Is there a standard function that computes `f x (g x)`?

Question

I couldn't find anything on Hoogle, but is there a standard function or operator with a signature like:

func :: (a -> b -> c) -> (a -> b) -> a -> c

I.e. given two functions f and g and an element x as arguments it computes f x (g x)?

Answer 1

The function you’re looking for is (<*>). Why? Well, it’s true that (<*>) has a more general type:

(<*>) :: Applicative f => f (a -> b) -> f a -> f b

But consider that we can specialize f to (->) r, which has an Applicative instance:

(<*>) :: (->) r (a -> b) -> (->) r a -> (->) r b

…then we can rearrange the type so -> is infix instead of prefix, as it normally is:

(<*>) :: (r -> a -> b) -> (r -> a) -> (r -> b)

…which is the same as your signature modulo alpha renaming.

This works because the function type, (->), has instances of Functor, Applicative, and Monad, which are idiomatically called “reader”. These instances thread an extra argument around to all their arguments, which is exactly what your function does.