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`?
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