Yeah, I realize that its probably not conveniently expressible in types or anything. I was more thinking along the lines of how the Monad laws are expressed as a side note in the docs, and not type enforced in Haskell itself.

I just thought it was vague to say that a fold takes an associative function instead of indicating what kind of topology a fold honors, as the former is only implying how the fold promises to operate. It would be surprising to me that this hasn't been formalized mathematically in some way.

Charlie

On Fri, Oct 23, 2015 at 7:01 PM, Clinton Mead <clintonmead@gmail.com> wrote:

Basically you want to force an argument to be associative yes?

I don't think there's a way to do that in Haskell, but what you could do is create a datatype:

data Associative a b = Associative (a -> b)

You could then make "Associative" a Category, or perhaps even an Arrow, so you could combine Associative functions to make new Associative functions.

But it would still be up to the user to ensure they only promote actual associative functions to "Associative".

On Sat, Oct 24, 2015 at 8:24 AM, Bardur Arantsson <spam@scientician.net> wrote:
On 10/23/2015 06:07 PM, Charles Durham 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)

"Exhaustive"?

... but then that's not really observable in a language like Haskell,
except if you monitor CPU heat.

Regards,

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