Hmm... it was my understanding that the example was showing how to *avoid* having to create a  lot of functions that do the same thing but have different numbers of arguments. From the Wiki page: "Anytime you feel the need to define different higher order functions to accommodate for function-arguments with a different number of arguments, think about how defining a proper instance of Applicative can make your life easier." Not so?

Very much so – instead of defining liftA2, liftA3 etc like this, just use pure to get things into the applicative, and write <*> instead of ' ' to apply applicatives and you're done.

Don't write

liftA3 sumsq (Just 3) (Just 4) (Just 5)

Write

(pure sumsq) <*> (pure 3) <*> (pure 4) <*> (pure 5)

or you can get rid of that first pure with a quick fmap:

sumsq <$> (pure 3) <*> (pure 4) <*> (pure 5)

Bob