AssociativeLaw.swift

///
/// 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> {}

public extension AssociativeLaw {
    ///
    /// It verifies  if the set of elements are **associative**.
    ///
    /// Given a set of 3 elements, and a binary operation, the associativity "verification" happens.
    ///
    /// - Parameters:
    ///   - a: The first element
    ///   - b: The second element
    ///   - c: The third element
    ///   - operation: The associative binary operation to evaluate on
    ///
    static func verify(a: Element, b: Element, c: Element, operation: (Element, Element) -> Element) -> Bool {
        // a <> (b <> c) = (a <> b) <> c
        operation(a, operation(b, c)) == operation(operation(a, b), c)
    }
}