2009/8/19 Dan Doel
On Wednesday 19 August 2009 12:14:24 am Jason McCarty wrote:
Interestingly, foldM can also be written as a left fold. To see this, note that it is a theorem that foldr f z xs = foldl f z xs as long as f is associative and z is a unit for f.
This is not true: f has to be commutative, not associative. Consider matrix multiplication.
It must also be the case that xs is finite in length, because if it is infinite, then 'foldl f z xs' is bottom, while 'foldr f z xs' needn't be. This difference holds over into foldM implemented with each, where you can write something like:
foldM (\f e -> if even e then Left (show e) else Right f) "no evens" [1..]
and get an answer of 'Left "2"' with a foldr implementation, but bottom with a foldl implementation.
This potentially translates into its own performance concerns, because in such monads, the computation can short-circuit upon finding a 'throw' when using the foldr implementation, but with the foldl implementation, you have to do at least a little shuffling of thunks for the entire list.
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