The answer
When a HOF takes a callback, the callback closes over variables from where it was defined. When a HOF returns a function, the returned function closes over the HOF's local variables. Closures are what make HOFs work.
Closures and Higher-Order Functions in JavaScript
How do higher-order functions use closures in JavaScript?
More FAQs in Closures and Higher-Order Functions in JavaScript
The callback passed to map closes over variables from where the callback was defined. For example, [1, 2, 3].map(n => n * multiplier) works because the arrow closes over the outer multiplier variable.
compose(f, g) returns a function that closes over f and g. Each call to the returned function invokes f(g(x)). The closure keeps f and g alive so the returned function can use them later.
Yes. They take a callback function as an argument, which makes them higher-order. The callbacks close over outer variables, which is why you can reference outer state inside them.
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