Math-like Operators in Swift

Mathematics.swift

// Paste this in Playground

infix operator ∘
prefix operator ∑^

typealias ItoD = (Int) -> Double

func *(lhs: Int, rhs: Double) -> Double {
    return Double(lhs)*rhs
}

func *(lhs: Double, rhs: Int) -> Double {
    return Double(rhs)
}

prefix func ∑^(range: @escaping ()->CountableRange<Int>) -> ((@escaping ItoD) -> ()->Double) {
    return {f in
        return {
            var sum = 0.0
            for i in range() {
                sum += f(i)
            }
            return sum
        }
    }
}

func ∘(lhs: ((@escaping ItoD) -> ()->Double), rhs: @escaping ItoD) -> Double {
    return lhs(rhs)()
}

let square = { (x: Int) in Double(x*x) }

let sum = ∑^{0..<4}∘square
sum

let sum2 = ∑^{0..<10}∘{ Double($0 * $0) }
sum2

let π = Double.pi
let trig_sum = ∑^{0..<100}∘{ sin($0 * π/4.0) }    // sin(iπ/4)
trig_sum

// Indefinite sum
prefix func ∑(f: @escaping ItoD) -> (() -> CountableRange<Int>) -> Double {
    return {
        range in
        var sum = 0.0
        for i in range() {
            sum += f(i)
        }
        return sum
    }
}

func ∘(lhs: (() -> CountableRange<Int>) -> Double, rhs: @escaping ()->CountableRange<Int>) -> Double {
    return lhs(rhs)
}

let an_indefinite_sum = ∑square

let a_sum = an_indefinite_sum∘{0..<3}
a_sum