On Wed, Jun 15, 2011 at 8:43 AM, Duncan Coutts wrote: 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. 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). I vaguely recall a discussion about adding them to the Foldable class with
the current definitions as defaults, but I don't think an actual
libraries@submission was ever made. I would definitely support this
motion.
-Edward