Examples of Haskell Applicative Transformers

Question

The wiki on www.haskell.org tells us the following about Applicative Transformers:

So where are applicative transformers? The answer is, that we do not ne

Answer 1

The wiki article says that liftA2 (<*>) can be used to compose applicative functors. It's easy to see how to use it from its type:

o :: (Applicative f, Applicative f1) =>
     f (f1 (a -> b)) -> f (f1 a) -> f (f1 b)
o = liftA2 (<*>)

So to if f is Maybe and f1 is [] we get:

> Just [(+1),(+6)] `o` Just [1, 6] 
Just [2,7,7,12]

The other way around is:

>  [Just (+1),Just (+6)] `o` [Just 1, Just 6]
[Just 2,Just 7,Just 7,Just 12]

As @McCann said your ex function is equivalent to liftA2 (:):

test1 = liftA2 (:) "abc" ["pqr", "xyz"]

To use (:) with deeper applicative stack you need multiple applications of liftA2:

*Main> (liftA2 . liftA2) (:) (Just "abc") (Just ["pqr", "xyz"])
Just ["apqr","axyz","bpqr","bxyz","cpqr","cxyz"]

However it only works when both operands are equally deep. So besides double liftA2 you should use pure to fix the level:

*Main> (liftA2 . liftA2) (:) (pure "abc") (Just ["pqr", "xyz"])
Just ["apqr","axyz","bpqr","bxyz","cpqr","cxyz"]