> Chris's original question:
>
> Is there a name for a fold that promises to call a function such that only
> an associative function will always return the same result. Or in other
> words, it has the property that it promises to call a function
> "associatively" on a set of data?
>
> So is the property that the function (h, say) satifises `h f = g . foldl f z`
> for all associative `f`?

That makes a lot of sense, Tom, as a property of h to satisfy, while quantifying over associative f inside that property. (Instead of as an equation-definition for h in terms of foldl.)

I now wonder why any g other than the identity function should be necessary, though. And for the type of non-empty lists, one should also be able to get rid of the z?

So, for the special case of non-empty lists, how about expressing the desired property as follows: "The function h must satisfy: for all associative f and all lists xs, it holds that h f xs = foldl1 f xs."

Chris's original question would then be whether there is a name for that property. And how to generalize the property to other types than non-empty lists (for example, ones for which it is not clear what "left" and "right" mean) would be a separate concern.


2015-10-25 9:33 GMT+01:00 Tom Ellis <tom-lists-haskell-cafe-2013@jaguarpaw.co.uk>:
On Sun, Oct 25, 2015 at 06:58:23AM +0100, Janis Voigtländer wrote:
> I don't think I see what you are getting at, Tom. Let's consider the
> special case of non-empty lists. One fold-like function that has the
> property I think Charles meant by 3., would be one that works as follows:
>
> foldBalanced :: (a -> a -> a) -> [a] -> a
> foldBalanced f [x] = x
> foldBalanced f [x,y] = f x y
> foldBalanced f [x,y,z] = f x (f y z)
> foldBalanced f [x,y,z,u] = f (f x y) (f z u)
> ... -- I hope you can see the pattern (building f-application trees that
> are as balanced as possible)
>
> I don't see how this function can be written as g . foldl f z for some g
> and z.

Ah, thank you Janis. I think you are clarifying for me the meaning of
Chris's original question:

     Is there a name for a fold that promises to call a function such that only
     an associative function will always return the same result. Or in other
     words, it has the property that it promises to call a function
     "associatively" on a set of data?

So is the property that the function (h, say) satifises `h f = g . foldl f z`
for all associative `f`?

Tom
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe