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