[Haskell-cafe] 'Associative' order of calling

[Matteo Acerbi]

On Sat, Oct 24, 2015 at 12:56 PM, Janis Voigtländer <
janis.voigtlaender at gmail.com> wrote:

> The "unitarity" and "linearity" laws are indeed relevant for Charles's
> question. But they won't give him his 2. or 3. point. They will exactly
> entail the property he mentions in his 1. point: that each data element is
> touched exactly once (whereas all permutations of the order will still be
> legal)
> ​
>
For proof of that, see http://dx.doi.org/10.1145/2503778.2503781, which
> establishes as fact the relevant conjecture from Jaskelioff & Rypacek's
> paper.
>

​Thanks for your clarifying comment, and for the link to this paper: it is
very interesting, indeed.

In my message I was just trying to point to research that looked relevant,
and which seemed to give an answer to at least question 1: for what
concerns the other two questions, I have yet to understand them. :-)

Question 2 seems to assume the existence of a "default" order, but it seems
to me that any such choice would be arbitrary. At least, it seems
impossible to capture the property of being "like a left fold" semantically
as Charles seemed to be wanting ("I was more thinking along the lines of
how the Monad laws are expressed as a side note in the docs"), without
actually specifying a reference order of traversal (for example, in the
form of an instance of Traversable).

For what concerns question 3, I didn't understand the idea of calling a
function "associatively".

Please let me know if I am missing an obvious interpretation.

Best,
Matteo
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