Idea for expanding the set of "pre" utilities

[chris-martin]

In base we have map and filter, and also mapMaybe which can do both, and concatMap that generalized a little further with the additional ability to increase the number of items.

map       :: (a ->       b) -> [a] -> [b]
filter    :: (a -> Bool   ) -> [a] -> [a]
mapMaybe  :: (a -> Maybe b) -> [a] -> [b]
concatMap :: (a -> []    b) -> [a] -> [b]

For manipulating fold inputs, we have analogs to map and filter. I think it would be quite handy to also have an analog to mapMaybe and concatMap.

premap       :: (a ->       b) -> Fold b r -> Fold a r
prefilter    :: (a -> Bool   ) -> Fold a r -> Fold a r
premapMaybe  :: (a -> Maybe b) -> Fold b r -> Fold a r
preconcatMap :: (a -> []    b) -> Fold b r -> Fold a r

An implementation for premapMaybe would be

premapMaybe f (Fold step begin done) = Fold step' begin done
 where
  step' x a = maybe x (step x) (f a)

For example, a fold that I'm currently writing as

Foldl.Fold (\set a -> maybe id Set.insert (f a) set) Set.empty id

could be then written as

Foldl.premapMaybe f Foldl.set

[Gabriella439]

Sure, I would accept a PR for these.