[Haskell-cafe] 'Associative' order of calling

[Charles Durham]

I said "associatively" to be a place holder for a property I was trying to
express, but unable to formalize. So yes, from what I understand
associativity is a property of a function and has a formalization.

As for the category theory, this is where I thought that this calling
hierarchy might already be formalized in. I thought it would be nice to say
something to the effect of "This fold has x property and exploits it to
support parallelization". Obviously f does not need to be associative if
the caller of the fold understands that only the x property is promised in
the implementation.

On Wed, Oct 28, 2015 at 3:05 PM, Marcin Mrotek <marcin.jan.mrotek at gmail.com>
wrote:

> And look at what we have: A definitive answer to OP's question:
>>
>> Question: What is a fold of type "(a -> a -> a) -> [a] -> a" that
>> promises to call its first parameter "associatively"?
>>
>> Answer: It is a fold equivalent to a fold1 (left or right, it doesn't
>> matter).
>>
>> That's nice.
>>
>> But is that all we can come up with? Does it really do justice to the
>> original question? Viz.
>>
>
> Hello,
>
> Sorry for jumping into the thread, but I've read the previous responses,
> and I still don't get it (perhaps it's because I'm not a native English
> speaker): what does "associatively" mean in this context? From what I
> understand, "associativity" is a property of a function, that f (f a b) c =
> f a (f b c). Nothing more, nothing less. In order to encode this property
> in the type of a "fold" function, you'd need dependent types and a
> type-level proof that a given function is associative. Without dependent
> types, you can only trust the user to either supply an associative
> function, or accept wrong results (like REPA does). Am I missing something?
>
> Best regards,
> Marcin Mrotek
>
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