[Haskell-cafe] 'Associative' order of calling

[Matteo Acerbi]

On Fri, Oct 23, 2015 at 6:07 PM, Charles Durham <ratzes at 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
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