eMdOS

XCTAssert(
    AssociativeLaw<String>.verify(a: "hello", b: " ", c: "wolrd!", operation: +)
)

eMdOS

XCTAssert(
    AssociativeLaw<String>.verify(a: "hello", b: " ", c: "wolrd!", operation: <>)
)

eMdOS

///
/// Associative Law
///
/// **Associativity** is the condition that the 2 ways to use a "binary composition" of morphisms to compose a sequence of 3 morphisms "are equal".
///
/// - Associative through **Addition**: `a + (b + c) = (a + b) + c`
/// - Associative through **Multiplication**: `a * (b * c) = (a * b) * c`
///
public enum AssociativeLaw<Element: Equatable> {}

eMdOS

[1, 2, 3] <> [4, 5, 6] 
// prints out: [1, 2, 3, 4, 5, 6]

eMdOS

extension Array: Semigroup {
    public static func <> (left: Array, right: Array) -> Array {
        left + right
    }
}

eMdOS

"Pac" <> "Man" 
// prints out: "PacMan"

eMdOS

extension String: Semigroup {
    public static func <> (left: String, right: String) -> String {
        left + right
    }
}

eMdOS

infix operator <> : AdditionPrecedence

public protocol Semigroup {
    static func <> (left: Self, right: Self) -> Self
}

eMdOS

func compose<A, B, C>(
    f: @escaping (A) -> B, // f: A -> B
    g: @escaping (B) -> C  // g: B -> C
) -> (A) -> C {            // h: A -> C = g • f
    return { a in
        g(f(a)) // g • f
    }
}

// ... then

eMdOS

func string(from int: Int) -> String {
    String(int)
}