:: (a -> b -> c) -> [a] -> [b] -> [c] package:rio

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

Lift a binary function to actions. Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>. This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap. Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
b <- bs
pure (f a b)

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

liftM2 (+) [0,1] [0,2] = [0,2,1,3]
liftM2 (+) (Just 1) Nothing = Nothing