Many Faces of Map - Episode 13, Exercise 10

[sam-mfb]

What's the answer to Exercise 10 in the Many Faces of Map?

Derive a relationship between r, any function f: (A) -> B, and the map on arrays and optionals. This relationship is the “free theorem” for r’s signature.

I have come up with the following examples of an r and an s:

func r<A>(_ xs: [A])->A? {
    xs.first
}

r([]) //nil
r([1,2]) //1

func s<A,B>(_ f: @escaping (A)->B, _ xs: [A])->B? {
    let value: B?
    switch xs.last {
    case .some(let a):
        value = f(a)
    case .none:
        value = nil
    }
    return value
}

s({$0*2},[]) //nil
s({$0*2},[1,2]) //4

I'm not even entirely sure I understand the question. What does it mean to have a relationship between three functions (r, f, map)?

Any hints? 😃