integral, sigma

integral.swift

extension Double : ForwardIndexType {
    public func successor() -> Double {
        return self + 1.0
    }
}

infix operator ∫ { associativity left precedence 120 }
func ∫ (left: Range<Double>, right: (Double -> Double)) -> Double {
    let dx = (left.endIndex - left.startIndex) / 1000
    let r = left.startIndex.stride(to: left.endIndex, by: dx)
    return r.reduce(0.0) { $0 + right($1) * dx }
}

sigma.swift

extension Double : ForwardIndexType {
	public func successor() -> Double {
		return self + 1.0
	}
}

infix operator ∑ { associativity left precedence 120 }
func ∑ (left: Range<Double>, right: (Double -> Double)) -> Double {
	let r = left.startIndex.stride(to: left.endIndex, by: 1)
	return r.reduce(0.0) { $0 + right($1) }
}