Is there a name for this function or pattern?

Question

Instead of fmap, which applies a function to a value-in-a-functor:

fmap :: Functor f => (a -> b) -> f a -> f b

I needed a function where the functor has a function and the value is plain:

thing :: Functor f => f (a -> b) -> a -> f b

but I can't find one.

What is this pattern called, where I apply a function-in-a-functor (or in an applicative, or in a monad) to a plain value?

_{I've implemented it already, I just don't quite understand what I did and why there wasn't already such a function in the standard libraries.}

Answer 1

You don't need Applicative for this; Functor will do just fine:

apply f x = fmap ($ x) f
-- or, expanded:
apply f x = fmap (\f' -> f' x) f

Interestingly, apply is actually a generalisation of flip; lambdabot replaces flip with this definition as one of its generalisations of standard Haskell, so that's a possible name, although a confusing one.

By the way, it's often worth trying Hayoo (which searches the entirety of Hackage, unlike Hoogle) to see what names a function is often given, and whether it's in any generic package. Searching for f (a -> b) -> a -> f b, it finds flip (in Data.Functor.Syntax, from the functors package) and ($#) (from the synthesizer package) as possible names. Still, I'd probably just use fmap ($ arg) f at the use site.