What is a term for iterating over many functions with the same input?

Question

When we call the same function on a list of things, we call that "map". What do we call it when we call a list of functions on the same data? I don't mean pipe - not feeding the output of each function in turn into the next function - but simply iterating over a list of functions, passing each the same input?

Answer 1

I do not know of any term for your operation, but it can be seen as a kind of mapping, so maybe you do not need a special name for it. I will illustrate this in Haskell, but it is easy to do the same in other languages, e.g. Python, Clojure, Javascript, etc.

In Haskell map has type:

map :: (a -> b) -> [a] -> [b]

For example, you can map length over a list strings:

xs = ["Good", "morning", "world"] :: [String]

> map length xs
[4,7,5]

Now suppose you have a list of functions, e.g.

fs = [(+ 1), (* 5), (* 2)] :: [Int -> Int]

How can you apply each function to the same number, say, 1? You can use the function:

($) :: (a -> b) -> a -> b

This function takes another function and applies it to an argument. If you partially apply it to the number 1, you get:

($ 1) :: Num a => (a -> b) -> b

This is a function that given a function from a numeric type to any type b, applies it to 1. So, now we can map ($ 1) over our list of functions:

> map ($ 1) fs
[2,5,2]

So, in general, given an input x :: a and a list of functions fs :: [a -> b] you can apply all the functions to x with map ($ x) fs, which gives you a result of type [b].