Functions in the Environment

Given the following snippet

function f(g) {
    return g(2);
}

f(x => x + 4);

Where does the function closure (or function object) point to?

It's very easy to glance through the code and think: "Well, the lambda function is in the function f, so we pass the entire lambda function into the function". To visualize this misconception, this is what you might THINK it looks like:

Wrong Expansion

function f(g) {
    return g(2);
}

f(x => x + 4);

// During evaluation:
// f(x => x + 4) {
//     return (x => x + 4)(2);
// }

But this isn't quite right. Our function objects (closures) are not created on application, like the above would suggest, but when it is first 'declared'. Think of it like an expression like:

f(3 + 4)

You wouldn't evaluate the 3+4 inside the f scope, but in the program environment. Similarly with lambda functions, you can think of the code snippet, after expanding the lambda functions as follows:

Correct Expansion

function f(g) {
    return g(2);
}

f(x => x + 4);

// Correct Expansion

// function lambda(x) {
//     return x + 4;
// }
// f(lambda)