Extension of constructed generic type in Swift

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This can be achieved using protocol extensions (See The Swift Programming Language: Protocols for more information).

To sum just Ints you could do:

extension Sequence where Iterator.Element == Int {
    var sum: Int {
        return reduce(0, +)
    }
}

Usage:

let nums = [1, 2, 3, 4]
print(nums.sum) // Prints: "10"

Or, for something more generic (Swift 5) you can use AdditiveArithmetic:

extension Sequence where Iterator.Element: AdditiveArithmetic {
    var sum: Iterator.Element {
        return reduce(.zero, +)
    }
}

For Swift 4 and below, you can use what @Wes Campaigne suggested and create an Addable protocol:

protocol Addable {
    init()
    func + (lhs: Self, rhs: Self) -> Self
}

extension Int   : Addable {}
extension Double: Addable {}
extension String: Addable {}
...

Next, extend Sequence to add sequences of Addable elements:

extension Sequence where Iterator.Element: Addable {
    var sum: Iterator.Element {
        return reduce(Iterator.Element(), +)
    }
}

Usage:

let doubles = [1.0, 2.0, 3.0, 4.0]
print(doubles.sum) // Prints: "10.0"

let strings = ["a", "b", "c"]
print(strings.sum) // Prints: "abc"

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