How much is applicative really about applying, rather than “combining”?

Question

For an uncertainty-propagating Approximate type, I\'d like to have instances for Functor through Monad. This however doesn\'t work because I need a

Answer 1

As I understand it (as a non---category theorist), the fundamental operation is zip :: f a -> f b -> f (a, b) (mapping a pair of effectful computations to an effectful computation resulting in a pair).

You can then define

• fx <*> fy = uncurry ($) <$> zip fx fy
• liftA2 g fx fy = uncurry g <$> zip fx fy

See this post by Edward Yang, which I found via the Typeclassopedia.