The answer
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.
Closures and Higher-Order Functions in JavaScript
Are map, filter, and reduce higher-order functions in JavaScript?
More FAQs in Closures and Higher-Order Functions in JavaScript
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.
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.
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