On 02.08.2011 08:16, Sebastian Fischer wrote:
Data.Foldable also provides the monoidal fold function foldMap. It is left unspecified whether the elements are accumulated leftwards, rightwards or in some other way, which is possible because the combining function is required to be associative. Does this additional freedom for implementors go so far as to allow for strict accumulation? Is it safe to implement foldMap (without prime) with a strict accumulator or are there examples where lazy accumulation is useful like in the above foldr example and distinguishable from strict accumulation without breaking the monoid laws?
Left and right folds behave identically for finite structures but they are different for infinite ones. Here is an example:
island = map First $ Just "Snark" : repeat Nothing
foldr mappend mempty island = First {getFirst = Just "Snark"} foldl mappend mempty island = ⊥
If mappend is lazy arguments then strict and lazy could be distingushed. And Last indeed offers an example:
island = [ error "Boojum", Last (Just "Snark") ]
foldl mappend mempty island = Last {getLast = Just "Snark"} foldl' mappend mempty island = Last {getLast = *** Exception: Boojum