Credit to reminder – My sweet piggy

Today is the last day of January. It would be my last chance to complete this blog, otherwise I will miss this lovely month.

In this month, I have went to a new company as a FTE, and simultaneously happened to meet an epic epidemic that overwhelming in Mainland China. The government suggests citizens stay at home, so I am suddenly aware of that I can enjoy this great time at home and read some books.

Semigroup is a fancy concept in math and programming. Let’s say there is a set S and a binary operation ✕ on this set: S ✕ S ➞ S, if ✕ meets the binding law, that is ∀ x, y, z ∈ S, (x ✕ y) ✕ z = x ✕ (y ✕ z). Then the ordered pair (S, ✕) is called a semigroup.

For example, S = {1,2,3,4,5, …}, (2 + 3) + 4 = 2 + (3 + 4) = 9.

infix operator <> : AdditionPrecedence

protocol Semigroup {
    static func <> (lhs: Self, rhs: Self) -> Self
}

Protocol semigroup declares a calculation method of that two arguments and the return value achieve an identical semigroup type. We called this method as Append. Following is the specific achievements of String and Array.

extension String: Semigroup {
    static func <> (lhs: String, rhs: String) -> String {
        return lhs + rhs
    }
}

extension Array: Semigroup {
    static func <> (lhs: [Element], rhs: [Element]) -> [Element] {
        return lhs + rhs
    }
}

func test() {
    let hello = "Hello "
    let world = "world"
    let helloWorld = hello <> world
    
    let one = [1,2,3]
    let two = [4,5,6,7]
    let three = one <> two
}

Next, we are moving to the Monoid part.

Monoid is a kind of semigroup, with an extra attribute named Identity, that is an element E on the set S of the semigroup. Any element A in the set S conforms to A ✕ E = E ✕ A = A.

e.g. 0 + x = x in the natural number set.

protocol Monoid: Semigroup {
    static var empty: Self { get }
}

extension String: Monoid {
    static var empty: String { return "" }
}

extension Array: Monoid {
    static var empty: [Element] { return [] }
}

func test() {
let str = "Hello world" <> String.empty // Always "Hello world"
let arr = [1,2,3] <> [Int].empty // Always [1,2,3]
}

This article is not finish, stay tuned.