linearity" which *might* entail what you are interested in:

M. Jaskelioff, O. Rypacek - An Investigation of the Laws of Traversals
http://arxiv.org/abs/1202.2919

I have never gone through the details of that very interesting paper: the analysis in section 4 gives some intuition, though.

I hope this is related to your questions.

Cheers,

Matteo