Swift running sum

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The general combinator you’re looking for is often called scan, and can be defined (like all higher-order functions on lists) in terms of reduce:

extension Array {
    func scan<T>(initial: T, _ f: (T, Element) -> T) -> [T] {
        return self.reduce([initial], combine: { (listSoFar: [T], next: Element) -> [T] in
            // because we seeded it with a non-empty
            // list, it's easy to prove inductively
            // that this unwrapping can't fail
            let lastElement = listSoFar.last!
            return listSoFar + [f(lastElement, next)]
        })
    }
}

(But I would suggest that that’s not a very good implementation.)

This is a very useful general function, and it’s a shame that it’s not included in the standard library.

You can then generate your cumulative sum by specializing the starting value and operation:

let cumSum = els.scan(0, +)

And you can omit the zero-length case rather simply:

let cumSumTail = els.scan(0, +).dropFirst()

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