On Wed, 2011-06-15 at 11:15 +0200, Milan Straka wrote:
Hi all,
currently we have the following folds in the containers package: Map: fold, foldWithKey, foldrWithKey, foldlWithKey Set: fold IntMap; fold, foldWithKey IntSet: fold
If the direction (right, left) is not specified, the fold is the right fold. So currently we have no left folds (except for the Map) and also Map and IntMap are not consistent.
My recommendation is that we add all four folds: foldr, foldl' foldl, foldr' Don't get confused with thinking about the "direction". Direction is an implementation issue (albeit an important one). As you know, the 'l' and 'r' in foldl and foldr are not direction but the left or right bracketing of the operations. left bracketing: ((0 + x_0) + x_1) + x_2 right bracketing: x_0 + (x_1 + (x_2 + 0)) Then the strictness is whether we reduce to WHNF before applying the operator. So I think those are the appropriate function names and abstract definitions, because they correspond to what we're all used to with lists. The implicit order of the order of the set/map keys, low to high. Now, when it comes to implementation the direction is important. The foldr and foldl' functions are best implemented as forwards/ascending traversals while foldl and foldr' are best implemented as backwards/descending traversals. In particular note that we can write things like: biggest = foldl (\y x -> x) undefined and evaluate it in O(log n) time. We get "early exit" behaviour. So by having all four traversals we cover the use cases where people want folds that start "from the back" (thinking about it operationally).
The Foldable module exports foldl' and foldr', which use foldr, foldl respectively, but needs some intermediate memory (it creates a thunk for every node of the structure). Apart from that, this does not cover the *WithKey variants as in b).
This is unfortunate. For data structures with equal access to all elements (arrays, map/set etc) we can implement foldl' and foldr' directly and more efficiently.
Personally I would add foldr, foldl, foldlWithKey, foldrWithKey and specialised foldr, foldl implementations in the Foldable classes. I am not sure about the strict folds -- I used an equivalent of the foldr' from the Foldable module in GHC and it was reasonable fast.
Any oppinions?
So I suggest all four folds. They are all useful and can all be implemented efficiently. Perhaps you need the withKey variety too. Do provide a Foldable instance, and perhaps later we can lobby for foldl' and foldr' to be made members of the Foldable class rather than fixed definitions in terms of foldl and foldr (bytestring, vector and text could benefit from this too). Duncan